Generalized variance
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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, {\displaystyle \det(\Sigma )}. It can be shown to be related to the multidimensional scatter of points around their mean.[1]
Minimizing the generalized variance gives the Kalman filter gain.[2]
References
[edit ]- ^ Kocherlakota, S.; Kocherlakota, K. (2004). "Generalized Variance". Encyclopedia of Statistical Sciences. Wiley Online Library. doi:10.1002/0471667196.ess0869. ISBN 0471667196 . Retrieved 30 October 2019.
- ^ Proof that the Kalman gain minimizes the generalized variance, Eviatar Bach https://arxiv.org/abs/2103.07275
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