Off-line Estimation of System Noise Covariance Matrices by a Special Choice of the Filter Gain

Estimation of noise covariance matrices for linear or nonlinear stochastic dynamic systems is treated. The stress is laid on the case when the initial state mean and covariance matrix are exactly known. The properties of the innovation sequence of the Kalman Filter and the local filters are discussed and the new offline method for estimation of the covariance matrices of the state and the measurement noise is designed. The proposed method is based on special choice of the filter gain and it takes an advantage of the well-known standard relations from the area of state estimation techniques and least square method. The theoretical results are verified in numerical examples.