An optimal mean-square combination of arbitrary number of correlated estimates is derived. In particular, for two estimates, this combination represents the well-known Millman and Bar-Shalom-Campo formulas for uncorrelated and correlated estimation errors, respectively. This new result is applied to various recursive filtering problems. A new approximate adaptive filter with a parallel structure is also herein proposed. It is shown that this filter is very effective for multisensor systems containing different types of sensors. A practical implementation issue of this filter is addressed. An example demonstrating the accuracy of the proposed filter is given.
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