AI-Aided Kalman Filters

TL;DR

The paper tackles state estimation for dynamic systems modeled by discrete-time state-space representations, where the true dynamics may be only partially known. It delivers a tutorial-style overview of AI-aided Kalman filters, categorizing approaches into task-oriented and SS-model-oriented designs, and detailing external pre-processing, integrated KG learning, and data-augmented dynamics models. A comprehensive qualitative and quantitative comparison (including Lorenz-attractor experiments) illustrates the trade-offs between interpretability, uncertainty, adaptivity, and computational efficiency across methods such as KalmanNet, DANSE, and APBM. The work demonstrates how hybrid model-based/data-driven designs can preserve principled uncertainty quantification and interpretability while embracing the flexibility of data-driven learning, with implications for robotics, communications, and signal processing in nonlinear/non-Gaussian regimes.

Abstract

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.

Figures (10)

• Figure 1: Illustration of conventional dnn architectures for tasks related to filtering and smoothing, including $(a)$rnn; $(b)$ Attention; and $(c)$cnn.
• Figure 2: Selective ssm.
• Figure 3: Illustrative comparison between model-based Kalman-type filters ($a$); ai-based filters ($b$); and ai-augmented kf ($c$) divided into task-oriented and ss-oriented designs.
• Figure 4: ekf with dnn pre-processing illustration.
• Figure 5: ekf with learned kg illustration.