In most filtering algorithms involving measurement data association, handling the complex computations due to multiple hypotheses is necessary. This paper introduces a novel Trajectory Poisson Multi-Bernoulli (TPMB) filter for tracking extended targets, facilitated by a synergy between the model and the data. This filter can track extended targets under unknown process and measurement noise. Initially, on the model-driven side, we compute multi-model transition probabilities using the posterior probabilities from models at two consecutive time points with the targets in high maneuverability state. The accuracy of the tracking algorithm is improved by calculating the improved Interacting Multiple Model (IMM) transition probability at each time step. For the data-driven aspect, the Gate-control Belief Propagation (GBP) is set in the message- passing algorithm to reduce the running time of false hypothesis associations. Thus, it is unnecessary to consider all message information when computing the likelihood matrix for target-measurement associations. Subsequently, the posterior density function of the Adaptive Square Root Cubature Kalman Filter (ASCKF) is constructed to adaptively estimate unknown process and measurement noises, while importance sampling in the current particle filter further mitigates particle degradation. Experiments demonstrate that our algorithm reduces the running time of data associations, alleviates particle degradation, and more accurately tracks maneuvering targets under nonlinear conditions and estimates their states.

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.