Bootstrap estimation of parameters and states of linear multivariable systems

A two-stage bootstrap algorithm is presented for on-line estimation of the parameters and states of a linear multivariable discrete-time system. A special canonical form of the state equations gives a pseudoparameter measurement equation the parameters of which are directly related to those of the canonical model. These parameters are estimated in stage 1 using a recursive least-squares algorithm. These parameter estimates are then utilized for estimating the states in stage 2 using stochastic approximation. The two stages are coupled in a bootstrap manner. The results of a simulated example are included.