Sequential method for checking covariance of renovating sequence of the Kalman filter

Effective methods are proposed for checking the covariance matrix of a renovating sequence of the Kalman filter. The quadratic form from the random Wishart matrix is used as controlled statistics. Solving the control problem is reduced to the classical problem about maximization of a quadratic form on unit sphere. As a result, the two algorithms of Kalman filter control are proposed: in the first one, the sum of all matrix elements is used as a checked scalar measure of Wishart matrix, and in the second one, the maximum eigenvalue of the matrix is used.