Probabilistic tracking of multiple extended targets using random matrices

Conventional tracking algorithms rely on the assumption that the targets under observation are point source objects. However, due to increasing resolution capabilities of modern sensors, the point source assumption is often not suitable and estimating the target extension becomes a crucial aspect. Recently, a Bayesian approach to extended target tracking using random matrices has been proposed. Within this approach, ellipsoidal object extensions are modeled by random matrices and treated as additional state variables to be estimated. However, only a single-target solution has been presented so far. In this work we present the multi-target extension of this approach. We derive a new variant of Probabilistic Multi-Hypothesis Tracking (PMHT) that simultaneously estimates the ellipsoidal shape and the kinematics of each target. For this purpose, the PMHT auxiliary function is extended by random matrices representing the target ellipsoids. Both, the ellipsoids and the kinematic states are iteratively optimized by specific Kalman filter formulae arising directly from the auxiliary function. The new method is demonstrated and evaluated by simulative examples.