When there exists the limitation of communication bandwidth between sensors and a fusion center, one needs to optimally pre-compress sensor outputs--sensor observations or estimates before sensors' transmission to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion. This paper will give an analytic solution of the optimal linear dimensionality compression matrix for the single sensor case and analyze the existence of the optimal linear dimensionality compression matrix for the multisensor case, as well as how to implement a Gauss-Seidel algorithm to search for an optimal solution to linear dimensionality compression matrix.
In a distributed estimation or tracking system, the global estimate are generated by the local estimates. Under the assumption of independence cross sensor noises, Bar-shalom proposed a two sensor tracking fusion formula, which used only the inverses of covariances of single sensor estimation errors. In this paper, we present more general multi-sensor estimation fusion formula, where the assumption of independence cross sensor noises and the direct computation of the generalized inverse of joint covariance of multiple sensor estimation errors are not necessary. Instead, as the number of sensors increases, a recursive algorithm is presented, in which only the inverses or the generalized inverses of the matrices having the same dimension as that of the covariance matrices of single sensor estimate errors are required.