Ondrej Straka

Ondrej Straka, Felipe Giraldo-Grueso, Renato Zanetti

Algorithms for Bayesian state estimation of nonlinear systems inevitably introduce approximation errors. These algorithms depend on parameters that influence the accuracy of the numerical approximations used. The parameters include, for example, the number of particles, scaling parameters, and the number of iterations in iterative computations. Typically, these parameters are fixed or adjusted heuristically, although the approximation accuracy can change over time with the local degree of nonlinearity and uncertainty. The approximation errors introduced at a time step propagate through subsequent updates, affecting the accuracy, consistency, and robustness of future estimates. This paper presents adaptive parameter selection in nonlinear Bayesian filtering as a sequential decision-making problem, where parameters influence not only the immediate estimation outcome but also the future estimates. The decision-making problem is addressed using reinforcement learning to learn adaptive parameter policies for nonlinear Bayesian filters. Experiments with the unscented Kalman filter and stochastic integration filter demonstrate that the learned policies improve both estimate quality and consistency.

Nir Shlezinger, Guy Revach, Anubhab Ghosh et al.

The Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple state-space (SS) models, which may be crude and inaccurate descriptions of the underlying dynamics. Emerging data-centric artificial intelligence (AI) techniques tackle these tasks using deep neural networks (DNNs), which are model-agnostic. Recent developments illustrate the possibility of fusing DNNs with classic Kalman-type filtering, obtaining systems that learn to track in partially known dynamics. This article provides a tutorial-style overview of design approaches for incorporating AI in aiding KF-type algorithms. We review both generic and dedicated DNN architectures suitable for state estimation, and provide a systematic presentation of techniques for fusing AI tools with KFs and for leveraging partial SS modeling and data, categorizing design approaches into task-oriented and SS model-oriented. The usefulness of each approach in preserving the individual strengths of model-based KFs and data-driven DNNs is investigated in a qualitative and quantitative study, whose code is publicly available, illustrating the gains of hybrid model-based/data-driven designs. We also discuss existing challenges and future research directions that arise from fusing AI and Kalman-type algorithms.