Minimax Robust Optimal Estimation Fusion for Distributed Multisensor Systems with a Relative Entropy Uncertainty

Hua Li,Jie Zhou

doi:10.1155/2014/910971

Abstract

This paper considers the robust estimation fusion problem for distributed multisensor systems with uncertain correlations of local estimation errors. For an uncertain class characterized by the Kullback-Leibler (KL) divergence from the actual model to nominal model of local estimation error covariance, the robust estimation fusion problem is formulated to find a linear minimum variance unbiased estimator for the least favorable model. It is proved that the optimal fuser under nominal correlation model is robust while the estimation error has a relative entropy uncertainty.

Highlights

During the past decades, multisensor systems have received much attention in many applications, such as signal processing, communication, target tracking, and remote sensing [1,2,3,4,5,6,7]
This paper considers the robust estimation fusion problem for distributed multisensor systems with uncertain correlations of local estimation errors
For the general systems with known auto- and cross-correlations of estimation errors from local sensors, in [6, 10,11,12], the optimal linear estimation fusion formulas were proposed in the sense of linear minimum variance (LMV)

Summary

Introduction

Multisensor systems have received much attention in many applications, such as signal processing, communication, target tracking, and remote sensing [1,2,3,4,5,6,7]. For the general systems with known auto- and cross-correlations of estimation errors from local sensors, in [6, 10,11,12], the optimal linear estimation fusion formulas were proposed in the sense of linear minimum variance (LMV). In [22], a robust estimation problem was addressed for a linear model in which the unknown parameter vector is norm-bounded and noise covariance matrix is uncertain with a special structure. It was to get a linear estimator which minimizes the worst-case MSE over all vectors and noise covariance matrices in a specified uncertain region. This paper considers the robust estimation fusion approach for distributed multisensor systems with uncertain correlations among local estimation errors. The expectation of a random variable (or random vector) is denoted by E[⋅]

Problem Formulation

Problem Conversion

Solution of the Robust Optimization Problem

Conclusion