Estimation of target states and signal strength in the probabilistic multiple hypothesis tracking framework

An approach is presented for simultaneously estimating target states and signal-to-noise ratio (SNR) in the framework of the probabilistic multiple hypothesis tracking (PMHT). The approach, named PMHT-S, utilises the expectation-maximisation (EM) algorithm to obtain the maximum a posteriori estimates of target states and SNR´s of multiple targets in the presence of false measurements. The missing data of the EM algorithm consists of measurement-to-target assignments as well as a set of fictitious geometric and signal strength measurements each associated with a target under the hypothesis that the target has been undetected. This formulation creates new algorithmic approaches for solving PMHT problems such that information on missed targets may be exploited. It is shown that the auxiliary function of the PMHT-S is additively separable as the sum of a function of target states and a function of target SNR´s. The pair, as a result, can be independently maximised in each EM iteration to update target states and SNR´s. The computational advantage of the separation is substantial even for a small number of targets. Explicit expressions of the auxiliary function of the PMHT-S are given. Monte Carlo simulations were performed to assess estimation performance of the PMHT-S for target tracking examples.