State-space estimation and tracking rely on accurate dynamical models to perform well. However, obtaining an accurate dynamical model for complex scenarios or adapting to changes in the system poses challenges to the estimation process. Recently, augmented physics-based models (APBMs) appear as an appealing strategy to cope with these challenges where the composition of a small and adaptive neural network with known physics-based models (PBM) is learned on the fly following an augmented state-space estimation approach. A major issue when introducing data-driven components in such a scenario is the danger of compromising the meaning (or interpretability) of estimated states. In this work, we propose a novel constrained estimation strategy that constrains the APBM dynamics close to the PBM. The novel state-space constrained approach leads to more flexible ways to impose constraints than the traditional APBM approach. Our experiments with a radar-tracking scenario demonstrate different aspects of the proposed approach and the trade-offs inherent in the imposed constraints.

This contribution presents a novel resampling scheme that leverages Gaussian Processes (GPs) to more accurately approximate the posterior distribution from a set of random measures and, ultimately, enhance resampling by sampling from such approximation. Resampling is a critical step in particle filtering, impacting its estimation performance and parallelization capabilities. The approach can be seen as a kernel-based density approximation. As a byproduct, we are able to i) derive an explicit formula for minimum mean squared error (MMSE) state estimation, and ii) provide a well defined optimization problem for determining the maximum a posteriori (MAP) state estimation. The results on a target tracking problem show the performance improvements of the so-called Gaussian Process Particle Filter (GPPF) when compared to standard particle filtering.