In many engineering applications, estimation accuracy can be improved by data from distributed sensors. Due to limited communication bandwidth and limited processing capability at the fusion center, it is crucial to compress these data for the final estimation at the fusion center. One way of accomplishing this is to reduce the dimension of the data with minimum or no loss of information. Based on the best linear unbiased estimation (BLUE) fusion results obtained in the previous parts of this

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... ries, in this paper we present optimal rules for compressing data at each local sensor to an allowable size (i.e., dimension) such that the fused estimate is optimal. We show that without any performance deterioration, all sensor data can be compressed to a dimension not larger than that of the estimatee (i.e., the quantity to be estimated). For some simple cases, these optimal compression rules are given analytically; for the general case, they can be found numerically by an algorithm proposed here. Supporting simulation results are provided.