Robust Recursive Estimation for Uncertain Systems With Delayed Measurements and Noises

Jianxin Feng,Haiying Liu,Rongni Yang,Biao Xu

doi:10.1109/access.2020.2966521

Abstract

In this article, the problem of robust recursive estimation is studied for a class of uncertain systems with delayed measurements and delayed noises. The system model is subject to stochastic uncertainties which can be described by multiplicative noises. The phenomenon of delayed measurements occurs in a random way and the delay rate is characterised by a binary switch sequence with known probability distribution. The process noise and the measurement noise are both deterministic delay. By combining the noise at present time and the delayed noise into a whole one, the original system is transformed into an auxiliary stochastic uncertain system with discrete autocorrelated noises across time. Then, based on the orthogonal projection theorem and an innovation analysis approach, the desired robust recursive estimators including robust recursive filter, robust recursive predictor and robust recursive smoother are derived. A numerical simulation example is exploited to show the effectiveness of the proposed approaches.

Highlights

In the past decades, the estimation theory and design techniques have received considerable attention due to extensive application backgrounds ranging from aerospace systems, navigation, target tracking, communication systems, signal processing, and elsewhere [1]–[6]
Motivated by the above analysis, in this paper, we aim to investigate the robust recursive estimation problem for a VOLUME 8, 2020 class of uncertain systems with delayed measurements and noises, where the system parameters are subject to stochastic uncertainties which can be described as multiplicative noises
In this paper, we have investigated the robust recursive estimation problem for a class of uncertain systems with randomly delayed measurements and deterministic delayed process noises and measurement noises

Summary

Introduction

The estimation theory and design techniques have received considerable attention due to extensive application backgrounds ranging from aerospace systems, navigation, target tracking, communication systems, signal processing, and elsewhere [1]–[6]. The traditional Kalman filter is a basic and classical state-space estimator, since its inception in the early 1960s, it has attracted a great deal of attention for its simple structure and good performance. The good performance of the traditional Kalman filter is based on the assumption that the system structure and parameter are exactly known. There are a variety of ways to describe the model uncertainties, such as the norm-bounded uncertainty [7]–[9], polytopic uncertainty [8], [10], stochastic uncertainty [9], [11]–[13] and so on. The norm-bounded uncertainty and polytopic uncertainty are treated by the inequality theory and extreme value theory.

Objectives

Results

Conclusion