Point Measurement Probabilistic Multi-hypothesis Tracking

Abstract

The H-PMHT is fundamentally the point measurement PMHT applied to a histogram interpretation of image measurements. The PMHT algorithm is derived by applying Expectation Maximisation (EM) to point measurement tracking. Each point measurement is assumed to be caused by exactly one source, either one of the targets or the background clutter, and the EM missing data is an indicator variable that links each measurement to its source. This chapter reviews the derivation of PMHT and acts as warm up for the remainder of the book. An understanding of the mechanics of PMHT is very helpful in the development of H-PMHT, so don’t be tempted to skip this chapter unless you’re sure you can do without it. Before tackling the full complexity of the H-PMHT machinery, we will gradually build momentum by first applying the Expectation Maximisation algorithm to a static mixture model. The mixture components are then allowed to randomly evolve according to a known process model and the solution to this problem is PMHT. For the case that the measurement function is a linear function of the target state and the measurement noise is Gaussian, the PMHT can be implemented as a Kalman Smoother over equivalent measurements: this equivalence is demonstrated. For non-linear non-Gaussian applications the implementation is more complicated: an analytic expression is developed for the generic E-step, but in the general case the M-step must be tackled numerically. Finally the chapter concludes with an illustration of the algorithm applied to the canonical multi-target scenario, introduced in Chap. 1.