Conservative Linear Unbiased Estimation Under Partially Known Covariances

Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible maintain knowledge about correlations. One example decentralized data fusion where cross-correlations between estimates are unknown, partly due information sharing. To avoid underestimating covariance of an estimate in such situations, conservative one option. In this paper linear unbiased estimator formalized including optimality criteria. Fundamental bounds derived. A main contribution a general approach for computing proposed based on robust optimization. Furthermore, shown that several existing algorithms special cases estimator. An evaluation verifies theoretical considerations and shows optimization performs better than methods certain cases.