Nonlinear Filter for Estimating a Process with Correlated Derivative under Unknown Observation Noise Intensity

The paper presents a nonlinear filter for state estimation of a process with correlated highest-order derivative from the observations corrupted by the Gaussian white noise of unknown intensity. The filtering scheme is based on nonlinear transformation of the innovation process to approximate the Kalman–Bucy gain matrix, given arbitrary noise intensity. The filter is defined by the differential system of the same dimension as the state vector avoiding equations on the error covariation matrix. Based on the results of computer simulations, recommendations are given for selecting the tuning parameter of the nonlinear filter to take into account the correlation in the signal model.