Generalized variance

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

1. 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.
2. Proof that the Kalman gain minimizes the generalized variance, Eviatar Bach https://arxiv.org/abs/2103.07275