Linear fusion of estimators with Gaussian mixture errors under unknown dependences

In decentralised state estimation, there are two key problems. The first one is how to fuse estimators that are given by the local processing of locally obtained data. The second one is to compute the description of the fused estimator error supposing the fusion rule is specified. Alternatively, if the global knowledge of the decentralised problem is not available, the second problem may be to provide such a description that does not overvalue the quality of the fused estimator. The last problem is followed in this paper. For local estimator errors with Gaussian mixture densities, an underlying joint Gaussian mixture is supposed. The component indices of the joint Gaussian mixture are supposed to be hidden discrete random variables with unknown probability function. The estimator fusion is considered to be linear with fixed weights. An upper bound of the mean square error matrix of the fused estimator is designed. In a case study, the newly designed upper bound is compared with a current upper bound and a density approach is discussed.