Measurement-Guided Likelihood Sampling for Grid-Based Bayesian Tracking

Bayesian inference is recognized as a general framework for performing optimal target tracking. Fundamentally, it assumes that the uncertainty in our knowledge of the state of the target (or targets) may be well represented by probabilities. Bayes’ theorem then provides the basic mechanism whereby measurements update these probabilities and, hence, our knowledge of the target state. For computer implementation of a Bayesian scheme, a representation of the probabilities must be selected. Various approaches have been developed, including Kalman filters, grid-based models, and particle filters, as summarized in [1, 35]. Existing approaches are valuable in a diverse set of applications, but there is room for improvement in other applications. The application area driving this research involves the goal of detecting and localizing a single target in a very loud environment, such as an active sonar system trying to detect and track a quiet target in a cluttered, reverberant environment. The undersea active sonar presents a rich diversity of contextual information, which can be vital for situational awareness, but too often is ignored by automated tracking and classification systems. In order to incorporate such details in the tracker, we pursue a track-before-detect paradigm. In this approach, the normalized matched filter output of the signal processing chain is incorporated directly into the tracker, as opposed to a contact-level approach in which clustered data is used. At this lower level in the signal processing, more information should be available. In order to keep the data load manageable, the matched filter output is thresholded. This thresholding, as well as details of the waveform ambiguity functions and beam patterns, are folded directly into the likelihood functions used in the Bayesian tracker. The form of these functions, which is described in Section 3, requires a detailed sampling of the likelihood function. We propose an advanced grid-based approach to Bayesian tracking in which the likelihood evaluations are performed using an intelligent sampling procedure. Previous work on Bayesian tracking is described in Section 2. The mathematical models used for our tracking applications are described in Section 3. The advanced implementation of the measurement update, which is the core contribution of this paper, is described in Section 4. The example problems and results comparing the proposed measurement update to standard implementations are given in Section 5. Additional discussion is given in Section 6, and a brief summary closes the paper in Section 7. An appendix contains a derivation of the likelihood function.