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Proceedings Paper

Multitarget nonlinear filtering based on spectral compression and probability hypothesis density
Author(s): Adel I. El-Fallah; Tim Zajic; Ronald P. S. Mahler; Barbara A. Lajza-Rooks; Raman K. Mehra
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Paper Abstract

The theoretically optimal approach to multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. However, this optimal filter is so computationally challenging that it must usually be approximated. We report on a novel approximation of a multi-target non-linear filtering based on the spectral compression (SPECC) non-linear filter implementation of Stein-Winter probability hypothesis densities (PHDs). In its current implementation, SPECC is a two-dimensional, four-state, FFT-based filter that is Bayes-Closed. It replaces a log-posterior or log-likelihood with an approximate log-posterior or log-likelihood, that is a truncation of a Fourier basis. This approximation is based on the minimization of the least-squares error of the log-densities. The ultimate operational utility of our approach depends on its computational efficiency and robustness when compared with similar approaches. Another novel aspect of the proposed algorithm is the propagation of a first-order statistical moment of the multitarget system. This moment, the probability hypothesis density (PHD) is a density function on single-target state space which is uniquely defined by the following property: its integral in any region of state space is the expected number of targets in that region. It is the expected value of the point process of the random track set (i.e., the density function whose integral in any region of state space is the actual number of targets in the region). The adequacy, and the accuracy of the algorithm when applied to simulated and real scenarios involving ground targets are demonstrated.

Paper Details

Date Published: 16 August 2001
PDF: 10 pages
Proc. SPIE 4380, Signal Processing, Sensor Fusion, and Target Recognition X, (16 August 2001); doi: 10.1117/12.436949
Show Author Affiliations
Adel I. El-Fallah, Scientific Systems Co., Inc. (United States)
Tim Zajic, Lockheed Martin Tactical Defence Systems (United States)
Ronald P. S. Mahler, Lockheed Martin Tactical Defence Systems (United States)
Barbara A. Lajza-Rooks, Air Force Research Lab. (United States)
Raman K. Mehra, Scientific Systems Co., Inc. (United States)


Published in SPIE Proceedings Vol. 4380:
Signal Processing, Sensor Fusion, and Target Recognition X
Ivan Kadar, Editor(s)

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