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

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 double-predictor 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.