Recursive locally minimum-variance filtering for two-dimensional systems: When dynamic quantization effect meets random sensor failure

This article deals with the recursive filtering issue for an array of two-dimensional systems with random sensor failures and dynamic quantizations. The phenomenon of sensor failure is introduced whose occurrence is governed by a random variable with known statistical properties. In view of the data transmission over networks of constrained bandwidths, a dynamic quantizer is adopted to compress the raw measurements into the quantized ones. The main objective of this article is to design a recursive filter so that a locally minimal upper bound is ensured on the filtering error variance. To facilitate the filter design, states of the dynamic quantizer and the target plant are integrated into an augmented system, based on which an upper bound is first derived on the filtering error variance and subsequently minimized at each step. The expected filter gain is parameterized by solving some coupled difference equations. Moreover, the monotonicity of the resulting minimum upper bound with regard to the quantization level is discussed and the boundedness analysis is further investigated. Finally, effectiveness of the developed filtering strategy is verified via a simulation example. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This article addresses the recursive filtering problem of a two-dimensional system array with random sensor failures and dynamic quantizations. The occurrence of sensor failures is governed by a random variable with known statistical properties. To deal with data transmission over networks with limited bandwidth, a dynamic quantizer is utilized to compress raw measurements into quantized ones. The main objective of this article is to design a recursive filter that guarantees a locally minimal upper bound on the filtering error variance. To support the filter design, the states of the dynamic quantizer and the target plant are integrated into an augmented system, which enables the derivation of an upper bound on the filtering error variance and its subsequent minimization at each step. The expected filter gain is parameterized by solving coupled difference equations. Furthermore, the article discusses the monotonicity of the resulting minimum upper bound with respect to the quantization level and investigates its boundedness. Finally, the effectiveness of the developed filtering strategy is demonstrated through a simulation example.