The generalized variance is a scalar value which generalizes variance for multivariate random variables. It was introduced by Samuel S. Wilks. The generalized variance is defined as the determinant of the covariance matrix, det ( Σ ) {\displaystyle \det(\Sigma )} . It can be shown to be related to the multidimensional scatter of points around their mean. Minimizing the generalized variance gives the Kalman filter gain.
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