Covariance intersection
Encyclopedia
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.
, 
and 
, 
, but the cross correlation is not known. The covariance intersection update gives mean and covariance for c as
The weighting coefficient ω is chosen so to have reasonable properties as the sizes of A and B vary: such a consideration gives
Corresponding formulae for the combination of more than two estimates are available.
Kalman filter
In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated...
when the correlation between them is unknown.
Specification
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, and , , but the cross correlation is not known. The covariance intersection update gives mean and covariance for c as
The weighting coefficient ω is chosen so to have reasonable properties as the sizes of A and B vary: such a consideration gives
Corresponding formulae for the combination of more than two estimates are available.