Estimation of the Covariance Parameters of Non-Stationary Time-Discrete Linear Systems
Smith, Patrick L. · Defense Technical Information Center (DTIC) · 1971
The Kalman filter sequentially generates the minimum variance estimate of the state of a linear dynamic system. This estimate is a function of the covariance parameters of the dynamic system model which implies that these be known a priori. Unfortunately some or all these covariance parameters are often unknown in engineering applications of the Kalman filter. In the report the maximum-likelihood estimates of the unknown covariance parameters of a time-discrete nonstationary linear system are computed from measurement residuals of a suboptimal sequential filter. Results for nonstationary linear systems are useful for nonlinear systems because most nonlinear estimation problems are solved by linearization which results in linear nonstationary plant and measurement models.