Adaptive observer with exponential forgetting factor for linear time varying systems

For the purpose of recursive joint estimation of state and parameters in continuous-time state space systems, the algorithm proposed in this paper improves the consistency of an adaptive observer for multi-input-multi-output (MIMO) linear time varying (LTV) systems. The new algorithm makes use of a time varying gain matrix for parameter estimation, instead of the constant gain matrix used by the previously reported algorithm. It is exponentially stable, converges in the mean for both state and parameter estimations. The covariance matrix of the parameter estimation error can be made arbitrarily small by choosing a sufficiently small forgetting factor.