Symmetric Star-convex Shape Tracking with Wishart Filter

In stochastic estimation problems, we aim to estimate an unknown state of interest given a set of measurements received from noisy sensory devices, such as radar, Light Detection and Ranging (LiDAR), etc. A common model of the measurements' random error is white Gaussian noise. This noise model is usually used to derive an estimator of the unknown state; accordingly, the state is described as a random variable with a Gaussian density. In some applications, the unknown state is known to take only positive values, e.g. estimating size or dimension. In such a case the classical approaches based on Gaussian densities might fail, i.e., produce a negative value. In this work, a recursive Bayesian filter is proposed based on modelling the unknown state as Wishart distributed random matrix. This model ensures that the probability densities of the random variables are restricted to positive real values, even though the measurement's noise is still modeled as white Gaussian noise. The feasibility of the proposed Bayesian Wishart filter is demonstrated within the framework of Extended Target Tracking (ETT). A target contour measurement model of a symmetric star-convex shape is presented and integrated in the proposed filter to track the target's extent.