# On Some Singularities in Parameter Estimation Problems

On Some Singularities in Parameter Estimation Problems Assume that there are two identical remote objects and we want to estimate the distance to the closest of them and the distance between objects. For that purpose, some device (like a radar) is used, and the observed signal is the sum of signals reflected by each object. Moreover, the observed signal is corrupted by white Gaussian noise. Singularity (i.e., very poor estimation accuracy) occurs in this problem if objects are very close to each other. Our aim is to demonstrate this inevitable singularity by the example of the maximum likelihood estimate and also to show that it takes place for any other estimate. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# On Some Singularities in Parameter Estimation Problems

, Volume 39 (4) – Oct 4, 2004
21 pages

/lp/springer_journal/on-some-singularities-in-parameter-estimation-problems-i9RlDQ9xa0
Publisher
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/B:PRIT.0000011274.44405.9b
Publisher site
See Article on Publisher Site

### Abstract

Assume that there are two identical remote objects and we want to estimate the distance to the closest of them and the distance between objects. For that purpose, some device (like a radar) is used, and the observed signal is the sum of signals reflected by each object. Moreover, the observed signal is corrupted by white Gaussian noise. Singularity (i.e., very poor estimation accuracy) occurs in this problem if objects are very close to each other. Our aim is to demonstrate this inevitable singularity by the example of the maximum likelihood estimate and also to show that it takes place for any other estimate.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 4, 2004

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