A new method for evaluating the log-likelihood gradient, the Hessian, and the Fisher information matrix for linear dynamic systems

A method is presented for evaluating the log-likelihood gradient (score), the Hessian, and the Fisher information matrix of the parameters of linear dynamic stochastic systems. The method incorporates the optimal Kalman smoothing equations and is therefore ideal for simultaneous state estimation and parameter identification. The result can be used for efficient implementation of gradient-based algorithms for maximum-likelihood identification of the unknown system parameters and for assessing the mean-square estimation accuracy.>