Adaptive divided difference filter for parameter and state estimation of non-linear systems

An adaptive divided difference filter for joint estimation of parameters and states of a non-linear signal model has been proposed. The adaptive non-linear estimator, developed on the framework of second-order divided difference filter is intended for situations where the measurement noise statistics is unknown. Unlike other alternatives, the proposed non-linear adaptive estimator always ensures positive definiteness of the adapted measurement noise covariance. Performance of the evolved filter has been assessed with a bench mark non-linear problem of joint estimation of parameters and states. Simulation with Monte Carlo results demonstrate that the root-mean-square errors of estimated states and parameters are (i) better than those obtained from non-adaptive filters with same initial values of measurement error covariance and (ii) consistent with the estimated error covariance. Furthermore, it is shown that even when the measurement noise covariance varies with time the adapted measurement noise covariance can track the time-varying truth value.