Comparative examinations of the nonlinear Kalman filters applied to positioning systems

In positioning systems Kalman filters are used for estimation and also for integration of data from navigation systems and sensors. The Kalman filter (KF) is an optimal linear estimator when the process noise and the measurement noise can be modeled by white Gaussian noise. In situations when the problems are nonlinear or the noise that distorts the signals is non-Gaussian, the Kalman filters provide a solution that may be far from optimal. Nonlinear problems can be solved with the extended Kalman filter (EKF). This filter is based upon the principle of linearizing the state transition matrix and the observation matrix with Taylor series expansions. Unscented Kalman filter with comparison to EKF does not linearize the model but operates on the statistical parameters of the measurement and state vectors that are subsequently nonlinearly transformed. The unscented Kalman filter is based on the unscented transformation (UT). This paper presents a comparison of the estimation quality for two nonlinear measurement models of the following Kalman filters: covariance filter (KF), extended filter (EKF) and unscented filter (UKF). There are descriptions of models and analysis of obtained results in this article. The comparison of filtration quality was done in MATLAB environment