Adaptive Gauss–Hermite filter for non-linear systems with unknown measurement noise covariance

A non-linear adaptive state estimator based on the Gauss-Hermite (GH) quadrature rule has been proposed to suit non-linear signal models where the measurement noise covariance remains unknown. The proposed algorithm which may be used for both parameter and state estimation incorporates online adaptation of the measurement noise covariance (R) following maximum-likelihood estimation-based method. The GH quadrature approach has been considered so that the proposed filter may inherit the enhanced estimation accuracy as exhibited by its non-adaptive counterpart. The proposed adaptation algorithm, in contrast to some other reported methods, automatically ensures positive definiteness of the adapted measurement noise covariance. The efficacy of the adaptive algorithm over the non-adaptive GH filter has been demonstrated using Monte Carlo simulation and two case studies. Performance comparison has also been carried out with respect to adaptive unscented Kalman filter with the help of same case studies.