Maximum Likelihood Estimation of Initial Conditions for Unknown Dynamical Systems

Abstract

The maximum-likelihood identification of linear time-varying systems in state-space form is considered. In particular, the case where it is desired to estimate the initial system state is examined. It is shown that the value of the expected initial state which maximises the likelihood function can be obtained as the solution of a linear algebraic equation. Thus the dimension of the space which it is necessary to search is reduced by the dimension of the state. The analysis shows that the expected initial state is often not identifiable when there are fewer outputs than states, even if the system is observable (assuming measurement noise) . Computational aspects are discussed, and an identification algorithm based Qn the above' is proposed.