Novel Multi-Target Tracking Method: PMBM Filter Combined SVD-SCKF with GP-Driven Measurements

Owing to multi-target tracking in scenarios with nonlinearity, uncertain measurement model and high clutter density, the Poisson multi-Bernoulli mixture (PMBM) recursion is prone to unstable covariance propagation under nonlinear dynamics as well as uncertainty in measurement-to-target association caused by mismatched gate that causes erroneous updates from clutters. In the prediction stage, the singular value decomposition (SVD) is used in place of Cholesky factorization to construct and propagate the square-root covariance factor in the square-root cubature Kalman filter (SCKF), yielding a numerically stable square-root implementation. Then, the resulting SVD-SCKF is incorporated into the PMBM prediction step and used to propagate the Gaussian-mixture components of both the Poisson point process (PPP) intensity and the Bernoulli component in the Multi-Bernoulli mixture (MBM), yielding predicted means and covariances under nonlinear dynamics. An adaptive fading factor is determined from innovation statistics, and covariance inflation is performed to improve robustness under target maneuvers and model mismatch. In the update stage, the unknown measurement function is regressed by Gaussian process (GP) using historical state-measurement samples, yielding an equivalent measurement mapping and state-dependent uncertainty. Furthermore, the predicted measurement distribution is generated from the GP-based conditional measurement distribution with state prior approximated by SVD-SCKF cubature points. An adaptive gate is determined from the GP-based conditional measurement distribution, which is approximated by an equivalent ellipsoidal gate via fitting for screening the current measurements and filtering out clutter. Residual in-gate clutter measurements are handled via Bayesian target discrimination, where the posterior probability of measurement originated from target is employed as a weight and incorporated into association weights and update likelihoods. Simulation results further confirm the effectiveness and stability of the proposed filter in complex scenarios.