Kernel Gaussian processes based extended target tracking in polar coordinate

Most of the traditional extended target tracking (ETT) methods struggle with the strong nonlinearity introduced by the polar coordinate measurements and the unknown maneuvering motion model. These factors either lead to high approximation errors or impose a high computational cost, making accurate and efficient tracking challenging. To address these problems, a kernel Gaussian process-based extended target tracking (KGP-ETT) algorithm is proposed. First, the kernel mean embedding (KME) algorithm embeds the posterior distribution into a high-dimensional reproducing kernel Hilbert space (RKHS) and propagates the state particles through the nonlinear motion model, thereby effectively capturing the inherent nonlinearity. Second, based on the KME method, a kernel-based measurement update is proposed to estimate the target state in a linearized manner by integrating kernel techniques into the Gaussian process (GP) framework. Finally, the computational complexity and the theoretical posterior Cramér-Rao lower bound (PCRLB) of the proposed algorithm are analyzed. Simulation and real-world experiments demonstrate that, during target maneuvering, KGP-ETT achieves up to 77% reduction in centroid root mean square error (RMSE), 64% reduction in extent RMSE, and a 148% improvement in intersection of union (IoU) compared to state-of-the-art GP and Variational Bayesian (VB) methods. These results highlight the robustness and accuracy of KGP-ETT in handling complex nonlinear ETT problems in polar coordinates.