UKF Based Nonlinear Filtering for Parameter Estimation in Linear Systems with Correlated Noise

Based on the Unscented Kalman Filter (UKF), the nonlinear filter is presented for parameter estimation in linear system with correlated noise where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new form of UKF, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system. Convergence properties of the proposed algorithm are analyzed and ensured. The algorithm is verified by using Matlab simulations on the vehicle navigation systems with aided GPS.