Gaussian mixture cardinalized PHD filter for ground moving target tracking

Abstract

The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with varying target number in clutter. In particular, the Gaussian mixture variant (GMCPHD) for linear, Gaussian systems is a candidate for real time multi target tracking. The present work addresses the following three issues: (i) we show the equivalence between the GMCPHD filter and the standard Multi Hypothesis Tracker (MHT) in the case of single targets; (ii) using a Gaussian sum approach, we extend the GMCPHD filter by employing digital road maps for road constraint targets. The utilization of such external information leads to more precise tracks and faster and more reliable target number estimates; (iii) we model the effect of Doppler blindness by a target state dependent detection probability, leading to more stable target number estimation in the case of low Doppler targets.

A phd Filter for Tracking Multiple Extended Targets Using Random Matrices

“…This is true either when p D ( · ) is a sufficiently smooth function, or when the signal to noise ratio (SNR) is high enough such that the uncertainty zone is sufficiently small. A similar approach to variable probability of detection has been taken in order to model the clutter notch in ground moving target indicator target tracking [25].…”

“…represents new targets that appear at time step k. The full predicted PHD D k+1|k (ξ k+1 ) is the sum of the PHD of predicted existing targets (24) and the birth PHD (25), and contains a total of J k+1|k = J k|k + J b,k+1 GIW components.…”

Intersection-Based Road User Tracking Using a Classifying Multiple-Model PHD Filter

“…Beside a generalization of the probabilities using exponential mixtures proposed in [VM06], an approximation first introduced by [UEW07] is feasible. Here an MC dependent probability of detection…”

“…Here the assumption of [UEW07] introduced in Section 4.3.5 is adopted which assumes that the detection probability of one sensor is constant within the uncertainty region of a Gaussian. Assuming for the example in Figure 5.5 that the p D inside the sensors' FOV is close to one and outside close to zero, the contradicting object detections of S 1 and S 2 can be resolved.…”

The multiple hypothesis tracker derived from finite set statistics

“…On the other hand, if Reid's MHT can be shown to fit nicely within the theoretical framework of FISST, then such concerns are much less warranted. The relationship between FISST and MHT has been discussed in many papers, including [8], [9] and [10]. However, the relationship between FISST and Reid's formula has not yet been fully elucidated.…”