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High precision 3-D coordinates for JSATS tagged fish in an acoustically noisy environment

High precision 3-D coordinates for JSATS tagged fish in an acoustically noisy environment Background: Acoustic tagging methods have been used to track fish for some time. Multiple systems have been developed, including those that give researchers the ability to position fish in three dimensions and time. However, proprietary positioning methods have suffered from a lack of transparency. The U.S. Department of Energy and the U.S. Army Corps of Engineers developed the Juvenile Salmon Acoustic Telemetry System (JSATS) to monitor the survivability of juvenile salmonids as they migrate downstream. With much smaller tags and high ping rates, JSATS positioning studies should be more prevalent, but implementation is difficult and often out of reach for small budget- minded studies. This study implemented a small scale JSATS positioning study using relatively inexpensive, autono- mous, independent receivers. We will show that proper synchronization of the transmissions and elimination of multipath allows the positions of a smolt to be determined in three spatial dimensions over time with high precision. Results: Tracking of 172 tagged smolts produced a total of nearly 2,00,000 positions. We compared the performance of four different supervised machine learning classifiers (Support Vector Classifier (SVC), Gaussian Naïve Bayes (NB), Classification Tree (CART ), and K-Nearest Neighbor (KNN). All algorithms performed well with high accuracy and precision, but recall rates decreased with distance from the source. The SVC and KNN were least restrictive in practice. Overall, the SVC had the longest time to solve. Conclusion: Positions determined from fish outside of the convex hull of the hydrophones were effectively being extrapolated, while positions determined from within the convex hull nearly always met or exceeded 1-m precision. Having stationary submerged hydrophones was necessary to produce three-dimensional positions. The main techni- cal advances presented are the hydrophone-clock synchronization scheme and the multipath rejection scheme, which found the best multipath classifier to be the K-Nearest Neighbor. Neither algorithm was capable of alleviating close proximity detection interference (CPDI), suggesting the need to reposition receivers from reflective surfaces or install baffling. Introduction are affixed to immobile objects in the study area; and Acoustic tagging technologies and positioning algo- data-logging equipment to record the data from the rithms have made it possible to track aquatic animals at hydrophones. A tag emits a sonic transmission that fine temporal and spatial scales, meaning, in theory, it the hydrophones can detect. The transmission includes could be possible to infer behavioral responses to stim- a unique digital signature (tag ID) to ensure correct uli. The system is comprised of a “tag” that is attached determination of which tag was detected. To obtain 3-D to, or embedded into, the animal; hydrophones that positions, four or more hydrophones must detect the same transmission from a tag. The positioning problem is then resolved by determining the distances from the *Correspondence: kevin.nebiolo@kleinschmidtgroup.com hydrophones to the tag at the moment of transmission Kleinschmidt Associates, 35 Pratt St. Suite 201, Essex, CT 06246, USA by inference from the speed of sound and the elapsed Full list of author information is available at the end of the article © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 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Given the 3-D positions of the hydro- ured by pressure sensors in the tag and encoded in the phones, the time of transmission, and the times of transmission message [4], which makes the message detections, the position is determined using multilat- longer than other technologies, leading to collisions eration, similar to positioning with a Global Positioning with other tag messages and potentially themselves. System (GPS) receiver. The manufacturer HTI has another comparable propri - The mathematics of multilateration require that the etary system, which also sees extensive use. Perry et al. clocks in the hydrophones be synchronized, so there [18] used an HTI array with unsynchronized clocks to must either be additional infrastructure to synchronize understand the effects of strobe lights on migrating the clocks in situ or resolution of the clock time biases resident salmonids. Bergé et  al. [3] tested a UTC syn- in software ex post facto. Hardware synchronization chronized HTI array to optimize receiver geometry either requires communication among the receivers among other variables and found the best configura - and a time standard, or the ability to do time trans- tion resulted in a 44 percent detection efficiency with fer from, for example, the GPS to synchronize to GPS an error of 3.6  m. In 2019, VEMCO and HTI were time, which is nominally equivalent to Coordinated acquired by Innovasea [12]. Universal Time (UTC) (in French, temps universel The open source Yet another positioning solution coordonné). (YAPS) algorithm [2] is an improvement over propri- For fish passage studies, these requirements dictate etary solutions, and it works with UTC-synchronized deploying an array of receivers in a complex and highly data. YAPS couples a maximum likelihood analysis reflective environment. Here, by ref lective we mean of time-of-arrival data with a state-space movement that the acoustic transmissions can reflect off objects model [2]. Using tags with a stable transmission rate, in the surroundings and, thus, take a non-direct route YAPS can anticipate the time of transmission allowing to the hydrophones. When reflections occur, a hydro- researchers to model time-of-arrival on a random-walk phone can detect one or more transmissions in the basis, making it easier to filter out multipath detections same epoch from a single tag, resulting in the mul- and improve accuracy. Vergeynst et al. [26] used YAPS tipath problem: a single transmission took multiple on a VPS data set in a highly reflective environment paths to reach a hydrophone [27]. Confusing a mul- and found significant accuracy improvement. However, tipath transmission for the direct-route transmission YAPS does not synchronize independent clocks. introduces error into the position estimate, often egre- The Juvenile Salmon Acoustic Telemetry System gious error. (JSATS) is a non-proprietary acoustic sensing technol- Open-source positioning algorithms have been pro- ogy developed for the U.S. Army Corps of Engineers posed to assist researchers who possess the appropri- to evaluate the behavior and survival of juvenile sal- ate data (UTC synched), but most acoustic positioning monids migrating through the Columbia River system solutions utilize proprietary software and value-added [27]. The JSATS tags’ transmissions are detected and vendor services. For cost-conscious studies that can- decoded by self-contained autonomous hydrophone not afford expensive systems or vendor services receivers (HRs) placed at strategic locations through- with recurring fees, this often means falling back out the project area [27]. Determining a 3-D position onto more simple presence/absence receiver arrays, of the fish in time requires transmission detection by because researchers lack a method of synchronizing four or more receivers [6]. Li et al. [14] improved upon independent receiver clocks and reliably removing the 2-d closed-form approximate maximum likelihood multipath. (AML) developed by Chan et  al. [5] by extending to a The VEMCO VPS system is a proprietary turn-key third dimension and using a linear least squares solu- acoustic positioning solution [4] that uses multiple tion as an initial guess. The AML is a non-exact solver independent receivers each with a single independent that alleviates influence from first-return multipath hydrophone. The VPS system uses hyperbolic exact with a weighting matrix and processing step on time of positioning algorithms to locate fish, where the hori - arrivals. Rauchenstein et al. [19] further improved upon zontal position error is a weight averaged position the AML using machine learning methods to identify among all combinations of receivers that detected a and remove multipath biased position estimates. In transmission [23]. The VPS system has enjoyed exten - 2019, Fu et  al. [10] developed a hierarchical localized sive use. Binder et al. [4] deployed 140 recivers to track regression technique using a series of two-way mes- lake trout within Lake Huron, North America, but sages to synchronize independent JSATS receivers. The found extensive multipath error after filtering. Roberts localized linear regression technique assumes a con- et  al. [20] used the VPS system to describe space-use stant clock drift. Multipath error present in beacon tag Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 3 of 15 transmissions could bias the regression parameters and impart error into the clocks, which could prove prob- lematic for studies in highly reflective environments. The approach employed in this study synchronizes clocks, removes multipath error, and produces 3-D positions of fish in time with nonlinear least squares estimation using relatively inexpensive autonomous JSATS hydrophone receivers. If the receivers have sufficient temporal resolution (microsecond) and the speed-of-sound is accurately measured, it is pos- sible to set up small-scale arrays that produce precise 3-D positions in highly reflective, acoustically noisy environments. Methods These methods were implemented on a juvenile smolt downstream passage study on the Cowlitz River, Wash- Fig. 2 Positions of the 9 Technologic receivers and their convex hull. ington, US (Fig. 1) at the Cowlitz Falls Dam. The study Units are in meters. Note, R05 is not on the convex hull, including it would create a depression, which is concave. Receiver R04 is located tagged 179 fish with Advanced Telemetry Systems adjacent to the fish passage entrance, while R07, R08 and R09 are Model SS400 JSATS acoustic tags and tracked them affixed to the trashrack. The Receivers R07, R04 and R01 are essentially with nine autonomous Teknologic (Model 11,497) on the face of the dam autonomous cabled hydrophone receivers (HR) fixed in position and encircling the area of interest for 3-D positions (Fig.  2). The HRs collected large amounts of data, which were managed by SQLite, an in-process microseconds since January 1, 1970 stored as a 32-bit library that implements a self-contained, server-less, floating point decimal). Following the initial data zero-configuration, transactional SQL database engine management, the study team enumerated beacon tag [24]. transmissions (epochs), synchronized clocks, removed For ease of computation, all time stamps were con- multipath errors, and finally produced 3-D coordinates verted to decimal microseconds in Unix time (decimal with a corrected time stamp for the fish. Mathematical model for positioning A fish tag periodically emits an acoustic pulse that uniquely identifies the tag’s transmission content, which consists entirely of the tag ID. The pulse is detected by the hydrophone receivers, which have internal clocks that record the moment they detect the pulse in a man- ner similar to how a GPS receiver records the moment it detects the radio transmission from satellites. How- ever, unlike GPS, the acoustic pulse does not encode a time stamp of when it was emitted. The tag-positioning problem is, therefore, different from the GPS position - ing problem in that there is an additional unknown, the moment when the pulse was emitted. Nonetheless, the conceptual basis of the two systems is quite similar, so similar solution methods pertain. The mathematics for three-dimensional positioning using JSATS can be found in Ehrenberg and Steig [7, 8]. Our positioning equation is formed from the difference of the equations for two receivers, a and b, positioning the smolt independently, which eliminates the time-of- Fig. 1 Location of the Cowlitz River, a tributary to the Columbia River transmission as an unknown, producing Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 4 of 15 (−1) 2 2 2 2 2 2 t −t +c ( (x − X) + (y − Y ) + (z − Z) − ((x − X) + (y − Y ) + (z − Z) )) = 0, a b b b b a a a not know, where a fish is when a tag fires, a good esti - where t and t are the (synchronized) times-of-detec- a b mate of water column temperature is the mean of all tions at the receivers; c is the instantaneous speed- interpolated temperature-at-depths. After determining of-sound in fresh water; x , y , and z are receiver a’s a a a water temperature (average temperature at time), the spatial coordinates (similar for receiver b); and X , Y , Z speed-of-sound on an epoch-by-epoch basis was calcu- are the desired coordinates of the smolt. This equation lated with a cubic spline fit to data provided by Seafloor is nonlinear in X , Y , Z , so it is solved iteratively using a Systems [24]. nonlinear least squares estimator. This equation reveals some subtle requirements. Clock synchronization Unlike the GPS equations in which receiver time-bias The mathematical model requires a priori synchronization terms can be determined mathematically, here we have of receiver clocks. This was accomplished using the con - the situation in which including the time biases always cept of a metronome; receiver R05 was the time standard results in more unknowns than equations. Therefore, and we synchronized the other clocks to it. Knowing the the receivers’ clocks must be synchronized prior to receivers’ spatial coordinates allows the positioning prob- the position estimation; for GPS, the receiver’s time lem to be inverted and solved for time-of-transmission, so bias is solved for as a fourth unknown. The speed-of- the clocks were synchronized using the beacon attached to sound must be known a priori epoch-by-epoch. Water receiver R05. temperature was continuously monitored at three sta- The goal was to determine the “true” times of transmis - tions within the impoundment with a string of HOBO sion and reception, as the exact moments in time (i.e., the Water Temperature Pro v2 probes at 0.5, 1, 3, 4.5, 6, 7.5, time of a perfect clock) when the transmitting receiver 9, 12, and 14.5  m depth. The positions of the receivers emitted its beacon signal and when that signal was detected must be known epoch-by-epoch, receivers mounted by the other hydrophone receivers (HRs). on infrastructure at the surface were located with a Explicit moments-in-time require an explicit time refer- Trimble Geox7 GPS with 10  cm of accuracy after post ence, such as UTC or GPS time; however, the positioning processing with Trimble Pathfinder. Six receivers were equations depend only on the differences of the times-of- mounted near the water surface; with three on immo- transmission and the times-of-reception, so their collective bile supports (R04, R05, R06), and the other three were bias from time external standards vanishes in the differ - affixed to the trash rack which tracked with the water ence. It is essential, however, that the HRs’ clocks are not surface (R07, R08, R09) and three were placed at the biased relative to each other. bottom of the forebay (R01, R02, R03) (Fig. 2). The posi - For HRs i and j located at x , y , z and x , y , z , respec- i i i j j j tions of the submerged receivers could not readily be tively, the fundamental geometric relationship for the dis- observed, so they were positioned using their attached tance separating them is beacons as if they were fish. This required an epoch- by-epoch vertical-coordinate determination. Thus, it is 2 2 2 (1) d = x − x + y − y + z − z . i,j j i j i j i possible to validate the receivers’ positions by inferring their separation using the beacon transmissions given It was assumed that the HRs’ epoch-by-epoch positions the speed-of-sound. are known correctly, so d was taken as correct. Some of i,j the HRs moved with the water surface elevation of the fore- bay, so, more specifically, d was taken as being correct i,j Speed of sound epoch-by-epoch and the notation implies distance at some The mathematical model requires a priori knowledge particular epoch or moment in time. of the per-epoch speed-of-sound. The study team It takes some time for a signal from, say, HR i to be deployed three temperature sensor vertical profile detected by some other HR j, namely, the true time of strings within the project area, which collected water r x reception τ minus the true time of transmission τ . Multi- j i temperature readings throughout the study at 5-min plying this difference by the speed of sound for this epoch, intervals with high precision. To estimate a water col- c , again gives the distance separating the receivers: umn temperature, we fit a piecewise linear spline to temperature data at each depth interval. The linear r x d = c τ − τ . i,j (2) j i spline allowed us to “sample” water temperature at depth at any time throughout the study. Because we do Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 5 of 15 The per-epoch speed-of-sound as determined with the r x ε = d /c − t − τ , i i,j (8) j i average forebay water temperature reading was taken as correct, as well. The clock in hydrophone R05, which was which is the time bias of the transmitting receiver, chosen to be the standard, will not generally run synchro- whichever one it happens to be. Knowing ε makes it pos- nized with the clocks in the other HRs—their clocks will sible to determine τ = t − ε , which, in turns, makes i i i not read the same value at the same moment in true time, it possible to determine the time biases of all the other and their clocks will generally run at different rates. The receivers in that epoch using Eq. (7): absolute offset of a clock’s reading from the true time can For two epochs τ <τ , the clock-drift rate for a e g be expressed as the reading of the clock, t, minus its bias receiver is given by from the true time, ε: ε − ε g e ε˙ = lim , τ = t − ε. (3) eg �τ→0 �τ By subtracting ε (as opposed to adding it), the study team where �τ = τ − τ , so the clock drift from epoch e to g e was consistent with the intuition that the clock is running epoch g is approximately fast when ε is positive, or the clock is running slow when ε ε − ε is negative. The clock drift rate is given by the time deriva - g e ε˙ ≈ . eg (9) tive of Eq. (3): τ − τ g e τ˙ = t −˙ε, The reception time of any signal—such as from a fish’s tag—can be estimated with the help of Eq. (9) as follows. where the dot notation denotes the time derivative of Suppose a signal is detected at time τ , and τ <τ <τ . e g f f the dotted quantity. However, τ˙ ≡ 1 , b e cause τ is true Then time, so τ ≈ τ +˙ε τ − τ . (10) f e eg f e t = 1 +˙ε. (4) After computing ε for every transmission interval, the Substituting Eq. (3) into Eq. (2) gives study team fit a piecewise linear interpolator to all epochs r x r x (τ , τ , τ , . . . , τ ) , then applied Eq.  (10) to all recaptures d = c t − ε − t − ε = c t − t − ε − ε 1 e g n i,j j i j i j i j i at receiver j . Of interest is the effect of water temperature so, in general, and other variables on ε ˙ . eg r x d = c t − t − c ε − ε . i,j j i (5) j i Multipath removal Tag transmissions can reflect off the water surface, sub - By convention, the true clock rate is the rate of R05’s strate, and infrastructure, which can cause a receiver to clock, so ε˙ ≡ 0 and ε ≡ 0 for R05. Suppose R05 is the record several nearly simultaneous transmissions from transmitting receiver, so ε = 0 . Then, Eq. (5) becomes a single tag in any epoch, the aforementioned multipath r x condition. The data revealed that mistaking a multipath d = c t − τ − cε , i,j j (6) j i signal for the primary signal can introduce tens of meters of error into the fish coordinates, so its mitigation was whose only unknown is ε . Solving Eq. (6) for ε gives j j essential. r x Multipath removal was a phased approach; the first ε = t − τ − d /c, j i,j (7) j i of which identified the first transmission among all the transmissions detected from a single source in any epoch. which is the time bias of the detecting receiver. All val- In this phase the correct transmission was assumed to ues on the right side of Eq.  (7) are known. Therefore, all be the first (earliest) transmission, as all others must be other HRs can have their time bias determined at any multipath. This assumption stemmed from the fact that a epoch in which they detect the transmission from R05. multipath signal travels a further distance to the receiver Now suppose R05 is not the transmitting receiver but it is than the direct signal, so it seemed unlikely that a signal a detecting receiver, so ε = 0 . Then, Eq. (5) becomes that traveled further would arrive prior to one that trave- r x led a shorter distance. d = c t − τ + cε , i,j i j i whose only unknown is ε . Solving for ε gives i i Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 6 of 15 Coordinating fish The first step enumerated metronome transmission Determining fish positions proceeded epoch-by-epoch epochs and grouped primary and multipath transmis- in Mathematica . Epochs with too few observations, less sions into a series of detections per epoch. The first than four, were insolvable and skipped. A nonlinear least- detection in series for every epoch was retained, as all squares estimation was attempted on the others, and not others must be multipath. However, sometimes the true all attempts were successful, meaning the normal matrix signal (the signal without multipath) was not detected was either singular or ill-conditioned, or the iteration at all, and the first detection in series was the result of failed to converge. All successful positions were retained multipath. In these cases, the primary filter failed and despite many having impossible coordinates, such as ver- required a second filter to scrutinize the first return tical coordinates above the water surface or horizontal further. coordinates on dry land. These data can serve as presence The second phase of multipath filtering removed erro - data, if nothing else, and retaining them costs nothing. neous transmissions with unsupervised and supervised machine learning algorithms. Training data was pro- Accuracy and precision duced in the first phase with information on the primary Li X et al. [15] describes methods to assess the accuracy detection and the multipath that followed. However, and precision of the positioning algorithm. We assessed this convention posed a dilemma, because the train- accuracy by comparing an epoch-by-epoch metronome ing data were known to be biased. We assume that there receiver (R05) position determination to its surveyed were instances, where the primary detection was missed position, and calculating the root-mean-square-error and multipath was mislabeled as true. To overcome this (RMSE). We also compared the solutions produced by potential bias, we fit a k-means (k = 2) unsupervised clas- the algorithm to a tag drag test. We described the fish sifier to normalized observations of the signal’s ampli - location’s precision with the standard deviation, because tude, noise bandwidth (NBW), and signal-to-noise they were solved with least squres. We then compared ratio (SNR) for all assumed primary detections with the mean of the precision estimates for fish tags within Scikit-Learn [17]. Then, we compared the distance from the convex hull to those outside. each cluster mean to the mean of the known multipath detections. If the distance between the known multipath Analysis workflow detections and the closer cluster’s center is smaller than Unsynchronized clocks, highly reflective acoustic envi - half the distance between cluster centers, we classified ronments, and not knowing the positions of the receivers the closer cluster as multipath. at depth makes implementing JSATS studies with auton- After enumerating epochs and removing biased omous receivers difficult. To overcome this and assist training data, the study team had confirmation on the other researchers, the study team developed jsats3d.py first transmission and the multipath detections that [16]. The open source software, written in Python, assists followed. Data was normalized or scaled (dependent with data management, clock synchronization, and upon algorithm) prior to classifying. We tested a suite multipath removal, while fish coordinates were solved of supervised classifiers: Support Vector Classifier with Mathematica. The data cleaning workflow starts (SVC), Gaussian Naïve Bayes (NB), Classification Tree with reception of study data from Teknologic Receivers, (CART), and K-Nearest Neighbor (KNN) with Scikit- HOBO water temperature sensors, and operations data Learn [17], and compared their accuracy, precision, (SCADA). Data were filtered so all timeseries have con - recall rates, and time to solve during the clock synchro- gruent ranges, then the data was imported into a project nization phase. database. There were some codes that did not produce any The workflow (Fig.  3) proceeds with enumerating met- known multipath detections at a receiver, meaning they ronome epochs and identifying metronome multipath. It had no training data. In these cases, we applied a Gauss- then proceeds to clock synchronization for those receiv- ian Mixture Model (GMM) to scaled observations of ers with known positions, followed by beacon tag mul- amplitude, NBW and SNR with SciKit-Learn [17]. The tipath removal associated with receivers at depth. After GMM assumed that the data are comprised of a mix- which, jsats3d.py positions receivers at depth with the ture of Gaussian distributions (i.e., more than one class solution provided in Deng et  al. [6]. With the positions of detection; multipath or not), and it determines, where of all receivers known, we synchronized the receivers at the split occurs and then classifies each point. Following depth with R05’s clock, and then applied the multipath multipath removal, the study team proceeded with coor- filter to fish tags. At this point, the final, filtered recap - dinating fish or receivers at depth, depending upon the tures data was exported from the jsats3d project database stage of analysis. Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 7 of 15 Fig. 3 jsats3d workflow from raw study data to fish positioning for positioning in Mathematica. At all steps, intermediate primary detections with low amplitude and signal to data is written to the jsats3d project database for further noise ratio, suggesting a need for an unsupervised clas- inspection. sifier. The k-means found two distinct groups (Fig.  6) and classified the cluster closer to known multipath as Results such. Forebay water temperature With reduced biased training data, we compared the The water-temperature data exhibited significant diur - performance of four different ML classifiers during nal variability with fluctuations of up to 3  °C by the end the clock synchronization phase: KNN, NB, SVC, and of the season and evidence of thermal stratification. The CART. The accuracy and precision of all 4 classifiers at study team fit a piecewise linear spline to the average of each receiver were very high (Tables  1, 2 respectively). all sensors in time (Fig. 4). In general, the closer receivers were to R05 the better their accuracy and precision rates. Recall, which was Multipath removal the ability of the classifier to find all multipath detec - The multipath filter was applied at three different tions, suffered the greatest the further receivers were stages in the data management process: beacon tag from R05 (Table  3). Perhaps, the greatest difference enumeration, clock synchronization, and when ana- between classification algorithms was the time to solve. lyzing fish tags. Figure  5 shows raw beacon transmis- The KNN, NB, and CART were similar at 97.98, 88.13, sions from receiver R05 at receiver R03 during the and 90.09 s, respectively. However, it took 8668.93 s to clock synchronization phase, where there were many fit SVC classifiers to each receiver. Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 8 of 15 Fig. 4 Water temperature at depth (m) over time at the Cowlitz Falls project. Note, the red line is the interpolated temperature used to calculate speed of sound, with stronger hue blues denoting temperature at depth. By the end of the study season, there is significant thermal stratification Fig. 5 Known multipath detections and assumed primary Fig. 6 Results of the unsupervised k-means classifier on primary detections. Note, there appears to be signals with low amplitude and detections. Note, k-means multipath appears different from known low signal to noise ratio multipath, but was closer than assumed primary detections While the algorithms were accurate and precise, in KNN removed 8431 detections as multipath, while the practice some were more restrictive than others sug- NB removed nearly an order of magnitude more as mul- gesting higher rates of false positives. Figures. 7, 8 depict tipath (83,864 detections). Removal of that many beacon multipath filtering with a KNN and NB respectively. The Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 9 of 15 Table 1 Comparison of accuracies for the multipath removal algorithm during the clock synchronization phase at all study receivers. Note, R05 is not in the table, because we were synchronizing the other clocks to it Method R01 R02 R03 R04 R06 R07 R08 R09 KNN 0.999 0.99 0.999 0.998 0.991 0.997 0.954 0.987 NB 0.994 0.969 0.993 0.997 0.993 0.989 0.914 0.985 CART 0.998 0.998 0.999 0.998 0.993 0.994 0.935 0.982 SVC 0.998 0.998 0.999 0.998 0.995 0.996 0.957 0.985 Table 2 Comparison of precision rates for the multipath removal algorithm during the clock synchronization phase at all study receivers. Note, R05 is not in the table, because we were synchronizing the other clocks to it Method R01 R02 R03 R04 R06 R07 R08 R09 KNN 0.999 0.999 0.999 0.998 0.972 0.992 0.934 0.988 NB 0.983 0.914 0.979 0.978 0.947 0.855 0.631 0.994 CART 0.999 0.998 0.998 0.992 0.966 0.954 0.75 0.903 SVC 0.999 0.999 0.999 0.997 0.966 0.993 0.941 0.961 Table 3 Comparison of recall rates for the multipath removal algorithm during the clock synchronization phase at all study receivers. Note, R05 is not in the table, because we were synchronizing the other clocks to it Method R01 R02 R03 R04 R06 R07 R08 R09 KNN 0.996 0.997 0.998 0.986 0.949 0.95 0.697 0.878 NB 0.997 0.998 0.999 0.988 0.999 0.978 0.844 0.853 CART 0.996 0.997 0.998 0.986 0.971 0.959 0.761 0.908 SVC 0.996 0.997 0.998 0.986 0.994 0.948 0.717 0.886 Fig. 7 Multipath filtering with a KNN. In general, low amplitude, low signal to noise ratio and high noise in bandwidth are associated with Fig. 8 Multipath filtering with a NB. Note this algorithm removes multipath detections. Note, values were scaled with SciKit Learn many more detections as multipath than the KNN (Fig. 7) Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 10 of 15 Fig. 9 Apparent distance (m) from R05 as measured in seconds given current water temperature. Note different y-scales Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 11 of 15 Fig. 10 Clock drift rate (ε ̇_eg) of each receiver measured in μs/s. Note different y-scales Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 12 of 15 Fig. 11 Three-dimensional Positions of a Smolt in the Forebay. Surface HRs encircled in red, and submerged HRs encircled in green. Units are in meters transmissions from R05 would impact our ability to accu- spatial separation. If left unsynchronized, the effect of rately synchronize clocks. clock drift would be severe with some receivers appar- ently drifting by as much as 10  km or more apart from Clock synchronization and validation each other (Fig.  9). Receiver R04 exhibited severe clock As discussed above, inter-receiver separation can be drift (Fig. 9, panel D) to the point, where epoch enumera- deduced from differencing the receivers’ clocks. There - tion failed at or around August 25. Consequently, recap- fore, if we suppose the clocks to not be drifting and ture data after this date at R04 was not useable. Figure 10 compute their apparent corresponding separation, we shows the drift rate ( ε ˙ ) expressed in units of (µs /s). eg can illustrate clock drift in terms of (apparent) changing Fig. 12 Positions developed with the Deng et al. [6] solution for tags 01C6 (left) and 0A88 (right). Both solutions suffer from CPDI and show considerable multipath error with elevations well above the surface of the water (262 m) in regions adjacent to the infrastructure (R07, R08, and R09) Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 13 of 15 Fish coordinates accuracy suffered with a known moving target. Over - Figure  11 provides one data set for an example. The fish all, the algorithm approximated the X and Y position was moving from lower right (upstream) to upper left of the tag during the tag-drag experiment well (Fig.  13); (downstream bypass). The disorganized positions in the however, we overestimated the elevation and our solu- lower right are outside the convex hull of the receiv- tion was above surface of the water for the duration of ers and are not very reliable. The trajectory suddenly the tag-drag experiment. The tag drag experiment used becomes sharp and clear as the fish slowly swims towards uncorrected code-only positions, which suffered from the upper left. Three slow circles are visible. Perhaps the the expected inaccuracies of the GPS system that state a fish lost the direction of the flow in the slack water near minimum user range error of 7.8 m 95% of the time. The the dam and began swimming in circles to redirect itself. RMSE in meters over the X-, Y- and Z-axes was 9.2, 15.6, The circular motion ends abruptly; the fish moves down - and 29.6 m, respectively. stream into the downstream bypass and vanishes. The two tags in Fig.  12 (01C6 and 0A88) suffered from Conclusions and discussion close proximity detection interference (CPDI), a type of The methods discussed herein managed a data set of multipath error, where the reflected transmission inter - more than 50-million detections, synchronized clocks feres with the primary transmission sequence [13]. The via temperature calibration using the concept of a metro- CPDI error occurred when the fish were adjacent to the nome, identified and removed multipath detections with metal trash rack (R07, R08, R09). These receivers also suf - supervised and unsupervised machine learning algo- fered from multipath bias in the clock synchronization rithms, and developed timestamped positions of fish as routine (Fig. 11, panel G and H). In both instances when they approach the downstream bypass with autonomous the fish swam away from the reflective surface, trajecto - JSATS receivers. The data management process was com - ries became well defined. plex and required the development of software (jsats3d. py), which was released under the MIT license [16]. Accuracy and precision of positions The study team’s approach reduced errors introduced Least squares positioning provides an estimate of preci- by clock biases and multipath detections; however, it sion, the standard deviation ( σ ). T able  4 lists the mean could not eliminate them all. Clock synchronization standard deviation for fish positions within the convex assumed that two clocks were drifting linearly across an hull vs outside of the convex hull. In total, there were epoch. When epochs from the master clock were not 1,23,247 least squares position determinations. When missed, the lag between detections occurred at the nomi- fish are within the convex hull, it is possible to position nal pulse rate (37.5  s), and clock drift was well approxi- within 6 cm horizontally and 12 cm vertically. When fish mated by a linear function. However, unsynchronized are outside of the convex hull, precisions worsen. clocks far from R05 will not detect its beacon every To assess the accuracy of the clock synchronization epoch, meaning the lag between received master clock and multipath removal approach, we used the beacon attached to receiver R05 and Deng et  al.’s [6] position- ing algorithm to compute an epoch-by-epoch position. Our position determination for R05 was the median of all solutions, which located the receiver at 14.13 m, 19.88 m, and 261.62  m. The receiver was surveyed at 14.13  m, 19.87 m, 261.62 m. We then calculated error between the algorithm’s position and the survey at every epoch and computed the RMSE, in meters, over the X-, Y-, and Z- axes at 0.02 m, 0.05 m, and 0.004 m, respectively. While the RMSE was very low for the stationary receiver that acted as the study’s metronome (R05), Table 4 Standard deviation about the X, Y and Z coordinates for fish within vs outside of the convex hull Convex Hull σ ˜ (m) σ ˜ (m) σ ˜ (m) Fig. 13 Tag drag (dotted) superimposed onto our solution (solid). x y z Note the tag drag data appears to suffer from error, exacerbating Inside 0.06 0.06 0.12 RMSE. There are regions, where we can see tag drag data bundle up Outside 0.25 0.33 0.27 into knots Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 14 of 15 signals can be much longer than the nominal pulse rate. with them to absorb multipath transmissions before The longer the lag, the less likely drift over that duration they arrive at a receiver. remains linear, and the more error is introduced into If the study site allows, the receiver-array geom- coordinates. etry should completely encircle the region-of-interest, Aside from clock-synchronization interpolation error, because positions outside the convex hull tend to be some multipath detections remained after two rounds unreliable. There should be receivers at depth, at the of filtering. Figure  4 panel G provides the computed surface, and around the entire fish passage zone. The distances between R08 and R05 at every epoch before mathematics require known positions at every times- synchronizing clocks. The sharp spike in distance at or tamp. Therefore, it is helpful for the receivers to remain around August 10, 2018, was the result of multipath, with stationary. Tethered receivers at depth are not useful this single epoch producing errors of 100  m or more at for positioning, because including their coordinates R08. Given that the study team relied upon statistical into the system of equations as unknowns introduces filters to remove metronome multipath detections, we more unknowns than equations. The temperature of must accept that misclassifications will occur, albeit with the region of interest (thus speed of sound) must be a low likelihood of occurrence. Out of the four super- measured with high accuracy and precision at every vised classifiers tested, the KNN performed the best, with time step, and there should be enough sensors to sta- high accuracy, precision and recall rates, quick time to tistically describe the temperature of the study area. solve, and low numbers of false positives. The SVC per - Because the study team was unsure of the temperature formed similarly as the KNN in terms of accuracy and between a transponder and receiver, best practices sug- precision; however, the SVC was much slower (8,668.93 s gest the best measure of speed of sound is the mean at vs 97.98 s). a given time. When positioning the study’s metronome (R05), Developing an efficient and cost-effective method to our approach was highly accurate (<  10  cm); however, coordinating that can be implemented on autonomous it suffered when we compared it with a known mov - unsynchronized receivers is a major challenge to 3-D ing target. Overall, the X and Y error for the tag drag positioning with JSATS technology. This approach pro - experiment was 9.2 and 15.5  m and the Z elevation duced a useful 3-D data set, which allowed for the rec- was overestimated and above the surface of the water. reation of trajectories within the Cowlitz Falls forebay. While the RMSE for a known moving target was poor, It is the study team’s desire that this advancement pro- we believe this may be due to the method of data col- vide the foundation for future research into inferential lection. A tag drag experiment using uncorrected code- statistics that analyze movement in continuous time only positions will have an expected user range error and space. Recent advances have developed methods to (URE) of 7.8 m 95% of the time. User accuracy depends extract behavioral mechanisms from continuous space– on a combination of satellite geometry at time of data time data sets [11]. Point clouds and/or fish aggregation collection, URE, and other local factors (i.e., signal areas can be described with Kernel Density Estimates blockage, atmospheric conditions, and receiver qual- (KDE) [22]. A KDE is a non-parametric, robust density ity) [25]. While the RMSE was high, the errors are well estimate that can be used to describe areas of aggregation within the ordinary, expected performance of the GPS and potential travel. Certain operations, environmental receiver, especially one operating on a body of water conditions, or time of day may lead to fish preferring one without a ground plane. In future efforts the position location in the forebay over another. These differences of the vessel performing the tag drag should be tracked in areas of use can be assessed with a Kernel Discrimi- with a robotic total station or phase-observing, differ - nant Analysis (KDA) [1]. With a robust data cleaning and entially corrected GNSS receiver. coordinating method, data sets worthy of further analysis Some fish tags suffered from CPDI multipath [13] will surely follow. error (Fig.  12) when they were adjacent to metal infra- Acknowledgements structure. When the fish are in the middle of the fore - Not applicable. bay this error does not exist. This suggests that the Authors’ contributions receivers were placed too close to a highly reflective The lead author, KPN wrote the clock synchronization, multipath removal, and surface. Either the receivers need to be moved further data management routines in Python and wrote much of the manuscript. out into the forebay to increase the time delay between THM developed positions using least squares in Mathematica, provided the mathematical basis for positioning and clock synchronization, and primary transmission and multipath arrival, or some co-authored the manuscript. All authors have read and approved the final type of baffling should be used. Bubble curtains have manuscript. been used for some time to reduce underwater noise of percussive piling [28]. Future efforts could experiment Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 15 of 15 Funding 11. Gurarie E, Andrews RD, Laidre KL. A novel method for identifying behav- The authors analyzed data under contract to a private business, AnchorQEA. ioural changes in animal movement data. Ecol Lett. 2009;12:395–408. The authors did not receive funding to produce this manuscript. 12. Innovasea. Innovative Tracking Technology. (2020) Retrieved 7 Nov 2020 from: https:// www. innov asea. com/ fish- track ing/ Availability of data and materials 13. Kessel ST, Hussey NE, Webber DM, Gruber SH, Young JM, Smale MJ, Fisk The data sets used and/or analyzed during the current study are available AT. Close proximity detection interference with acoustic telemetry: the from the corresponding author on reasonable request. importance of considering tag power output in low ambient noise environments. Anim Biotelemetry. 2015;3:1–14. 14. Li X, Deng ZD, Sun Y, Martinez JJ, Fu T, McMichael GA, Carlson TJ. A 3D Declarations approximate maximum likelihood solver for localization of fish implanted with acoustic transmitters. Sci Rep. 2014. https:// doi. org/ 10. 1038/ srep0 Ethics approval and consent to participate Not applicable. 15. Li X, Deng Z, Martinez JJ, Fu T, Titzler PS, Hughes JS, Weiland MA. Three- Dimensional Tracking of Juvenile Salmon at Mid-Reach Location between Consent for publication Dams. Fish Res. 2015. https:// doi. org/ 10. 1016/j. fishr es. 2015. 01. 018. Not applicable. 16. Nebiolo K. jsats3d. (2021) Retrieved 28 Mar 2021 from: https:// github. com/ knebi olo/ jsats 3d Competing interests 17. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, The authors have no competing interests. Duchesnay E. Scikit-learn: Machine Learning in Python. J Mach Learn Res. 2011;12:2825–30. Author details 18. Perry RW, Farley J, Darland TJ, Hansen GS, Feil DH, Rondorf DW, LeClaire 1 2 Kleinschmidt Associates, 35 Pratt St. Suite 201, Essex, CT 06246, USA. Depar t- R(2003) Feasibility of Using 3D Acoustic Telemetry to Assess the Response ment of Natural Resources and the Environment, University of Connecticut, of Resident Salmonids to Strobe Lightsin Lake Roosevelt, Washington. U-4087, 1376 Storrs Rd, Storrs, CT 06269, USA. Bonneville Power Administration. Portland, OR: U.S. Department of Energy Received: 27 October 2020 Accepted: 24 May 2021 19. Rauchenstein LT, Vishnu A, Li X, Deng ZD. Improving underwater localiza- tion accuracy with machine learning. Rev Sci Instrum. 2018;89:074902. 20. Roberts DT, Udyawer V, Franklin C, Dwyer RG, Campbell HA. Using an acoustic telemetry array to assess fish volumetric space use: a case study on impoundments, hypoxia and an air-breathing species (Neoceratodus References forsteri). Mar Freshw Res. 2017;68:1532–43. 1. Aspillaga E, Safi K, Hereu B, Bartumeus F. Modeling the three-dimensional 21. Seafloor Systems Inc. (2015, 10 6). Speed of Sound in Freshwater. space use of aquatic animals combining topography and Eulerian telem- Retrieved 18 Oct 2018 from Seafloor Systems Support: https:// seafl oorsy etry data. Methods Ecol Evol. 2019. https:// doi. org/ 10. 1111/ 2041- 210X. stems. com/ suppo rt/ softw are- suppo rt/ 86- sound- veloc ity/ file 22. Simpfendorfer CA, Olsen EM, Heupel MR, Moland E. Three-dimensional 2. Baktoft H, Gjelland KØ, Økland F, Thygesen UH. Positioning of aquatic kernel utilization distributions improve estimates of space use in aquatic animals based on time-of-arrival and random walk models using YAPS animals. Can J Fish Aquat Sci. 2012;69:565–72. (Yet Another Positioning Solver). Sci Rep. 2017;7:1–10. 23. Smith F. Understanding HPE in the VEMCO positioning system ( VPS). 3. Bergé J, Capra H, Pella H, Steig T, Ovidio M, Bultel E, Lamouroux N. Prob- (2013) http:// vemco. com/ wp- conte nt/ uploa ds/ 2013/ 09/ under stand ing- ability of detection and positioning error of a hydro acoustic telemetry hpe- vps. pdf system in a fast-flowing river: intrinsic and environmental determinants. 24. SQLite (2016). About SQLite. Retrieved 1 Oct 2018 from SQLite: https:// Fish Res. 2012;125:1–13. www. sqlite. org/ about. html 4. Binder TR, Holbrook CM, Hayden TA, Krueger CC. Spatial and temporal 25. USSF. (2021). GPS Accuracy. (National coordination office for space-based variation in positioning probability of acoustic telemetry arrays: fine-scale positioning, navigation and timing) from GPS.gov: https:// www. gps. gov/ variability and complex interactions. Anim Biotelemetry. 2016;4:4. syste ms/ gps/ perfo rmance/ accur acy/. 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Development of an air bubble 8. Ehrenberg JE, Steig TW. Improved techniques for studying the tem- curtain to reduce underwater noise of percussive piling. Mar Environ Res. poral and spatial behavior of fish in a fixed location. ICES J Mar Sci. 2000;49:79–93. 2003;60:700–6. 9. Ehrenberg JE, Steig TW. A study of the relationship between tag-signal Publisher’s Note characteristics and achievable performances in acoustic fish-tag studies. Springer Nature remains neutral with regard to jurisdictional claims in pub- ICES J Mar Sci. 2009;66:1278–83. lished maps and institutional affiliations. 10. Fu T, Lin X, Hou Z, Deng Z. Integrating Hybrid-Clustering and Localized Regression for Time Synchronization of a Hierarchical Underwater Acous- tic Sensor Array. OCEANS 2019 MTS/IEEE. 2019.pp. 27–31 Seattle, IEEE http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Animal Biotelemetry Springer Journals

High precision 3-D coordinates for JSATS tagged fish in an acoustically noisy environment

Animal Biotelemetry , Volume 9 (1) – Jun 2, 2021

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Abstract

Background: Acoustic tagging methods have been used to track fish for some time. Multiple systems have been developed, including those that give researchers the ability to position fish in three dimensions and time. However, proprietary positioning methods have suffered from a lack of transparency. The U.S. Department of Energy and the U.S. Army Corps of Engineers developed the Juvenile Salmon Acoustic Telemetry System (JSATS) to monitor the survivability of juvenile salmonids as they migrate downstream. With much smaller tags and high ping rates, JSATS positioning studies should be more prevalent, but implementation is difficult and often out of reach for small budget- minded studies. This study implemented a small scale JSATS positioning study using relatively inexpensive, autono- mous, independent receivers. We will show that proper synchronization of the transmissions and elimination of multipath allows the positions of a smolt to be determined in three spatial dimensions over time with high precision. Results: Tracking of 172 tagged smolts produced a total of nearly 2,00,000 positions. We compared the performance of four different supervised machine learning classifiers (Support Vector Classifier (SVC), Gaussian Naïve Bayes (NB), Classification Tree (CART ), and K-Nearest Neighbor (KNN). All algorithms performed well with high accuracy and precision, but recall rates decreased with distance from the source. The SVC and KNN were least restrictive in practice. Overall, the SVC had the longest time to solve. Conclusion: Positions determined from fish outside of the convex hull of the hydrophones were effectively being extrapolated, while positions determined from within the convex hull nearly always met or exceeded 1-m precision. Having stationary submerged hydrophones was necessary to produce three-dimensional positions. The main techni- cal advances presented are the hydrophone-clock synchronization scheme and the multipath rejection scheme, which found the best multipath classifier to be the K-Nearest Neighbor. Neither algorithm was capable of alleviating close proximity detection interference (CPDI), suggesting the need to reposition receivers from reflective surfaces or install baffling. Introduction are affixed to immobile objects in the study area; and Acoustic tagging technologies and positioning algo- data-logging equipment to record the data from the rithms have made it possible to track aquatic animals at hydrophones. A tag emits a sonic transmission that fine temporal and spatial scales, meaning, in theory, it the hydrophones can detect. The transmission includes could be possible to infer behavioral responses to stim- a unique digital signature (tag ID) to ensure correct uli. The system is comprised of a “tag” that is attached determination of which tag was detected. To obtain 3-D to, or embedded into, the animal; hydrophones that positions, four or more hydrophones must detect the same transmission from a tag. The positioning problem is then resolved by determining the distances from the *Correspondence: kevin.nebiolo@kleinschmidtgroup.com hydrophones to the tag at the moment of transmission Kleinschmidt Associates, 35 Pratt St. Suite 201, Essex, CT 06246, USA by inference from the speed of sound and the elapsed Full list of author information is available at the end of the article © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. The Creative Commons Public Domain Dedication waiver (http:// creat iveco mmons. org/ publi cdoma in/ zero/1. 0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 2 of 15 time for the transmission to propagate from the tag to with a kernel distribution. With VPS, depth is meas- the hydrophones. Given the 3-D positions of the hydro- ured by pressure sensors in the tag and encoded in the phones, the time of transmission, and the times of transmission message [4], which makes the message detections, the position is determined using multilat- longer than other technologies, leading to collisions eration, similar to positioning with a Global Positioning with other tag messages and potentially themselves. System (GPS) receiver. The manufacturer HTI has another comparable propri - The mathematics of multilateration require that the etary system, which also sees extensive use. Perry et al. clocks in the hydrophones be synchronized, so there [18] used an HTI array with unsynchronized clocks to must either be additional infrastructure to synchronize understand the effects of strobe lights on migrating the clocks in situ or resolution of the clock time biases resident salmonids. Bergé et  al. [3] tested a UTC syn- in software ex post facto. Hardware synchronization chronized HTI array to optimize receiver geometry either requires communication among the receivers among other variables and found the best configura - and a time standard, or the ability to do time trans- tion resulted in a 44 percent detection efficiency with fer from, for example, the GPS to synchronize to GPS an error of 3.6  m. In 2019, VEMCO and HTI were time, which is nominally equivalent to Coordinated acquired by Innovasea [12]. Universal Time (UTC) (in French, temps universel The open source Yet another positioning solution coordonné). (YAPS) algorithm [2] is an improvement over propri- For fish passage studies, these requirements dictate etary solutions, and it works with UTC-synchronized deploying an array of receivers in a complex and highly data. YAPS couples a maximum likelihood analysis reflective environment. Here, by ref lective we mean of time-of-arrival data with a state-space movement that the acoustic transmissions can reflect off objects model [2]. Using tags with a stable transmission rate, in the surroundings and, thus, take a non-direct route YAPS can anticipate the time of transmission allowing to the hydrophones. When reflections occur, a hydro- researchers to model time-of-arrival on a random-walk phone can detect one or more transmissions in the basis, making it easier to filter out multipath detections same epoch from a single tag, resulting in the mul- and improve accuracy. Vergeynst et al. [26] used YAPS tipath problem: a single transmission took multiple on a VPS data set in a highly reflective environment paths to reach a hydrophone [27]. Confusing a mul- and found significant accuracy improvement. However, tipath transmission for the direct-route transmission YAPS does not synchronize independent clocks. introduces error into the position estimate, often egre- The Juvenile Salmon Acoustic Telemetry System gious error. (JSATS) is a non-proprietary acoustic sensing technol- Open-source positioning algorithms have been pro- ogy developed for the U.S. Army Corps of Engineers posed to assist researchers who possess the appropri- to evaluate the behavior and survival of juvenile sal- ate data (UTC synched), but most acoustic positioning monids migrating through the Columbia River system solutions utilize proprietary software and value-added [27]. The JSATS tags’ transmissions are detected and vendor services. For cost-conscious studies that can- decoded by self-contained autonomous hydrophone not afford expensive systems or vendor services receivers (HRs) placed at strategic locations through- with recurring fees, this often means falling back out the project area [27]. Determining a 3-D position onto more simple presence/absence receiver arrays, of the fish in time requires transmission detection by because researchers lack a method of synchronizing four or more receivers [6]. Li et al. [14] improved upon independent receiver clocks and reliably removing the 2-d closed-form approximate maximum likelihood multipath. (AML) developed by Chan et  al. [5] by extending to a The VEMCO VPS system is a proprietary turn-key third dimension and using a linear least squares solu- acoustic positioning solution [4] that uses multiple tion as an initial guess. The AML is a non-exact solver independent receivers each with a single independent that alleviates influence from first-return multipath hydrophone. The VPS system uses hyperbolic exact with a weighting matrix and processing step on time of positioning algorithms to locate fish, where the hori - arrivals. Rauchenstein et al. [19] further improved upon zontal position error is a weight averaged position the AML using machine learning methods to identify among all combinations of receivers that detected a and remove multipath biased position estimates. In transmission [23]. The VPS system has enjoyed exten - 2019, Fu et  al. [10] developed a hierarchical localized sive use. Binder et al. [4] deployed 140 recivers to track regression technique using a series of two-way mes- lake trout within Lake Huron, North America, but sages to synchronize independent JSATS receivers. The found extensive multipath error after filtering. Roberts localized linear regression technique assumes a con- et  al. [20] used the VPS system to describe space-use stant clock drift. Multipath error present in beacon tag Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 3 of 15 transmissions could bias the regression parameters and impart error into the clocks, which could prove prob- lematic for studies in highly reflective environments. The approach employed in this study synchronizes clocks, removes multipath error, and produces 3-D positions of fish in time with nonlinear least squares estimation using relatively inexpensive autonomous JSATS hydrophone receivers. If the receivers have sufficient temporal resolution (microsecond) and the speed-of-sound is accurately measured, it is pos- sible to set up small-scale arrays that produce precise 3-D positions in highly reflective, acoustically noisy environments. Methods These methods were implemented on a juvenile smolt downstream passage study on the Cowlitz River, Wash- Fig. 2 Positions of the 9 Technologic receivers and their convex hull. ington, US (Fig. 1) at the Cowlitz Falls Dam. The study Units are in meters. Note, R05 is not on the convex hull, including it would create a depression, which is concave. Receiver R04 is located tagged 179 fish with Advanced Telemetry Systems adjacent to the fish passage entrance, while R07, R08 and R09 are Model SS400 JSATS acoustic tags and tracked them affixed to the trashrack. The Receivers R07, R04 and R01 are essentially with nine autonomous Teknologic (Model 11,497) on the face of the dam autonomous cabled hydrophone receivers (HR) fixed in position and encircling the area of interest for 3-D positions (Fig.  2). The HRs collected large amounts of data, which were managed by SQLite, an in-process microseconds since January 1, 1970 stored as a 32-bit library that implements a self-contained, server-less, floating point decimal). Following the initial data zero-configuration, transactional SQL database engine management, the study team enumerated beacon tag [24]. transmissions (epochs), synchronized clocks, removed For ease of computation, all time stamps were con- multipath errors, and finally produced 3-D coordinates verted to decimal microseconds in Unix time (decimal with a corrected time stamp for the fish. Mathematical model for positioning A fish tag periodically emits an acoustic pulse that uniquely identifies the tag’s transmission content, which consists entirely of the tag ID. The pulse is detected by the hydrophone receivers, which have internal clocks that record the moment they detect the pulse in a man- ner similar to how a GPS receiver records the moment it detects the radio transmission from satellites. How- ever, unlike GPS, the acoustic pulse does not encode a time stamp of when it was emitted. The tag-positioning problem is, therefore, different from the GPS position - ing problem in that there is an additional unknown, the moment when the pulse was emitted. Nonetheless, the conceptual basis of the two systems is quite similar, so similar solution methods pertain. The mathematics for three-dimensional positioning using JSATS can be found in Ehrenberg and Steig [7, 8]. Our positioning equation is formed from the difference of the equations for two receivers, a and b, positioning the smolt independently, which eliminates the time-of- Fig. 1 Location of the Cowlitz River, a tributary to the Columbia River transmission as an unknown, producing Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 4 of 15 (−1) 2 2 2 2 2 2 t −t +c ( (x − X) + (y − Y ) + (z − Z) − ((x − X) + (y − Y ) + (z − Z) )) = 0, a b b b b a a a not know, where a fish is when a tag fires, a good esti - where t and t are the (synchronized) times-of-detec- a b mate of water column temperature is the mean of all tions at the receivers; c is the instantaneous speed- interpolated temperature-at-depths. After determining of-sound in fresh water; x , y , and z are receiver a’s a a a water temperature (average temperature at time), the spatial coordinates (similar for receiver b); and X , Y , Z speed-of-sound on an epoch-by-epoch basis was calcu- are the desired coordinates of the smolt. This equation lated with a cubic spline fit to data provided by Seafloor is nonlinear in X , Y , Z , so it is solved iteratively using a Systems [24]. nonlinear least squares estimator. This equation reveals some subtle requirements. Clock synchronization Unlike the GPS equations in which receiver time-bias The mathematical model requires a priori synchronization terms can be determined mathematically, here we have of receiver clocks. This was accomplished using the con - the situation in which including the time biases always cept of a metronome; receiver R05 was the time standard results in more unknowns than equations. Therefore, and we synchronized the other clocks to it. Knowing the the receivers’ clocks must be synchronized prior to receivers’ spatial coordinates allows the positioning prob- the position estimation; for GPS, the receiver’s time lem to be inverted and solved for time-of-transmission, so bias is solved for as a fourth unknown. The speed-of- the clocks were synchronized using the beacon attached to sound must be known a priori epoch-by-epoch. Water receiver R05. temperature was continuously monitored at three sta- The goal was to determine the “true” times of transmis - tions within the impoundment with a string of HOBO sion and reception, as the exact moments in time (i.e., the Water Temperature Pro v2 probes at 0.5, 1, 3, 4.5, 6, 7.5, time of a perfect clock) when the transmitting receiver 9, 12, and 14.5  m depth. The positions of the receivers emitted its beacon signal and when that signal was detected must be known epoch-by-epoch, receivers mounted by the other hydrophone receivers (HRs). on infrastructure at the surface were located with a Explicit moments-in-time require an explicit time refer- Trimble Geox7 GPS with 10  cm of accuracy after post ence, such as UTC or GPS time; however, the positioning processing with Trimble Pathfinder. Six receivers were equations depend only on the differences of the times-of- mounted near the water surface; with three on immo- transmission and the times-of-reception, so their collective bile supports (R04, R05, R06), and the other three were bias from time external standards vanishes in the differ - affixed to the trash rack which tracked with the water ence. It is essential, however, that the HRs’ clocks are not surface (R07, R08, R09) and three were placed at the biased relative to each other. bottom of the forebay (R01, R02, R03) (Fig. 2). The posi - For HRs i and j located at x , y , z and x , y , z , respec- i i i j j j tions of the submerged receivers could not readily be tively, the fundamental geometric relationship for the dis- observed, so they were positioned using their attached tance separating them is beacons as if they were fish. This required an epoch- by-epoch vertical-coordinate determination. Thus, it is 2 2 2 (1) d = x − x + y − y + z − z . i,j j i j i j i possible to validate the receivers’ positions by inferring their separation using the beacon transmissions given It was assumed that the HRs’ epoch-by-epoch positions the speed-of-sound. are known correctly, so d was taken as correct. Some of i,j the HRs moved with the water surface elevation of the fore- bay, so, more specifically, d was taken as being correct i,j Speed of sound epoch-by-epoch and the notation implies distance at some The mathematical model requires a priori knowledge particular epoch or moment in time. of the per-epoch speed-of-sound. The study team It takes some time for a signal from, say, HR i to be deployed three temperature sensor vertical profile detected by some other HR j, namely, the true time of strings within the project area, which collected water r x reception τ minus the true time of transmission τ . Multi- j i temperature readings throughout the study at 5-min plying this difference by the speed of sound for this epoch, intervals with high precision. To estimate a water col- c , again gives the distance separating the receivers: umn temperature, we fit a piecewise linear spline to temperature data at each depth interval. The linear r x d = c τ − τ . i,j (2) j i spline allowed us to “sample” water temperature at depth at any time throughout the study. Because we do Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 5 of 15 The per-epoch speed-of-sound as determined with the r x ε = d /c − t − τ , i i,j (8) j i average forebay water temperature reading was taken as correct, as well. The clock in hydrophone R05, which was which is the time bias of the transmitting receiver, chosen to be the standard, will not generally run synchro- whichever one it happens to be. Knowing ε makes it pos- nized with the clocks in the other HRs—their clocks will sible to determine τ = t − ε , which, in turns, makes i i i not read the same value at the same moment in true time, it possible to determine the time biases of all the other and their clocks will generally run at different rates. The receivers in that epoch using Eq. (7): absolute offset of a clock’s reading from the true time can For two epochs τ <τ , the clock-drift rate for a e g be expressed as the reading of the clock, t, minus its bias receiver is given by from the true time, ε: ε − ε g e ε˙ = lim , τ = t − ε. (3) eg �τ→0 �τ By subtracting ε (as opposed to adding it), the study team where �τ = τ − τ , so the clock drift from epoch e to g e was consistent with the intuition that the clock is running epoch g is approximately fast when ε is positive, or the clock is running slow when ε ε − ε is negative. The clock drift rate is given by the time deriva - g e ε˙ ≈ . eg (9) tive of Eq. (3): τ − τ g e τ˙ = t −˙ε, The reception time of any signal—such as from a fish’s tag—can be estimated with the help of Eq. (9) as follows. where the dot notation denotes the time derivative of Suppose a signal is detected at time τ , and τ <τ <τ . e g f f the dotted quantity. However, τ˙ ≡ 1 , b e cause τ is true Then time, so τ ≈ τ +˙ε τ − τ . (10) f e eg f e t = 1 +˙ε. (4) After computing ε for every transmission interval, the Substituting Eq. (3) into Eq. (2) gives study team fit a piecewise linear interpolator to all epochs r x r x (τ , τ , τ , . . . , τ ) , then applied Eq.  (10) to all recaptures d = c t − ε − t − ε = c t − t − ε − ε 1 e g n i,j j i j i j i j i at receiver j . Of interest is the effect of water temperature so, in general, and other variables on ε ˙ . eg r x d = c t − t − c ε − ε . i,j j i (5) j i Multipath removal Tag transmissions can reflect off the water surface, sub - By convention, the true clock rate is the rate of R05’s strate, and infrastructure, which can cause a receiver to clock, so ε˙ ≡ 0 and ε ≡ 0 for R05. Suppose R05 is the record several nearly simultaneous transmissions from transmitting receiver, so ε = 0 . Then, Eq. (5) becomes a single tag in any epoch, the aforementioned multipath r x condition. The data revealed that mistaking a multipath d = c t − τ − cε , i,j j (6) j i signal for the primary signal can introduce tens of meters of error into the fish coordinates, so its mitigation was whose only unknown is ε . Solving Eq. (6) for ε gives j j essential. r x Multipath removal was a phased approach; the first ε = t − τ − d /c, j i,j (7) j i of which identified the first transmission among all the transmissions detected from a single source in any epoch. which is the time bias of the detecting receiver. All val- In this phase the correct transmission was assumed to ues on the right side of Eq.  (7) are known. Therefore, all be the first (earliest) transmission, as all others must be other HRs can have their time bias determined at any multipath. This assumption stemmed from the fact that a epoch in which they detect the transmission from R05. multipath signal travels a further distance to the receiver Now suppose R05 is not the transmitting receiver but it is than the direct signal, so it seemed unlikely that a signal a detecting receiver, so ε = 0 . Then, Eq. (5) becomes that traveled further would arrive prior to one that trave- r x led a shorter distance. d = c t − τ + cε , i,j i j i whose only unknown is ε . Solving for ε gives i i Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 6 of 15 Coordinating fish The first step enumerated metronome transmission Determining fish positions proceeded epoch-by-epoch epochs and grouped primary and multipath transmis- in Mathematica . Epochs with too few observations, less sions into a series of detections per epoch. The first than four, were insolvable and skipped. A nonlinear least- detection in series for every epoch was retained, as all squares estimation was attempted on the others, and not others must be multipath. However, sometimes the true all attempts were successful, meaning the normal matrix signal (the signal without multipath) was not detected was either singular or ill-conditioned, or the iteration at all, and the first detection in series was the result of failed to converge. All successful positions were retained multipath. In these cases, the primary filter failed and despite many having impossible coordinates, such as ver- required a second filter to scrutinize the first return tical coordinates above the water surface or horizontal further. coordinates on dry land. These data can serve as presence The second phase of multipath filtering removed erro - data, if nothing else, and retaining them costs nothing. neous transmissions with unsupervised and supervised machine learning algorithms. Training data was pro- Accuracy and precision duced in the first phase with information on the primary Li X et al. [15] describes methods to assess the accuracy detection and the multipath that followed. However, and precision of the positioning algorithm. We assessed this convention posed a dilemma, because the train- accuracy by comparing an epoch-by-epoch metronome ing data were known to be biased. We assume that there receiver (R05) position determination to its surveyed were instances, where the primary detection was missed position, and calculating the root-mean-square-error and multipath was mislabeled as true. To overcome this (RMSE). We also compared the solutions produced by potential bias, we fit a k-means (k = 2) unsupervised clas- the algorithm to a tag drag test. We described the fish sifier to normalized observations of the signal’s ampli - location’s precision with the standard deviation, because tude, noise bandwidth (NBW), and signal-to-noise they were solved with least squres. We then compared ratio (SNR) for all assumed primary detections with the mean of the precision estimates for fish tags within Scikit-Learn [17]. Then, we compared the distance from the convex hull to those outside. each cluster mean to the mean of the known multipath detections. If the distance between the known multipath Analysis workflow detections and the closer cluster’s center is smaller than Unsynchronized clocks, highly reflective acoustic envi - half the distance between cluster centers, we classified ronments, and not knowing the positions of the receivers the closer cluster as multipath. at depth makes implementing JSATS studies with auton- After enumerating epochs and removing biased omous receivers difficult. To overcome this and assist training data, the study team had confirmation on the other researchers, the study team developed jsats3d.py first transmission and the multipath detections that [16]. The open source software, written in Python, assists followed. Data was normalized or scaled (dependent with data management, clock synchronization, and upon algorithm) prior to classifying. We tested a suite multipath removal, while fish coordinates were solved of supervised classifiers: Support Vector Classifier with Mathematica. The data cleaning workflow starts (SVC), Gaussian Naïve Bayes (NB), Classification Tree with reception of study data from Teknologic Receivers, (CART), and K-Nearest Neighbor (KNN) with Scikit- HOBO water temperature sensors, and operations data Learn [17], and compared their accuracy, precision, (SCADA). Data were filtered so all timeseries have con - recall rates, and time to solve during the clock synchro- gruent ranges, then the data was imported into a project nization phase. database. There were some codes that did not produce any The workflow (Fig.  3) proceeds with enumerating met- known multipath detections at a receiver, meaning they ronome epochs and identifying metronome multipath. It had no training data. In these cases, we applied a Gauss- then proceeds to clock synchronization for those receiv- ian Mixture Model (GMM) to scaled observations of ers with known positions, followed by beacon tag mul- amplitude, NBW and SNR with SciKit-Learn [17]. The tipath removal associated with receivers at depth. After GMM assumed that the data are comprised of a mix- which, jsats3d.py positions receivers at depth with the ture of Gaussian distributions (i.e., more than one class solution provided in Deng et  al. [6]. With the positions of detection; multipath or not), and it determines, where of all receivers known, we synchronized the receivers at the split occurs and then classifies each point. Following depth with R05’s clock, and then applied the multipath multipath removal, the study team proceeded with coor- filter to fish tags. At this point, the final, filtered recap - dinating fish or receivers at depth, depending upon the tures data was exported from the jsats3d project database stage of analysis. Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 7 of 15 Fig. 3 jsats3d workflow from raw study data to fish positioning for positioning in Mathematica. At all steps, intermediate primary detections with low amplitude and signal to data is written to the jsats3d project database for further noise ratio, suggesting a need for an unsupervised clas- inspection. sifier. The k-means found two distinct groups (Fig.  6) and classified the cluster closer to known multipath as Results such. Forebay water temperature With reduced biased training data, we compared the The water-temperature data exhibited significant diur - performance of four different ML classifiers during nal variability with fluctuations of up to 3  °C by the end the clock synchronization phase: KNN, NB, SVC, and of the season and evidence of thermal stratification. The CART. The accuracy and precision of all 4 classifiers at study team fit a piecewise linear spline to the average of each receiver were very high (Tables  1, 2 respectively). all sensors in time (Fig. 4). In general, the closer receivers were to R05 the better their accuracy and precision rates. Recall, which was Multipath removal the ability of the classifier to find all multipath detec - The multipath filter was applied at three different tions, suffered the greatest the further receivers were stages in the data management process: beacon tag from R05 (Table  3). Perhaps, the greatest difference enumeration, clock synchronization, and when ana- between classification algorithms was the time to solve. lyzing fish tags. Figure  5 shows raw beacon transmis- The KNN, NB, and CART were similar at 97.98, 88.13, sions from receiver R05 at receiver R03 during the and 90.09 s, respectively. However, it took 8668.93 s to clock synchronization phase, where there were many fit SVC classifiers to each receiver. Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 8 of 15 Fig. 4 Water temperature at depth (m) over time at the Cowlitz Falls project. Note, the red line is the interpolated temperature used to calculate speed of sound, with stronger hue blues denoting temperature at depth. By the end of the study season, there is significant thermal stratification Fig. 5 Known multipath detections and assumed primary Fig. 6 Results of the unsupervised k-means classifier on primary detections. Note, there appears to be signals with low amplitude and detections. Note, k-means multipath appears different from known low signal to noise ratio multipath, but was closer than assumed primary detections While the algorithms were accurate and precise, in KNN removed 8431 detections as multipath, while the practice some were more restrictive than others sug- NB removed nearly an order of magnitude more as mul- gesting higher rates of false positives. Figures. 7, 8 depict tipath (83,864 detections). Removal of that many beacon multipath filtering with a KNN and NB respectively. The Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 9 of 15 Table 1 Comparison of accuracies for the multipath removal algorithm during the clock synchronization phase at all study receivers. Note, R05 is not in the table, because we were synchronizing the other clocks to it Method R01 R02 R03 R04 R06 R07 R08 R09 KNN 0.999 0.99 0.999 0.998 0.991 0.997 0.954 0.987 NB 0.994 0.969 0.993 0.997 0.993 0.989 0.914 0.985 CART 0.998 0.998 0.999 0.998 0.993 0.994 0.935 0.982 SVC 0.998 0.998 0.999 0.998 0.995 0.996 0.957 0.985 Table 2 Comparison of precision rates for the multipath removal algorithm during the clock synchronization phase at all study receivers. Note, R05 is not in the table, because we were synchronizing the other clocks to it Method R01 R02 R03 R04 R06 R07 R08 R09 KNN 0.999 0.999 0.999 0.998 0.972 0.992 0.934 0.988 NB 0.983 0.914 0.979 0.978 0.947 0.855 0.631 0.994 CART 0.999 0.998 0.998 0.992 0.966 0.954 0.75 0.903 SVC 0.999 0.999 0.999 0.997 0.966 0.993 0.941 0.961 Table 3 Comparison of recall rates for the multipath removal algorithm during the clock synchronization phase at all study receivers. Note, R05 is not in the table, because we were synchronizing the other clocks to it Method R01 R02 R03 R04 R06 R07 R08 R09 KNN 0.996 0.997 0.998 0.986 0.949 0.95 0.697 0.878 NB 0.997 0.998 0.999 0.988 0.999 0.978 0.844 0.853 CART 0.996 0.997 0.998 0.986 0.971 0.959 0.761 0.908 SVC 0.996 0.997 0.998 0.986 0.994 0.948 0.717 0.886 Fig. 7 Multipath filtering with a KNN. In general, low amplitude, low signal to noise ratio and high noise in bandwidth are associated with Fig. 8 Multipath filtering with a NB. Note this algorithm removes multipath detections. Note, values were scaled with SciKit Learn many more detections as multipath than the KNN (Fig. 7) Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 10 of 15 Fig. 9 Apparent distance (m) from R05 as measured in seconds given current water temperature. Note different y-scales Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 11 of 15 Fig. 10 Clock drift rate (ε ̇_eg) of each receiver measured in μs/s. Note different y-scales Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 12 of 15 Fig. 11 Three-dimensional Positions of a Smolt in the Forebay. Surface HRs encircled in red, and submerged HRs encircled in green. Units are in meters transmissions from R05 would impact our ability to accu- spatial separation. If left unsynchronized, the effect of rately synchronize clocks. clock drift would be severe with some receivers appar- ently drifting by as much as 10  km or more apart from Clock synchronization and validation each other (Fig.  9). Receiver R04 exhibited severe clock As discussed above, inter-receiver separation can be drift (Fig. 9, panel D) to the point, where epoch enumera- deduced from differencing the receivers’ clocks. There - tion failed at or around August 25. Consequently, recap- fore, if we suppose the clocks to not be drifting and ture data after this date at R04 was not useable. Figure 10 compute their apparent corresponding separation, we shows the drift rate ( ε ˙ ) expressed in units of (µs /s). eg can illustrate clock drift in terms of (apparent) changing Fig. 12 Positions developed with the Deng et al. [6] solution for tags 01C6 (left) and 0A88 (right). Both solutions suffer from CPDI and show considerable multipath error with elevations well above the surface of the water (262 m) in regions adjacent to the infrastructure (R07, R08, and R09) Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 13 of 15 Fish coordinates accuracy suffered with a known moving target. Over - Figure  11 provides one data set for an example. The fish all, the algorithm approximated the X and Y position was moving from lower right (upstream) to upper left of the tag during the tag-drag experiment well (Fig.  13); (downstream bypass). The disorganized positions in the however, we overestimated the elevation and our solu- lower right are outside the convex hull of the receiv- tion was above surface of the water for the duration of ers and are not very reliable. The trajectory suddenly the tag-drag experiment. The tag drag experiment used becomes sharp and clear as the fish slowly swims towards uncorrected code-only positions, which suffered from the upper left. Three slow circles are visible. Perhaps the the expected inaccuracies of the GPS system that state a fish lost the direction of the flow in the slack water near minimum user range error of 7.8 m 95% of the time. The the dam and began swimming in circles to redirect itself. RMSE in meters over the X-, Y- and Z-axes was 9.2, 15.6, The circular motion ends abruptly; the fish moves down - and 29.6 m, respectively. stream into the downstream bypass and vanishes. The two tags in Fig.  12 (01C6 and 0A88) suffered from Conclusions and discussion close proximity detection interference (CPDI), a type of The methods discussed herein managed a data set of multipath error, where the reflected transmission inter - more than 50-million detections, synchronized clocks feres with the primary transmission sequence [13]. The via temperature calibration using the concept of a metro- CPDI error occurred when the fish were adjacent to the nome, identified and removed multipath detections with metal trash rack (R07, R08, R09). These receivers also suf - supervised and unsupervised machine learning algo- fered from multipath bias in the clock synchronization rithms, and developed timestamped positions of fish as routine (Fig. 11, panel G and H). In both instances when they approach the downstream bypass with autonomous the fish swam away from the reflective surface, trajecto - JSATS receivers. The data management process was com - ries became well defined. plex and required the development of software (jsats3d. py), which was released under the MIT license [16]. Accuracy and precision of positions The study team’s approach reduced errors introduced Least squares positioning provides an estimate of preci- by clock biases and multipath detections; however, it sion, the standard deviation ( σ ). T able  4 lists the mean could not eliminate them all. Clock synchronization standard deviation for fish positions within the convex assumed that two clocks were drifting linearly across an hull vs outside of the convex hull. In total, there were epoch. When epochs from the master clock were not 1,23,247 least squares position determinations. When missed, the lag between detections occurred at the nomi- fish are within the convex hull, it is possible to position nal pulse rate (37.5  s), and clock drift was well approxi- within 6 cm horizontally and 12 cm vertically. When fish mated by a linear function. However, unsynchronized are outside of the convex hull, precisions worsen. clocks far from R05 will not detect its beacon every To assess the accuracy of the clock synchronization epoch, meaning the lag between received master clock and multipath removal approach, we used the beacon attached to receiver R05 and Deng et  al.’s [6] position- ing algorithm to compute an epoch-by-epoch position. Our position determination for R05 was the median of all solutions, which located the receiver at 14.13 m, 19.88 m, and 261.62  m. The receiver was surveyed at 14.13  m, 19.87 m, 261.62 m. We then calculated error between the algorithm’s position and the survey at every epoch and computed the RMSE, in meters, over the X-, Y-, and Z- axes at 0.02 m, 0.05 m, and 0.004 m, respectively. While the RMSE was very low for the stationary receiver that acted as the study’s metronome (R05), Table 4 Standard deviation about the X, Y and Z coordinates for fish within vs outside of the convex hull Convex Hull σ ˜ (m) σ ˜ (m) σ ˜ (m) Fig. 13 Tag drag (dotted) superimposed onto our solution (solid). x y z Note the tag drag data appears to suffer from error, exacerbating Inside 0.06 0.06 0.12 RMSE. There are regions, where we can see tag drag data bundle up Outside 0.25 0.33 0.27 into knots Nebiolo and Meyer Anim Biotelemetry (2021) 9:20 Page 14 of 15 signals can be much longer than the nominal pulse rate. with them to absorb multipath transmissions before The longer the lag, the less likely drift over that duration they arrive at a receiver. remains linear, and the more error is introduced into If the study site allows, the receiver-array geom- coordinates. etry should completely encircle the region-of-interest, Aside from clock-synchronization interpolation error, because positions outside the convex hull tend to be some multipath detections remained after two rounds unreliable. There should be receivers at depth, at the of filtering. Figure  4 panel G provides the computed surface, and around the entire fish passage zone. The distances between R08 and R05 at every epoch before mathematics require known positions at every times- synchronizing clocks. The sharp spike in distance at or tamp. Therefore, it is helpful for the receivers to remain around August 10, 2018, was the result of multipath, with stationary. Tethered receivers at depth are not useful this single epoch producing errors of 100  m or more at for positioning, because including their coordinates R08. Given that the study team relied upon statistical into the system of equations as unknowns introduces filters to remove metronome multipath detections, we more unknowns than equations. The temperature of must accept that misclassifications will occur, albeit with the region of interest (thus speed of sound) must be a low likelihood of occurrence. Out of the four super- measured with high accuracy and precision at every vised classifiers tested, the KNN performed the best, with time step, and there should be enough sensors to sta- high accuracy, precision and recall rates, quick time to tistically describe the temperature of the study area. solve, and low numbers of false positives. The SVC per - Because the study team was unsure of the temperature formed similarly as the KNN in terms of accuracy and between a transponder and receiver, best practices sug- precision; however, the SVC was much slower (8,668.93 s gest the best measure of speed of sound is the mean at vs 97.98 s). a given time. When positioning the study’s metronome (R05), Developing an efficient and cost-effective method to our approach was highly accurate (<  10  cm); however, coordinating that can be implemented on autonomous it suffered when we compared it with a known mov - unsynchronized receivers is a major challenge to 3-D ing target. Overall, the X and Y error for the tag drag positioning with JSATS technology. This approach pro - experiment was 9.2 and 15.5  m and the Z elevation duced a useful 3-D data set, which allowed for the rec- was overestimated and above the surface of the water. reation of trajectories within the Cowlitz Falls forebay. While the RMSE for a known moving target was poor, It is the study team’s desire that this advancement pro- we believe this may be due to the method of data col- vide the foundation for future research into inferential lection. A tag drag experiment using uncorrected code- statistics that analyze movement in continuous time only positions will have an expected user range error and space. Recent advances have developed methods to (URE) of 7.8 m 95% of the time. User accuracy depends extract behavioral mechanisms from continuous space– on a combination of satellite geometry at time of data time data sets [11]. Point clouds and/or fish aggregation collection, URE, and other local factors (i.e., signal areas can be described with Kernel Density Estimates blockage, atmospheric conditions, and receiver qual- (KDE) [22]. A KDE is a non-parametric, robust density ity) [25]. While the RMSE was high, the errors are well estimate that can be used to describe areas of aggregation within the ordinary, expected performance of the GPS and potential travel. Certain operations, environmental receiver, especially one operating on a body of water conditions, or time of day may lead to fish preferring one without a ground plane. In future efforts the position location in the forebay over another. These differences of the vessel performing the tag drag should be tracked in areas of use can be assessed with a Kernel Discrimi- with a robotic total station or phase-observing, differ - nant Analysis (KDA) [1]. With a robust data cleaning and entially corrected GNSS receiver. coordinating method, data sets worthy of further analysis Some fish tags suffered from CPDI multipath [13] will surely follow. error (Fig.  12) when they were adjacent to metal infra- Acknowledgements structure. When the fish are in the middle of the fore - Not applicable. bay this error does not exist. This suggests that the Authors’ contributions receivers were placed too close to a highly reflective The lead author, KPN wrote the clock synchronization, multipath removal, and surface. Either the receivers need to be moved further data management routines in Python and wrote much of the manuscript. out into the forebay to increase the time delay between THM developed positions using least squares in Mathematica, provided the mathematical basis for positioning and clock synchronization, and primary transmission and multipath arrival, or some co-authored the manuscript. All authors have read and approved the final type of baffling should be used. Bubble curtains have manuscript. been used for some time to reduce underwater noise of percussive piling [28]. Future efforts could experiment Nebiolo and M eyer Anim Biotelemetry (2021) 9:20 Page 15 of 15 Funding 11. Gurarie E, Andrews RD, Laidre KL. A novel method for identifying behav- The authors analyzed data under contract to a private business, AnchorQEA. ioural changes in animal movement data. Ecol Lett. 2009;12:395–408. The authors did not receive funding to produce this manuscript. 12. Innovasea. Innovative Tracking Technology. (2020) Retrieved 7 Nov 2020 from: https:// www. innov asea. com/ fish- track ing/ Availability of data and materials 13. Kessel ST, Hussey NE, Webber DM, Gruber SH, Young JM, Smale MJ, Fisk The data sets used and/or analyzed during the current study are available AT. Close proximity detection interference with acoustic telemetry: the from the corresponding author on reasonable request. importance of considering tag power output in low ambient noise environments. Anim Biotelemetry. 2015;3:1–14. 14. Li X, Deng ZD, Sun Y, Martinez JJ, Fu T, McMichael GA, Carlson TJ. A 3D Declarations approximate maximum likelihood solver for localization of fish implanted with acoustic transmitters. Sci Rep. 2014. https:// doi. org/ 10. 1038/ srep0 Ethics approval and consent to participate Not applicable. 15. Li X, Deng Z, Martinez JJ, Fu T, Titzler PS, Hughes JS, Weiland MA. Three- Dimensional Tracking of Juvenile Salmon at Mid-Reach Location between Consent for publication Dams. Fish Res. 2015. https:// doi. org/ 10. 1016/j. fishr es. 2015. 01. 018. Not applicable. 16. Nebiolo K. jsats3d. (2021) Retrieved 28 Mar 2021 from: https:// github. com/ knebi olo/ jsats 3d Competing interests 17. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, The authors have no competing interests. Duchesnay E. Scikit-learn: Machine Learning in Python. J Mach Learn Res. 2011;12:2825–30. Author details 18. Perry RW, Farley J, Darland TJ, Hansen GS, Feil DH, Rondorf DW, LeClaire 1 2 Kleinschmidt Associates, 35 Pratt St. Suite 201, Essex, CT 06246, USA. Depar t- R(2003) Feasibility of Using 3D Acoustic Telemetry to Assess the Response ment of Natural Resources and the Environment, University of Connecticut, of Resident Salmonids to Strobe Lightsin Lake Roosevelt, Washington. U-4087, 1376 Storrs Rd, Storrs, CT 06269, USA. Bonneville Power Administration. Portland, OR: U.S. Department of Energy Received: 27 October 2020 Accepted: 24 May 2021 19. Rauchenstein LT, Vishnu A, Li X, Deng ZD. Improving underwater localiza- tion accuracy with machine learning. Rev Sci Instrum. 2018;89:074902. 20. Roberts DT, Udyawer V, Franklin C, Dwyer RG, Campbell HA. 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Published: Jun 2, 2021

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