Mean-Squared-Error Prediction for Bayesian Direction-of-Arrival Estimation

In this article, we study the mean-squared-error performance of Bayesian direction-of-arrival (DOA) estimation in which prior belief about the target location is incorporated into the estimation process. Our primary result is an extension of the method of interval errors (MIE) to the case of maximum a posteriori (MAP) direction-of-arrival estimation. We work in a general framework in which the prior information used in the MAP estimation may not match the actual target distribution. In particular, when the prior is incorrect, the MAP estimator degrades relative to the performance of a MAP estimator with the correct prior. Our methods are able to accurately predict the performance of a MAP estimator in this more general situation. We apply our methods to investigate the sensitivity of MAP direction-of-arrival estimation to mismatches between the chosen prior and the actual angular distribution of the target.

[1]  A. Gualtierotti H. L. Van Trees, Detection, Estimation, and Modulation Theory, , 1976 .

[2]  Wen Xu,et al.  A bound on mean-square estimation error with background parameter mismatch , 2004, IEEE Transactions on Information Theory.

[3]  Thomas Mathew,et al.  On the Matrix Convexity of the Moore-Penrose Inverse and Some Applications. , 1989 .

[4]  Christ D. Richmond,et al.  Aspects of threshold region mean squared error prediction: Method of interval errors, bounds, Taylor's theorem and extensions , 2012, 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[5]  S. T. Smith Statistical resolution limits and the complexified Crame/spl acute/r-Rao bound , 2005, IEEE Transactions on Signal Processing.

[6]  H. E. Daniels,et al.  Tail Probability Approximations , 1987 .

[7]  Frank McNolty A Contour-Integral Derivation of the Non-Central Chi-Square Distribution , 1962 .

[8]  H. Daniels Saddlepoint Approximations in Statistics , 1954 .

[9]  S. Rice,et al.  Saddle point approximation for the distribution of the sum of independent random variables , 1980, Advances in Applied Probability.

[10]  C.D. Richmond On the Threshold Region Mean-Squared Error Performance of Maximum-Likelihood Direction-of Arrival Estimation in the Presence of Signal Model Mismatch , 2006, Fourth IEEE Workshop on Sensor Array and Multichannel Processing, 2006..

[11]  A. Lee Swindlehurst,et al.  A Bayesian approach to direction finding with parametric array uncertainty , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  T. Singh,et al.  Efficient particle filtering for road-constrained target tracking , 2005, 2005 7th International Conference on Information Fusion.

[13]  Kristine L. Bell,et al.  A Bayesian approach to robust adaptive beamforming , 2000, IEEE Trans. Signal Process..

[14]  B. A. D. H. Brandwood A complex gradient operator and its applica-tion in adaptive array theory , 1983 .

[15]  Philip M. Woodward,et al.  Probability and Information Theory with Applications to Radar , 1954 .

[16]  Christ D. Richmond,et al.  Mean-squared error and threshold SNR prediction of maximum-likelihood signal parameter estimation with estimated colored noise covariances , 2006, IEEE Transactions on Information Theory.

[17]  S.T. Smith Statistical Resolution Limits and the Complexified , 2005 .

[18]  Peter M. Schultheiss,et al.  Array shape calibration using sources in unknown locations-Part I: Far-field sources , 1987, IEEE Trans. Acoust. Speech Signal Process..

[19]  J. R. Guerci,et al.  Cognitive radar: A knowledge-aided fully adaptive approach , 2010, 2010 IEEE Radar Conference.

[20]  Huang Jianguo,et al.  Bayesian high resolution DOA estimator based on importance sampling , 2005, Europe Oceans 2005.