State Noise Density Identification of LTV System by Kernel Deconvolution

This paper focuses on identification of the state noise density of a linear time-varying system described by the state-space model with the known measurement noise density. For this purpose, a novel method extending the capabilities of the measurement difference method (MDM) is proposed. The proposed method is based on the enhanced MDM residue calculation being a sum of the state and measurement noise, and on the construction of the residue sample kernel density. The state noise density is then estimated by the density deconvolution algorithm utilising the Fourier transform. The developed method is supplemented with automatic selection of the deconvolution user-defined parameters based on the proposed method of the noise moment equality. The state noise density estimation performance is evaluated in numerical examples and supplemented with the MALAB example implementation.

AI-Aided Kalman Filters

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.