Recursive maximum likelihood and related algorithms for parameter identification of dynamical processes

An algorithm recursive in the data (time) is developed for efficient computation of the approximate maximum of the exact log likelihood function (LLF) for general dynamical processes of finite state order. A numerical quadratic hill-climbing approach is used to incrementally determine the maximum interval (in time) of data for which the LLF is acceptably quadratic and simultaneously the corresponding Newton step in parameter space. The extended Kalman filter (EKF) for parameter identification is shown to be a special case of the recursive maximum likelihood algorithm with particular terms left out. The absence of one such term has been shown to cause divergence of the EKF. A hierarchy of self-checking, adaptive algorithms is outlined that enables choosing an algorithm of appropriate complexity and efficiency for a given application.