Covariance intersection

Covariance intersection is an algorithm for combining two or more estimates of state variables in a Kalman filter when the correlation between them is unknown.

Items of information a and b are known and are to be fused into information item c. We know a and b have mean/covariance ${\displaystyle {\hat {a}}}$, ${\displaystyle A}$ and ${\displaystyle {\hat {b}}}$, ${\displaystyle B}$, but the cross correlation is not known. The covariance intersection update gives mean and covariance for c as

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