State and parameter estimation of linear stochastic multivariable sampled data systems

The problem of combined parameter and state estimation was originally posed as a nonlinear filtering problem using the extended Kalman filter. This led to problems of divergence and excessive computation, especially for multivariable systems. A two-stage online parameter and state estimator for multivariable stochastic systems is proposed that avoids these difficulties. A special canonical form of the state-space equations that simplifies the parameter estimation problem is used. In the first stage the parameters of the system matrices and of the steady-state Kalman filter matrix are estimated by a normalized stochastic approximation algorithm assuming known states. These parameter estimates are then utilized for state estimation in the second stage using the linear Kalman filter. The two stages are then coupled in a bootstrap manner.