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In this paper, we propose two random matrix based extended target tracking models, which apply to the trajectory‐aligned and drifting target motions. The trajectory‐aligned model is specifically designed to handle targets moving along the direction of their extent orientations, while the drift model is tailored to targets whose trajectories deviate from their orientations in time. We utilise the well‐known variational Bayes method to perform inference and obtain posterior densities via computationally efficient, analytical, iterative steps. Through comprehensive experiments conducted on simulated and real data, our methods have demonstrated superior performance compared to previous approaches in scenarios involving both drifting and trajectory‐aligned targets. These results highlight the efficacy of our proposed models in accurately tracking targets and estimating their extent. [ABSTRACT FROM AUTHOR]

Abstract: Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear Gaussian models, Adaptive Kalman filters (AKF) estimate unknown parameters in the noise distributions jointly with the state. For nonlinear models, we provide a Bayesian solution for the estimation of the noise distributions in the exponential family, leading to a marginalized adaptive particle filter (MAPF) where the noise parameters are updated using finite dimensional sufficient statistics for each particle. The time evolution model for the noise parameters is defined implicitly as a Kullback–Leibler norm constraint on the time variability, leading to an exponential forgetting mechanism operating on the sufficient statistics. Many existing methods are based on the standard approach of augmenting the state with the unknown variables and attempting to solve the resulting filtering problem. The MAPF is significantly more computationally efficient than a comparable particle filter that runs on the full augmented state. Further, the MAPF can handle sensor and actuator offsets as unknown means in the noise distributions, avoiding the standard approach of augmenting the state with such offsets. We illustrate the MAPF on first a standard example, and then on a tire radius estimation problem on real data. [Copyright &y& Elsevier]