Optimal Linear Filtering for Discrete-Time Systems With Infinite-Dimensional Measurements

• 成果类型: Article
• 署名作者: Varley, Maxwell M.; Molloy, Timothy L.; Nair, Girish N.
• 署名单位: University of Melbourne; Australian National University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3464892
• 发表日期: 2025
• 页码: 1637-1651
• 关键词: NOISE; Noise measurement; Maximum likelihood detection; nonlinear filters; Gain measurement; vectors; Kalman filters; Discrete-time linear systems; Distributed parameter systems; Kalman filtering; State estimation; stochastic fields; Stochastic processes

摘要

Systems equipped with modern sensing modalities such as vision and Lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of high-dimensional measurements and analyze state estimation in linear time-invariant systems with infinite-dimensional measurements but finite-dimensional states, both corrupted by additive noise. We propose a linear filter and derive the corresponding optimal gain functional in the sense of the minimum mean square error, analogous to the classic Kalman filter. By modeling the measurement noise as a wide-sense stationary random field, we are able to derive the optimal linear filter explicitly, in contrast to previous derivations of Kalman filters in distributed-parameter settings. Interestingly, we find that we need only impose conditions that are finite-dimensional in nature to ensure that the filter is asymptotically stable. The proposed filter is verified via simulation of a linearized system with a pinhole camera sensor.