2024/06/25 by Barron Han, Han, Barron, Oron Sabag +5 · 1 citation
Computer Science · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2406.17196
openalex publication_date 2024/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of remotely stabilizing a dynamical system. A sensor (encoder) co-located with the system communicates with a controller (decoder), whose goal is to stabilize the system, over a noisy communication channel with feedback. To accomplish this, the controller must estimate the system state with finite mean squared error (MSE). The vector-valued dynamical system state follows a Gauss-Markov law with additive control. The channel is a multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) channel with feedback. For such a source, a linear encoder, and a MIMO AWGN channel, the minimal MSE decoder is a Kalman filter. The parameters of the Kalman filter and the linear encoder can be jointly optimized, under a power constraint at the channel input. We term the resulting encoder-decoder pair a coded Kalman filter. We establish sufficient and necessary conditions for the coded Kalman filter to achieve a finite MSE in the real-time estimation of the state. For sufficiency, we introduce a coding scheme where each unstable mode of the state is estimated using the channel outputs of a single sub-channel. We prove a coinciding necessity condition when either the source or channel is scalar and present a matrix-algebraic condition which implies the condition is necessary in general. Finally, we provide a new counter-example demonstrating that linear codes are generally sub-optimal for coding over MIMO channels.