Recursive Filtering With Measurement Fading: A Multiple Description Coding Scheme

• Published in: IEEE transactions on automatic control Vol. 66; no. 11; pp. 5144 - 5159
• Main Authors: Wang, Licheng, Wang, Zidong, Shen, Bo, Wei, Guoliang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coders; Coding; Communication networks; Data transmission; Decoders; Decoding; Difference equations; Discrete time systems; Fading; Fading channels; Filtering; IIR filters; Independent variables; Mathematical model; multiple description coding (MDC); nonlinear stochastic systems; Nonlinear systems; packet dropout; Random variables; recursive filtering; Stochastic systems; Upper bounds
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3034196

In this article, the recursive filtering problem is studied for a class of discrete-time nonlinear stochastic systems subject to fading measurements. In order to facilitate the data transmission in a resource-constrained communication network, the multiple description coding scheme is adopted to encode the fading measurements into two descriptions with the identical importance. Two independent Bernoulli distributed random variables are introduced to govern the occurrences of the packet dropouts in two channels from the encoders to the decoders. The channel fading phenomenon is characterized by the <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula>th-order Rice fading model whose coefficients are mutually independent random variables obeying certain probability distributions. The purpose of the problem addressed is to design a recursive filter, such that in the simultaneous presence of the stochastic noises, the channel fading and the data coding-decoding mechanism, an upper bound of the filtering error variance is obtained and then minimized at each time step. In virtue of the Riccati difference equation technique and the stochastic analysis approach, the explicit form of the desired filter parameters is derived by solving a sequence of coupled algebraic Riccati-like difference equations. Finally, a simulation experiment is provided to show the applicability of the developed filtering scheme.