Finite-Horizon $H_{\infty} $ Filtering With Missing Measurements and Quantization Effects

Abstract

In this paper, a new <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering approach is developed for a class of discrete time-varying systems subject to missing measurements and quantization effects. The missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval [0,1] . The measured output is quantized by a logarithmic quantizer. Attention is focused on the design of a stochastic <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter such that the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> estimation performance is guaranteed over a given finite-horizon in the simultaneous presence of probabilistic missing measurements, quantization effects as well as external non-Gaussian disturbances. A necessary and sufficient condition is first established for the existence of the desired time-varying filters in virtue of the solvability of certain coupled recursive Riccati difference equations (RDEs). Owing to its recursive nature, the proposed RDE approach is shown to be suitable for online application without the need of increasing the problem size. The simulation experiment is carried out for the mobile robot localization problem with non-Gaussian disturbances, missing measurements and quantization effects. The effectiveness of the proposed method is demonstrated in the numerical example.