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Advanced Research in Naval Engineering pp 61–83Cite as

Tracking with Deterministic Batch Trackers

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Abstract

In this chapter, we present two deterministic (i.e., non-Bayesian) batch trackers—the Maximum Likelihood Probabilistic Data Association (ML-PDA) tracker and the Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT). Both trackers formulated by making assumptions about the target and the environment in which the target is present. Using these assumptions, in both cases, a log-likelihood ratio (LLR) is formulated, and then the state vector x that maximizes this LLR is usually chosen as the target state. Both the ML-PDA and the ML-PMHT LLRs are developed. We specifically consider two different amplitude likelihood ratios that have been used in these trackers—a fluctuating Gaussian model and a heavier-tailed clutter model. Finally, we present a method for determining a “tracking threshold” for ML-PMHT—i.e., if the maximum ML-PMHT likelihood value for a batch of data is above this level, it is determined to be a target; if it is below this level, the peak is rejected as clutter originated.

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Notes

  1. 1.

    There are several different ways of actually computing sbb(t); however, they will all produce a complex signal with a spectrum centered at f = 0.

  2. 2.

    This entire section is a summary of the work presented in [23].

  3. 3.

    A common misconception is that (64) allows a measurement to originate from multiple targets (i.e., a measurement can be shared between targets); this is not correct. Consider a single term of the sum—this represents the likelihood ratio for a single measurement. It can either originate from clutter or target 1 or target 2 …or target K.

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Authors and Affiliations

  1. Naval Undersea Warfare Center, Newport, RI, USA

    Steven Schoenecker

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  1. Steven Schoenecker
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Correspondence to Steven Schoenecker .

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Editors and Affiliations

  1. Naval Undersea Warfare Center, Newport, RI, USA

    Anthony A. Ruffa

  2. Department of Mathematics, Howard University, Washington, DC, USA

    Bourama Toni

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Schoenecker, S. (2018). Tracking with Deterministic Batch Trackers. In: Ruffa, A., Toni, B. (eds) Advanced Research in Naval Engineering. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-319-95117-1_5

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