Proof that the Kalman gain minimizes the generalized variance (2103.07275v1)

Abstract: The optimal gain matrix of the Kalman filter is often derived by minimizing the trace of the posterior covariance matrix. Here, I show that the Kalman gain also minimizes the determinant of the covariance matrix, a quantity known as the generalized variance. When the error distributions are Gaussian, the differential entropy is also minimized.