Gaussian processes based extended target tracking in polar coordinates with input uncertainty

Gaussian processes (GP) based extended target tracking (ETT) technique has attracted the attention of scientists since it can accurately estimate the kinematic states as well as the contour states of irregular-shape targets. Most traditional GP methods consider the ETT problem with a linear measurement model in Cartesian coordinates and ignore the input uncertainty of GP for simplicity. In many applications, however, measurements are generated with high-resolution sensors in polar coordinates. More importantly, the ignorance of input uncertainty in GP will exacerbate the tracking performance in these cases. In order to track an irregular-shape extended target in polar coordinates with input uncertainty, an improved GP-based probabilistic data association (IGP-PDA) algorithm is developed that includes the following enhancements: Firstly, a nonlinear measurement model is used and the unbiased converted measurement technique is invoked for the ETT problem. Secondly, the analytical form of statistical properties of the input uncertainty due to measurements noise and predicted error is derived. Thirdly, an IGP-PDA taking into account measurement origin uncertainty as well as input uncertainty is proposed, and three sub-optimal implementations are provided. Last, the posterior Cramer-Rao lower bound of ETT with input uncertainty is derived. Simulation results verify the effectiveness of the proposed method.