A robust estimation fusion with unknown cross-covariance in distributed systems

In a distributed estimation system, the fusion center receives the local estimates from sensors and fuses them to be an optimal estimation in terms of some criterion. Recently, the best linear unbiased estimation (BLUE) fusion was proposed to minimize the mean square error of the fused estimate, in which the weights to optimally combine the local estimates are determined by the covariance matrix of estimation errors. While the cross-correlations of estimation errors are unknown, which is very often in practice, the covariance intersection (CI) filter provides an estimate of the determinate parameters or states according to the minimax criterion. Unfortunately, there are still some obviously disadvantages in that strategy. In this paper, for the case of the estimation error covariance between different sensors being unknown, a robust estimation fusion (REF) is derived to minimize the worst-case estimation error on some given parameter set, in which the fusion weights are determined by solving a semidefinite program. Specifically, the REF is the nonlinear combination of local estimates. The simulations show that the proposed approach has better performance than the CI filter.