Real Time Coding and Estimation of Linear Discrete Time System Over Networks

Abstract

This study deals with the real time coding and estimation of linear discrete time scalar system over communication networks. With the mean-squared error (MSE) distortion criterion, the information rate distortion function describing the performance limit of the coding-estimation system is analyzed and discussed. To achieve near instantaneous encoding and decoding, an asymptotic design scheme has been presented as a realization of real time coding-estimation system. The outputs of standard Kalman filter relying on unquantized observations are encoded using the Lloyd-Max quantization rules and transmitted over the noiseless channel. The decoder side runs the corresponding decoding and reconstruction algorithms to produce the optimal real time state estimate of system. To synchronize the encoder and decoder, a doublepredictor regime on the updating rules of the encoder-decoder pair is proposed, and it does not require any feedback information. The rate distortion function of the proposed scheme is derived and when comparing with the information theoretical lower bound, there is only a factor discrepancy related to the quantization rules. The rate distortion performance results of various design schemes are compared and demonstrated with numerical simulations. INDEX TERMS Real time coding and estimation, mean-squared error, information rate distortion function, Lloyd-Max quantization, double-predictor regime.

On the Structure and Realization of Real-Time Coding and Estimation Over Noiseless Channel

“…In our previous work in [19], we derived the information rate-distortion function for the real-time coding and estimation of a linear scalar dynamic system, and a specific realization scheme was proposed and the corresponding ratedistortion performance was analyzed. In this paper, we focus on the optimal structural analysis of real-time coding and estimation functions and the corresponding realization scheme with structural equivalence based on the vector state Gauss-Markov system.…”