Research report

Šimandl M., Duník J.

Plzeň

2007

50

Ing. Jindřich Duník, Ph.D. (FAV Západočeská univerzita, katedra kybernetiky)

stochastic systems, state estimation, estimation theory

report_CE_JD.pdf [file]

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 the initial state covariance matrix are exactly known. The properties of the innovation sequence of the Kalman Filter and the Extended Kalman Filter are discussed and the new 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 allowing the significant simplification of relations for computation of the covariance matrices of the innovation sequence 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.