Power and robustness of a track-loss detector based on Kolmogorov-Smirnov tests

It is important in the practical application of data association algorithms to target tracking in cluttered environments to be able to effectively and efficiently detect track-loss in the absence of truth data. We recently developed a track-loss detector using Kolmogorov-Smirnov tests to determine the regime of filter operation in the absence of truth data for data association algorithms where estimates of the innovations covariance are available. Among advantages to this method are that confidence intervals are associated with the regime tests, and that the number of measurement samples required can be determined adaptively. In this paper, results are developed for the exact and asymptotic power of the test, as well as a measure of the robustness of the method to errors in parameters such as clutter density. Simulation results are provided

[1]  AN Kolmogorov-Smirnov,et al.  Sulla determinazione empírica di uma legge di distribuzione , 1933 .

[2]  L. Guttman.  An Inequality for Kurtosis , 1948 .

[3]  W. Feller.  On the Kolmogorov–Smirnov Limit Theorems for Empirical Distributions , 1948 .

[4]  F. Massey,et al.  A Note on the Power of a Non-Parametric Test , 1950 .

[5]  M. Donsker.  Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems , 1952 .

[6]  Z. Birnbaum.  Numerical Tabulation of the Distribution of Kolmogorov's Statistic for Finite Sample Size , 1952 .

[7]  D. Quade.  On the Asymptotic Power of the One-Sample Kolmogorov-Smirnov Tests , 1965 .

[8]  G. P. Steck.  Rectangle Probabilities for Uniform Order statistics and the Probability That the Empirical Distribution Function Lies Between Two Distribution Functions , 1971 .

[9]  W. Conover.  A Kolmogorov Goodness-of-Fit Test for Discontinuous Distributions , 1972 .

[10]  J. Durbin.  Distribution theory for tests based on the sample distribution function , 1973 .

[11]  Leon Jay Gleser,et al.  Exact Power of Goodness-of-Fit Tests of Kolmogorov Type for Discontinuous Distributions , 1985 .

[12]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[13]  Y. Bar-Shalom.  Tracking and data association , 1988 .

[14]  D. Salmond.  Mixture reduction algorithms for target tracking , 1989 .

[15]  David J. Salmond.  Mixture reduction algorithms for target tracking in clutter , 1990 .

[16]  Y. Bar-Shalom,et al.  Stability evaluation and track life of the PDAF for tracking in clutter , 1990, 29th IEEE Conference on Decision and Control.

[17]  K. Kastella,et al.  Event-averaged maximum likelihood estimation and mean-field theory in multitarget tracking , 1995, IEEE Trans. Autom. Control..

[18]  Lucy Y. Pao,et al.  Determining track loss without truth information for distributed target tracking applications , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[19]  Lucy Y. Pao,et al.  A comparison of several different approaches for target tracking with clutter , 2003, Proceedings of the 2003 American Control Conference, 2003..

[20]  Lucy Y. Pao,et al.  Detecting track-loss for the Probabilistic Data Association Filter in the absence of truth data , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[21]  L.Y. Pao,et al.  Using Kolmogorov-Smirnov Tests to Detect Track-Loss in the Absence of Truth Data , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.