Optimal Linear Estimation Fusion—Part IV: Optimality and Efficiency of Distributed Fusion

Abstract – This paper is concerned with the performance of distributed and centralized fusion with best linear unbiased estimation (BLUE), also known as linear minimum mean-square error (LMMSE) estimation, and optimal weighted least squares (WLS) estimation. Necessary and sufficient conditions for optimal distributed fusion rules to have identical performance as their centralized counterparts are presented. The conditions are general—e.g., no assumption is made that measurements are linear in the estimatee. Further, measures of relative efficiency of distributed fusion compared with centralized fusion are proposed. General and explicit formulas in terms of MSE matrix for performance degradation of the optimal distributed fusion relative to the optimal centralized fusion are given. It is shown both theoretically and by simulation results that the optimal distributed and centralized fusion rules using linear measurements have identical performance in general when measurement errors are uncorrelated across sensors and the measurement matrix has full column rank; the former is inferior to the latter in general when the measurement errors are correlated across sensors or are correlated with the estimatee. Numerical examples that demonstrate the relative efficiency of the distributed fusion are given. It is also illustrated that the optimal distributed fusion could be quite poor compared with the optimal centralized fusion.