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Hindawi Publishing Corporation International Journal of Navigation and Observation Volume 2012, Article ID 753206, 12 pages doi:10.1155/2012/753206 Research Article Particle-Filter-Based WiFi-Aided Reduced Inertial Sensors Navigation System for Indoor and GPS-Denied Environments 1 1 2 M. M. Atia, M. J. Korenberg, and A. Noureldin Queen’s University Kingston, ON, Canada T2L 2K7 Royal Military College of Canada Kingston, ON, Canada K7K 7B4 Correspondence should be addressed to M. M. Atia, mohamed.m.atia@queensu.ca Received 1 September 2011; Revised 14 February 2012; Accepted 5 March 2012 Academic Editor: Yuei-An Liou Copyright © 2012 M. M. Atia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Indoor navigation is challenging due to unavailability of satellites-based signals indoors. Inertial Navigation Systems (INSs) may be used as standalone navigation indoors. However, INS suﬀers from growing drifts without bounds due to error accumulation. On the other side, the IEEE 802.11 WLAN (WiFi) is widely adopted which prompted many researchers to use it to provide positioning indoors using ﬁngerprinting. However, due to WiFi signal noise and multipath errors indoors, WiFi positioning is scattered and noisy. To beneﬁt from both WiFi and inertial systems, in this paper, two major techniques are applied. First, a low-cost Reduced Inertial Sensors System (RISS) is integrated with WiFi to smooth the noisy scattered WiFi positioning and reduce RISS drifts. Second, a fast feature reduction technique is applied to ﬁngerprinting to identify the WiFi access points with highest discrepancy power to be used for positioning. The RISS/WiFi system is implemented using a fast version of Mixture Particle Filter for state estimation as nonlinear non-Gaussian ﬁltering algorithm. Real experiments showed that drifts of RISS are greatly reduced and the scattered noisy WiFi positioning is signiﬁcantly smoothed. The proposed system provides smooth indoor positioning of 1 m accuracy 70% of the time outperforming each system individually. 1. Introduction vehicles using only single vertically aligned gyroscope, and the vehicle speed sensor (odometer) (see Figure 1). This Inertial Navigation Systems (INSs) [1, 2] are self-contained conﬁguration is suitable for wheeled vehicles such as robots inertial-sensors-based navigation systems that can work in which the motion is mainly in 2D assuming ﬂat ground. independently without any kind of help from an external Although RISS utilizes the vehicle odometer which is navigation source. INS solutions utilize inertial sensors to more accurate than MEMS-based inertial sensors, the drifts provide navigation information continuously with time at in the gyroscope still cause the overall system accuracy to deteriorate over short periods of time. For the above high rates. Although INS provides good short-term accuracy without any external help, small sensors errors accumulate reasons, INS and RISS systems are usually integrated with due to mathematical integration resulting in large drifting other navigation systems that have complementary errors characteristics such as Global Positioning Systems [1, 5]. that grows without bounds. Additionally, if low-cost MEMS- grade [3] inertial sensors are considered, errors exhibit However, for indoor areas, GPS and other satellite-based complex stochastic characteristics which are hard to model positioning systems do not work due to signal blockage. using linear estimator such as Kalman Filter because of Thus, other wireless infrastructures that provide strong the high inherent nonlinearity and randomness. In [4], a coverage indoors are to be utilized. Reduced Inertial Sensors System (RISS) suitable for wheeled The IEEE 802.11 WLAN (WiFi) [6] is a freely available vehicles navigation was introduced. The aim was to reduce wireless infrastructure that provides strong coverage indoors. sensors cost and to simplify navigation equations reducing According to WiFi-Alliance [7], Wi-Fi is used by over 700 million people and there are about 800 million new sources of errors. For this reasons, this paper utilizes an RISS system that provides navigation information for wheeled Wi-Fi devices every year. This freely available wireless 2 International Journal of Navigation and Observation not require the wireless access points to be located in known locations as long as they are ﬁxed. Furthermore, W an interesting advantage of ﬁngerprint-based positioning methods is that they do not require time synchronization. According to many research results [12–14], although the ﬁngerprint positioning method requires time-consuming oﬄine wireless survey, it is the most accurate wireless positioning method in indoors. The explanation is that radiomap accurately models the hard signal strength patterns in indoor areas. Thus, in this paper, an optimized WiFi ﬁngerprint-based positioning system is utilized. The WiFi ﬁngerprint-based positioning system introduced here utilizes a novel approach based on Fast Orthogonal Search (FOS) Odometer: V [15] to automatically and quickly select the best arrangement of WiFi access points to obtain the best positioning accuracy. Although this approach achieves meter-level accuracy, the Figure 1: 2D RISS platform. solution is not smooth enough and contains many outliers due to signal strength noises (see Figures 7, 8,and 9)which prompted many researchers to explore the possibility of integration between diﬀerent navigation systems [16, 17]. infrastructure prompted many researchers to develop WiFi- based positioning systems for indoor environments [8, 9]. The possibility of integrating WiFi-based positioning Mainly, three approaches for WiFi-based positioning exist systems with INS has been recently explored by researchers [10, 11]. Time-based, Angle-based, and Signal-Strength- [16, 17]. Kalman Filter [3, 16] is usually the preferred based approaches. Time of arrival (ToA) and Time Diﬀerence integration technique. However, KF has limitations such as system dynamic models linearity and the assumption of Arrival (TDoA) are two common Time-based wireless positioning approaches [10]. In Time-based wireless posi- of Gaussian states distribution which is not suitable for tioning systems, distance estimation between the user device low-cost MEMS-based inertial sensors and the noisy WiFi- based positioning indoors. The limitations of KF were very and at least three reference locations is suﬃcient to provide 3D positioning information using Trilateration technique. clear in [16] in which WiFi positioning was integrated In Angle-based wireless positioning systems, Triangulation with INS providing an accuracy of 5 m which doesn’t [10, 11] is used to provide 3D positioning information. fulﬁll the accuracy requirements of indoor location-based One of the drawbacks of both Time-based and Angle- services (LBSs). In Atia et al. [18], the authors proposed based methods is the need for additional hardware to be set a particle-ﬁltering-based 2D WiFi/INS solution in which up on top of the existing WiFi network. Moreover, a special WiFi positioning is integrated with vertical gyroscope and time synchronization system is required to correct for clock two accelerometers. In this paper, the authors introduce a new conﬁguration that integrates RISS and optimized WiFi drifts like the case in GPS [1, 5]. For the Angle-based posi- tioning methods, high-cost directional antennas arrays are system. The basic advance in this work is as follows. (1) A required. Another drawback of both Time-based and Angle- new RISS system is used. (2) The WiFi ﬁngerprint technique is optimized by a novel feature reduction algorithm to based approaches is the need for a direct line of sight (LOS) between transmitters and receivers. Thus, these two methods identify the best few WiFi Access Points for positioning. (3) are not suitable for indoor environments due to lack of LOS The area of experiments is bigger and more complex and in most scenarios because of dense multipath resulting from challenging. wireless signal reﬂection and refraction on diﬀerent surfaces indoors. Thus, in this paper, an optimized Signal Strength- 2. RISS Navigation System based WiFi Fingerprint positioning algorithm is developed. Fingerprint-based wireless positioning systems [10–13] In RISS systems for wheeled vehicles such as robots, the depend on the fact that signal strength attenuates with motion is mainly in 2D assuming ﬂat ground. The gyroscope signal propagation. Signal propagation in free space can be is attached with the z (vertical) axis and measures the easily modelled using logarithmic relationships that relate rotation rate around z axis as shown in Figure 1.Motion signal strength received by a receiver to distance between equations are implemented in a local navigation frame which transmitter and receiver. However, inside buildings and in is usually taken as east, north, and up (vertical) rectangular indoor areas, signal propagation suﬀers from multipath, and, frame. In 2D, we are concerned only with azimuth (heading), hence, simple mathematical formulas cannot be used to north, and east velocity and position components. The model signal strength/distance relationship. As a solution azimuth angle A of the vehicle is calculated using the to this problem, exhaustive signal strength survey is used following equation: to accurately model signal strength measurements from multiple wireless access points to a speciﬁc location or V tan φ position (not distance). This approach has the advantage A = w − w sin φ − dt, (1) R + h of accurate modeling of multipath. Additionally, it does N International Journal of Navigation and Observation 3 Odometer od reading Gyroscope V cosA V sinA od od readings V V n e ∫∫ Heading North position East position Figure 2: RISS system block diagram. Figure 3: Experiments Trajectory in Computer Engineering Department Queen’s University. Kingston, ON, Canada. where w is the gyroscope reading, w the earth rotation rate (15 /hr), V is the velocity in east direction, φ is the 3D RISS trajectory solution latitude, R is the normal radius of curvature of earth, and 0 h is the altitude. Once the heading angle A of the platform −5 is calculated, it can be used along with the vehicle odometer −10 V to calculate east and north velocities as follows: od −15 V = V sin A, e od (2) −20 V = V cos A. n od −25 −20 −10 0 10 20 30 40 Position (latitude φ and longitude λ)are givenby East position (m) φ = dt, 3D RISS R + h Reference (3) Figure 4: RISS solution showing eﬀects of gyroscope drifts and λ = dt, (R + h) cos φ odometer errors. where R is the meridian radius of curvature of the earth at current position. 3. WiFi Fingerprint Positioning System Latitude φ and longitude λ canbethenconverted to meters using the following equations: The basic unit in a WiFi network is the Wireless Access Point (AP). Each AP periodically sends beacon frames [6]. The P = φ − φ (R + h), (4) North 0 M beacon messages contain MAC Address which is a unique identiﬁcation set by the manufacturer. When the beacon P = (λ − λ )(R + h) cos φ. (5) East 0 N frame is received by a WiFi client’s network card, the interface The RISS conﬁguration is shown in the following block card reports the received signal strength indicator (RSSI) diagram in Figure 2. in dBm. Figure 5 shows a histogram of 200 RSSI values Due to lack of a reference solution to compare results and measured in the same location with LOS conditions. The calculate errors, an experiment was done on a predeﬁned measurements were taken from 10 m distance from Netgear trajectory with known waypoints 5 to 7 meters apart. To AP. calculate the root mean square position error (RMSE), In WiFi Fingerprint-based positioning method [12–14], the solution trajectory is compared with the reference the signal strength from multiple APs is recorded from many trajectory at the way-points. Figure 3 shows the testing reference known locations. These radio records are saved in trajectory inside the sixth ﬂoor of Department of Electrical an oﬄine phase to build a radiomap of the environment. & Computer Engineering in Queen’s University, Kingston, In online phase, the signal strength measured by the WiFi Ontario, Canada. Figure 4 shows the results of RISS system client from multiple APs is matched with the signal strength on the testing trajectory shown in Figure 3. The eﬀect of records of the radiomap to estimate the client position. the gyroscope drifts can be seen clearly in Figure 4 from Building the radiomap can be automated like the work done the heading errors which causes the trajectory to deviate in [19]. Many pattern matching and classiﬁcation algorithms from the reference. Also the eﬀect of odometer error is clear can be used for positioning [10, 11]. Since the main focus from the graph where we can see stretch in the most right in this paper is to show the beneﬁts of integration with part of the trajectory. Odometer error is also known from inertial sensors to smooth the positioning output, a k- calculations since the reference distance travelled is 110.5 m nearest neighbour (K-NN) method with weighted averaging while the odometer reading shows a distance travelled of modiﬁcation is used as an eﬃcient ﬁngerprinting algorithm. 118.8 m. K-NN algorithm selects the k points in the radiomap that North position (m) 4 International Journal of Navigation and Observation −85 −80 −75 RSS (dBm) Figure 5: WiFi measurements histogram in a single location. are nearest to the current client RSSI measurements. Instead of averaging these points, a weighted average is performed by giving the highest weight to the nearest reference point. Thus, given current WiFi RSSI , the current position P is c c calculated by Figure 6: Radiomap collection process. P = w1P1+ w2P2+··· + w P , c k k exp −[RSSI − RSSI ] c i (6) and the odometer errors. The eﬀects of these two sources w = , of errors are clear in Figure 4. The challenges with the exp − RSSI − RSSI c j WiFi-positioning system are mainly due to signal strength noise and the too large number of MAC addresses in the where RSSI is the WiFi readings recorded with point P in i i constructed radiomap. Based on these challenges, the overall the radio-map database. ultimate objective of this work is to provide a low-cost indoor In this work, a radiomap was collected using a laptop on a RISS/WiFi integrated navigation system that can provide mobile robot (see Figure 6) in the experiments area shown in meter-level accuracy with smooth output in indoor and GPS- Figure 3. A total of 132 unique MAC addresses were recorded denied environments such as large buildings, hospital, and in this area which is considered as a large number that may airports. To achieve this objective, the following problems are negatively aﬀect the accuracy and speed of the presented tackled: WiFi-positioning system. Online WiFi measurements were recorded while following the testing prespeciﬁed trajectory (1) removing the drifts due to gyroscope and odometer using the mobile robot. K-NN-weighted average algorithm errors in RISS system; was applied and the solution obtained is shown in Figures 7, (2) ﬁltering out the outliers and scattered noisy position- 8,and 9. East and North positions are plotted separately to ing of the WiFi system; show the outliers points and the noisy scattered nature of the WiFi-positioning system. Although the WiFi-positioning is (3) reducing the feature dimensionality of the WiFi noisy and scattered, the accuracy is consistent without drifts radiomap from 132 columns to only 4 columns by over the time without bounds like the case in inertial solution selecting the 4 most signiﬁcant WiFi access points’ (see Figure 4). Thus, there is a clear complementary error combinations to improve the accuracy and reduce behaviour between WiFi-positioning and inertial navigation processing time to meet real-time embedded systems which prompts researchers to integrate both systems to requirements. obtain more accurate and smooth results. 5. Methodology 4. Challenges and Research Objectives 5.1. Bayesian Filtering. The moving object state x is deﬁned After having a detailed view on the performance of the as a vector that contains the vehicle 2D position, velocity, MEMS-based RISS system and the WiFi-based positioning and heading. Instead of dealing with the state as crisp values, system separately, a summary of the challenges followed by Bayesian ﬁltering [2] considers the state as a probability. the research objectives of this work is given. The challenges Let p(x | Z ) be the probability density function (PDF) k k in the RISS system side are mainly the gyroscope drifts of a moving object state conditioned on measurements Number of occurances International Journal of Navigation and Observation 5 East position in meters KNN WiFi trajectory solution −5 −10 −15 −10 −20 0 500 1000 1500 −10 0 10 20 30 Time (s) East position (m) Reference KNN WiFi KNN WiFi Reference Figure 7: WiFi east position solution. Figure 9: WiFi trajectory solution. North position in meters Figure 10 is a simpliﬁed explanation for the sequence of −5 prediction and update to estimate p(x | Z ). k k −10 5.2. Particle Filtering (PF). Bayesian Filtering problems −15 formulation yields integral equations that are analytically −20 intractable in case of nonlinear non-Gaussian states [22]. 0 500 1000 1500 Thus, PF was proposed as a Monte-Carlo-based solution for Time (s) the Bayesian Filtering problem [20–22]. It is an approximate solution to Bayesian Filtering that represents PDFs by Reference suﬃcient number of samples (particles). At each time KNN WiFi step k, the PDF p(x | Z ) is approximated by a set of N k k Figure 8: WiFi North position solution. (1) (N) random samples or particles S ={s ,... , s }.Here k k k (i) the ith sample has value x as the value of the state (i) Z (sensors measurements and aiding source observations). and π as the value of weight. At k = 0, the sample set k k (i) (i) Bayesian ﬁltering considers the aiding sources assumes S ={(x , π ) | i = 1,... , N} is initialized with equal 0 0 0 that the sates are 1st order Markov process [20, 21]. The weights based on any knowledge about the object’s initial estimated p(x | Z ) represents all the knowledge about state. An iteration of PF has three important steps: prediction k k the moving object state x which is obtained from two phase, update phase, and resampling step. probabilistic models; those are the state transition model In prediction phase, starting from the set of samples (i) (i) (i) p(x | x , u ) (system model) and the observation k k−1 k−1 S ={(x , π ) | i = 1,... , N} (where π = k−1 k−1 k−1 k−1 (i) likelihood p(z | x ) (observation or measurement model). k k 1/N) the transition model is applied to each sample s = k−1 (i) (i) In p(x | x , u ), the u is the input control signal that (i) k k−1 k−1 k−1 (x ,1/N) and a new sample s = (x ,1/N)isdrawn k−1 k k stimulates the transition from state x to state x . k−1 k (i) from p(x | x , u ). Thus, a new sample set S is k k−1 k−1 To estimate the navigation states, the new density p(x | obtained that approximates the predictive probability density Z ) is computed recursively at each time step in two p(x | Z ). k k−1 phases [20, 21]: prediction phase and update phase. In the In the update phase, the observations Z are taken into prediction phase, the transition is performed according to account and each of the samples in S is weighted according state transition model (system model). Knowing the PDF to its Euclidean distance from the observations according p(x | Z )attimestep k− 1, the state transition model is k−1 k−1 (Hx −Z ) − k k to the formula: w = Ae ,where w is the new i i used to predict the current state PDF p(x | Z ) as follows: k k−1 sample weight, H is a design matrix that maps the state x to observables, A is a weighting factor, and Z is the k k p(x | Z ) = p(x | x , u )p(x | Z )dx . k k−1 k k−1 k−1 k−1 k−1 k−1 observations. (7) Then all weights are normalized. The weighted sample set S approximates the posterior PDF p(x | Z ). In resampling k k k In the update phase, the observation likelihood is used to (i) (i) step, the sample set S ={(x , π ) | i = 1,... , N} (where obtain the posterior PDF p(x | Z ) using Bayes rule: k k k k k (i) π = 1/N) is obtained by randomly selecting from the (i) (i) p(z | x )p(x | Z ) k k k k−1 weighted set S ={(x , π ) | i = 1,... , N} such that p(x | Z ) = , k k k k p(z | Z ) k k−1 each sample is selected number of times proportional to its (8) weight. Thus, the obtained S still approximates the required p(z | Z ) = p(z | x )p(x | Z )dx . k k−1 k k k k−1 k p(x | Z ). k k North position (m) East position (m) North position (m) 6 International Journal of Navigation and Observation Update Prediction p(x | Z ) p(z | x )p(x | Z ) k−1 k−1 p(x | Z ) k k k k−1 k k−1 p(x | Z ) = k k p(z | Z ) k k−1 Prior state PDF Predicted state PDF Posterior state PDF p(z | x ) k k Observation likelihood Figure 10: Basic Bayesian ﬁltering concept. 5.4. Fast Mixture Particle Filtering. The mixture PF is further optimized for real-time operation using the fast median- Weighting factor cut clustering algorithm developed by Atia et al. (2010) [25] applied to INS/GPS integration. In this paper, we extended the usage of the optimization to WiFi/RISS case since the weighting of those samples includes a large number of complex mathematical operations. The proposed optimization is to use a fast clustering algorithm (which is a modiﬁed fast version of median cut clustering [25]) Motion Stop Motion to reduce the number of required calculations. Only the representative samples in the predicted sample set are used. RISS This optimization step reduces the computation complexity WiFi needed in Mixture PF by 80%. In the work done in Figure 11: Adaptive PF weighting scheme. Atia et al. [25], Mixture PF iteration takes 0.0978 secs on Arm-Cortex A8 600 MHz CPU on WinCE Operating System. 5.3. Mixture Particle Filtering. If sensors worked without aiding source (measurement model), errors may be too large (1) (N) 5.5. Adaptive Mixture Particle Filter. In the weighting steps such that the sample set S ={s ,... , s } that was k k k (Hx −Z ) − k k predicted by the system model will be very apart from the of Mixture PF, the weighting formulas w = Ae (Hx −Z ) − k k observations. This means that the PDFs p(x | x , u ) k k−1 k−1 and w = Be depend on Euclidean distance and p(z | x ) will not overlap and they are very apart k k between observations z (WiFi positions in our case) and from each other. Then, all the weights (which depend on Hx (the predicted positions calculated by RISS in our the Euclidean distance) will be too small or tend to zero. case) and the weighting factors A and B. In this work, Thus, the new PDF p(x | Z )willnot be accurate and k k an adaptive mechanism is utilized by changing A and B very large number of particles will be required to cover dynamically at run-time according to conditions of motion this gap between the predicted states and the aiding source as follows: in the early beginning of the navigation mission observation. To overcome this problem mixture PF was and shortly in motion after each stop during the trajectory, introduced [23]. In mixture PF, the idea is to add to the the RISS solution is more accurate due to the good short- (i) (i) sample set S ={(x , π ) | i = 1,... , N} some samples k k k term accuracy of RISS. Therefore, the weighting factor from the aiding observations (WiFi observations in this A is set larger than B giving more conﬁdence to RISS case). This assures better coverage of the state space with output (the prediction). After a period of few seconds of a much smaller number of samples than traditional PF. In continuous motion, more conﬁdence is gradually given to [24], the importance weights of these new samples were the WiFi solution by increasing B and decreasing A gradually calculated according to the probability that they came from which, in turn, prevents the large RISS drifts. This adaptive the previous sample set and the latest system model output. mechanism maximizes the beneﬁts from the good short- The new samples weights are calculated using the formula term RISS accuracy and the general consistent long-term (Hx −Z ) − k k w = Be ,where x is the mean of the predicted accuracy of WiFi-positioning solution. This dynamic change i k samples. The weights of the new sample set are normalized of weighting factors of RISS output and WiFi output is and the resampling step is implemented normally. illustrated in Figure 11. International Journal of Navigation and Observation 7 5.6. Formulating WiFi/RISS Navigation System into Particle minimum total mean square error over all data columns N−1 M ( (1/M) e [n]) [27]. Finding such columns set is Filtering Problem j=0 n=1 j equivalent to ﬁnding the most informative “true” APs in the 5.6.1. Initialization. For WiFi/RISS integration, the algo- radiomap. rithm is initialized with samples from a Gaussian density with mean equivalent to the WiFi-positioning solution in 5.7.1. Fast Orthogonal Search (FOS). In Orthogonal Search static state because WiFi in this case is accurate [10, 11, 14]. techniques [27], Gram-Schmidt procedure is used to replace This approximates the prior PDF p(x | Z ). k−1 k−1 the functions P [n]in(9) by a set of orthogonal basis functions W [n] where the model for a speciﬁc j in (9)is 5.6.2. Prediction. Predictive PDF p(x | Z ) is approxi- k k−1 represented by the following corresponding model: mated by applying RISS mechanization equations in (1)– (5) on every sample in the prior PDF adding to the sensors C−1 measurements (u ) a randomly generated noise with k−1 Y [n] = g W [n] + e[n]. (10) m m m=0 certain probability distribution p(w ) (system noise). k−1 In orthogonal basis function space, the coeﬃcient g that 5.6.3. Update. The posterior PDF p(x | Z ) is generated k k minimizes the mean square error over the observations is approximated by weighting the samples in the predictive given by [27] PDF p(x | Z ) according to the Euclidean distance from k k−1 the WiFi K-Nearest ﬁngerprinting output given by (6)and [ ] [ ] Y n W n the standard deviation of measurement noise p(v ). In this k−1 g = . (11) W [n] implementation, Gaussian distribution for both system and m measurements noises is assumed. The overbar in (11) denotes the time average. The mean square error is given by 5.7. Automatic Selection of Best WiFi Access Points for Optimized Positioning. Incorporating too large a number ⎡ ⎤ C−1 C−1 of WiFi APs may deteriorate the positioning accuracy and ⎣ ⎦ (12) e = Y [n] − g W [n] = Y [n] − Q , m m m includes unnecessary computation time. The objective of the m=0 m=0 presented work is to identify the minimal set of APs in a Wi- Fi area with the highest positioning discrepancy power to be where used for power patterns matching in a ﬁngerprint-based Wi- Fi positioning system. Principle Component Analysis (PCA) 2 Y [n]W [n] may be used to reduce features dimensionality as done in (13) Q = . [26]. However, PCA has two major drawbacks. The ﬁrst is the W [n] expensive computation of covariance matrix, eigenvectors, and data transformation computation. Another drawback of The reduction in mean square error resulting from adding a term a P [n]is Q . The fast orthogonal search procedure PCA is that the new features are combinations of the original m m m features. Thus, the physical meaning of original features is [27] makes use of the fact that it is not necessary to lost. create the orthogonal functions W [n] explicitly. Only their correlations with P [n], the data Y [n], and with themselves The canonical form of a radiomap is a table of M rows by N columns. Each row contains a known location and are required. N signal strength measurements (power pattern) from N APs. Our strategy to reduce the feature dimensionality of the 5.7.2. FOS Feature Reduction of WiFi Radiomaps. In an M by radiomap without the costly Principle Component Analysis N radiomap, the aim is to reduce columns from N columns and without transformations is to treat every data column to C. Thus, we have N observations set and the model that as observations Y [n] that need to be modeled using a small needs to be optimized is given by (9). Signiﬁcance of a subset of the other N − 1 data columns. This can be achieved data column is evaluated by adding it to the model and the using the following model: total mean square error reduction over all data columns is calculated using (13). The column with the greatest RMSE C−1 reduction is selected. By eliminating orthogonalization, Y [n] = a P [n] + e [n], (9) j jm m j number of multiplications is greatly reduced. The complexity m=0 of the cross-correlations between all pairs of data columns where j = 0, 1...N − 1, n = 1, 2...M, P [n] is a set is C = O(MN ). The complexity of applying FOS mean m corr 2 2 of size C of basis functions that will be selected from the square error reduction N times is C = O(MN + N C). FOS other N − 1 columns set, and a are coeﬃcients calculated Due to the fact that C is much smaller than M, the overall jm by optimization techniques such that the error e [n] is complexity is dominant by O(MN ). By comparing this minimized. The problem then is reduced to a search in complexity with that of PCA, the term N resulting from the the space of N columns to ﬁnd C columns that if they eigenvectors computations is eliminated and the overhead of areusedasbasis functionsin(9) they would achieve the transformation is also eliminated. 8 International Journal of Navigation and Observation Laptop used for data logging and navigation algorithm running RISS sensors Robot control unit Figure 12: Experimental mobile robot used to perform experiments. Raw sensors measurements 0.3 0.25 0.2 0.15 0.1 0.05 −0.05 −0.1 −0.15 −0.2 6.5 6.55 6.6 6.65 6.7 6.75 6.8 6.85 6.9 6.95 7 × 10 Time (milliseconds) Gyro in rad/s Speed m/s Figure 13: RISS raw measurements. Sensors measurements after noise ﬁltering 0.35 0.3 0.25 0.2 0.15 0.1 0.05 −0.05 −0.1 6.5 6.6 6.7 6.8 6.9 7 ×10 Time (milliseconds) Gyro in rad/s Speed m/s Figure 14: RISS downsampled measurements. Sensors measurements Sensors measurements International Journal of Navigation and Observation 9 Table 1: SPECs of gyroscope of an ADIS16300 IMU. on a windows XP system to collect online measurements from WiFi access points and from RISS system (speed Range ±300 /sec and gyroscope readings). The collected measurements were Reference to z-axis accelerometer: 0.1 processed by the integrated navigation algorithm and all Misalignment Axis-to-frame (package): ±0.5 data (raw measurements and navigation output) were saved T = 25 C in ﬁles for further processing and analysis. All readings ◦ ◦ Initial bias ±3 /sec ± 1σ At 25 were time-synchronized by the laptop processor clock value. ◦ ◦ So, whenever the laptop records a WiFi signal strength or In-run bias stability 0.007 /sec At 25 speed and gyroscope readings, the software calls the function Random walk 1.9 / hr “GetTickCount ()”to time-tag the measured signals. In order to ﬁlter out the noisy measurements from RISS system, a downsampling step was performed. Instead of working on the raw RISS measurements in the high rate (which is 100 Hz), the measurements were down-sampled to 50 Hz. The eﬀect of this noise-ﬁltering technique is shown in Figures 13 and 14. 6.4. WiFi-Positioning System Results. Using the raw radiomap as it is without FOS-feature reduction on the predeﬁned trajectory shown in Figure 3, the K- NN positioning algorithm achieved an RMSE of 3.4 m. Figure 15: The 4 access points selected by FOS feature reduction to Additionally, Figures 7, 8,and 9 show how noisy and perform best positioning. scattered the positioning output of this WiFi conﬁguration is. To see the eﬀect of optimizing the radiomap using FOS-based feature reduction algorithm, the algorithm was applied to reduce the number of unique MAC addresses 6. Experiments and Results from 132 to only 4 best MAC addresses. In this experiment, 6.1. Experimental Setup. A mobile robot equipped with a the data column corresponding to each WiFi access point WiFi-enabled Dell Latitude laptop and the RISS system may be selected if it achieves a mean square error reduction sensors arrangement was used to perform the experiments. in the model of (9) greater than a threshold. This mean This mobile robot is shown in Figure 12 and can be operated square error reduction threshold was adjusted such that by a human operator. The gyroscope used in the experiment after processing the whole 132 data columns we get a total is part of an inertial measurement unit ADIS16300. The number of selected WiFi access points of only 4. Those 4 APs speciﬁcations of this gyroscope are shown in Table 1.The selected by the FOS-feature reduction approach are shown speed was measured using the robot wheels encoders’ circuit. in Figure 15. Figures 16, 17,and 18 show the WiFi-only FOS- optimized positioning solution output. The FOS-optimized solution achieved a better RMSE of 3.01 m with only 4 data 6.2. WiFi Radiomap Construction. The experiments were columns of the radiomap (4 MAC addresses). In addition to performed in an indoor area that does not have any GPS achieving slightly better RMSE with fewer WiFi access points access. This indoor area is in Sixth ﬂoor in Electrical & and less processing time, Figures 16 and 17 show that the Computer Engineering Department, Queen’s University, in scattered noisy solution and outliers are reduced in many Kingston, ON, Canada (see Figure 3). The area is 30 m × portions of the trajectory. 30 m with ﬂat ﬂoors. The radiomap used in this research was collected using the laptop on the mobile robot seen in Figure 12. This experiment’s area is shown in Figure 3.The 6.5. RISS/WiFi Integrated System. The adaptive fast mixture WiFi signal strength from all visible WiFi access points was PF was applied on the collected WiFi measurements and RISS measured in 67 reference locations distributed in this area. sensors measurements. The integrated RISS/WiFi system After collecting the signal strength patterns from those 67 output is shown in Figures 19, 20, 21,and 22. Figures 19 and points, we got a radiomap of 67 points by a 132 unique 20 show the North and East position output, respectively. MAC address. This radiomap will be referred to as “the raw Since we don’t have an accurate reference solution indoors radiomap.” (note that GPS is not available indoors), the reference solution is plotted at the way-points and these way-points 6.3. Online Trajectory Recording and Noise Filtering. An are connected which gives a general shape of the reference online trajectory data set was collected following the trajectory. The drifts of RISS system output and the WiFi predeﬁned trajectory shown in Figure 3.The robotwas noisy scattered output are clearly shown in Figures 19, operated to follow thistrajectorywithdiﬀerent speeds. At 20,and 22. Figures 19 and 20 show that the integration each way- point, the reference location was recorded for between RISS and WiFi systems not only improves the accuracy and error calculations purposes. Software written overall accuracy and reduces RISS drifts, but also smooths in C language was developed and run on the Dell laptop and ﬁlters out the noisy scattered output resulting from 10 International Journal of Navigation and Observation Table 2: RMSE and maximum position errors of all systems combinations. WiFi K-NN positioning WiFi/RISS With FOS-reduced map RISS Using 67 × 4 radio map Using full 67 × 132 radio Adaptive fast mixture PF optimized and reduced by map FOS RMSE 4.4743 m 3.4 m 3.01 m 1.6 m MAX POS ERROR 10.1719 m 4.2422 m 3.2422 m 2.9681 m East position in meters WiFi trajectory solution −5 −10 −15 −5 −10 −20 0 500 1000 1500 −10 −5 0 5 1015202530 East position (m) Time (s) Reference WiFi WiFi Reference Figure 16: East position WiFi solution using FOS-selected 4 access Figure 18: WiFi trajectory solution using FOS-selected 4 access points. points. WiFi/RISS solution: north position North position in meters −5 −5 −10 −10 −15 −15 −20 −20 −25 0 500 1000 1500 0 500 1000 1500 Time (s) Time (seconds) Reference RISS WiFi-RISS WiFi WiFi Reference Figure 17: North position WiFi solution using FOS-selected 4 Figure 19: WiFi/RISS integrated system output: north position. access points. 7. Conclusions WiFi noisy signal strength eﬀect. Figure 21 shows the 2D position components conﬁdence intervals. Figure 22 show In this work, a WiFi-Assisted RISS Navigation system for the 2D solution from all systems conﬁgurations at the indoor positioning was introduced. Two main contributions way-points only. The total RMSE achieved by integrating were introduced. The ﬁrst contribution is the proposing of both RISS and WiFi is 1.6 meters. Comparing to RISS an adaptive fast mixture particle ﬁltering state estimation only accuracy (4.4743 m) and WiFi only accuracy (3.01 m), for integrating WiFi ﬁngerprint-based positioning with RISS the integration between WiFi and RISS systems reduced navigation system. The aim was to make use of the reliable the RMSE by approximately 40%. Figure 23 shows the short-term accuracy of RISS under the general accurate guid- cumulative error percentage which shows that the integrated ance of the WiFi positioning. Particle Filter was necessary WiFi/RISS navigation system achieves an accuracy of 1 meter in this work due to the low-cost MEMS-based RISS sensors for 70% of the time. Table 2 shows a summary of RMSE and and the noisy indoor WiFi signal strength which introduce maximum positioning error for each system conﬁguration a high nonlinearity and non-Gaussian nature to systems individually and for the integrated system. models. This nonlinearity and non-Gaussian nature of signal East position (m) North position (m) North position (meters) North position (m) International Journal of Navigation and Observation 11 WiFi/RISS solution: east position Trajectory referenced to trajectory initial point −5 −10 −15 −20 −10 −25 −10 −5 0 5 10 15 20 25 30 35 −20 East position (meters) 0 500 1000 1500 Reference Time (seconds) WiFi WiFi-RISS RISS RISS WiFi-RISS Reference Figure 22: WiFi/RISS integrated system output. WiFi Figure 20: WiFi/RISS integrated system output: east position. Cumulative error (%) Conﬁdence interval for east and north positions in meters (95% conﬁdence level) 0 200 400 600 800 1000 1200 1400 0 510 15 20 Time (seconds) Error (meters) East position WiFi/RISS mixture PF North position RISS WiFi Figure 21: Conﬁdence intervals for position components (95% conﬁdence level). Figure 23: Cumulative error percentages. [3] P. Aggarwal, Z. Syed, N. El-Sheimy, and A. Noureldin, MEMS- prevents the usage of Kalman Filter as a systems integration Based Integrated Navigation, Artech House, 2010. approach. Comparing the results of this work with those [4] U. Iqbal, A. F. Okou, and A. Noureldin, “An integrated reduced in [16] in which a Kalman Filter is used, it is obvious that inertial sensor system—RISS / GPS for land vehicle,” in particle ﬁltering outperforms Kalman Filter in this context. Proceedings of the Position, Location and Navigation Sympo- sium (IEEE/ION ’08), pp. 1014–1021, USA, May 2008. 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Noureldin, “Real-time implementation of mixture particle ﬁlter for 3D International Journal of Rotating Machinery International Journal of Journal of The Scientific Journal of Distributed Engineering World Journal Sensors Sensor Networks Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Volume 2014 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Submit your manuscripts at http://www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2010 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014
International Journal of Navigation and Observation – Hindawi Publishing Corporation
Published: Jun 25, 2012
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