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Proceedings Paper

Batch maximum likelihood (ML) and maximum a posteriori (MAP) estimation with process noise for tracking applications
Author(s): Aubrey B. Poore; Benjamin J. Slocumb; Brian J. Suchomel; Fritz H. Obermeyer; Shawn M. Herman; Sabino M. Gadaleta
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Paper Abstract

Batch maximum likelihood (ML) and maximum a posteriori (MAP) estimation with process noise is now more than thirty-five years old, and its use in multiple target tracking has long been considered to be too computationally intensive for real-time applications. While this may still be true for general usage, it is ideally suited for special needs such as bias estimation, track initiation and spawning, long-term prediction of track states, and state estimation during periods of rapidly changing target dynamics. In this paper, we examine the batch estimator formulation for several cases: nonlinear and linear models, with and without a prior state estimate (MAP vs. ML), and with and without process noise. For the nonlinear case, we show that a single pass of an extended Kalman smoother-filter over the data corresponds to a Gauss-Newton step of the corresponding nonlinear least-squares problem. Even the iterated extended Kalman filter can be viewed within this framework. For the linear case, we develop a compact least squares solution that can incorporate process noise and the prior state when available. With these new views on the batch approach, one may reconsider its usage in tracking because it provides a robust framework for the solution of the aforementioned problems. Finally, we provide some examples comparing linear batch initiation with and without process noise to show the value of the new approach.

Paper Details

Date Published: 5 January 2004
PDF: 12 pages
Proc. SPIE 5204, Signal and Data Processing of Small Targets 2003, (5 January 2004); doi: 10.1117/12.506442
Show Author Affiliations
Aubrey B. Poore, Numerica Corp. (United States)
Benjamin J. Slocumb, Numerica Corp. (United States)
Brian J. Suchomel, Numerica Corp. (United States)
Fritz H. Obermeyer, Numerica Corp. (United States)
Shawn M. Herman, Numerica Corp. (United States)
Sabino M. Gadaleta, Numerica Corp. (United States)

Published in SPIE Proceedings Vol. 5204:
Signal and Data Processing of Small Targets 2003
Oliver E. Drummond, Editor(s)

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