Several types of nonlinear filters (EKF -extended Kalman filter, UKF -unscented Kalman filter, PF -particle filter) are widely used for location estimation and their algorithms are described in this paper. In the article filtering accuracy for non-linear form of measurement equation is presented. The results of complex simulations that compare the quality of estimation of analyzed non-linear filters for complex non-linearities of state vector are presented. The moves of maneuvering object are described in two--dimensional Cartesian coordinates and the measurements are described in the polar coordinate system. The object dynamics is characterized by acceleration described by the univariate non-stationary growth model (UNGM) function. The filtering accuracy was evaluated not only by the root-mean-square errors (RMSE) but also by statistical testing of innovations through the expected value test, the whiteness test and the WSSR (weighted sum squared residual) test as well. The comparison of filtering quality was done in the MATLAB environment. The presented results provide a basis for designing more accurate algorithms for object location estimation.

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The paper presents a method of calculation of position deviations from a theoretical, nominally rectilinear trajectory for a SAR imaging system installed on board of UAV. The UAV on-board system consists of a radar sensor, an antenna system, a SAR processor and a navigation system. The main task of the navigation part is to determine the vector of differences between the theoretical and the measured trajectories of UAV center of gravity. The paper includes chosen results of experiments obtained during ground and flight tests.

The paper presents methods of on-line and off-line estimation of UAV position on the basis of measurements from its integrated navigation system. The navigation system installed on board UAV contains an INS and a GNSS receiver. The UAV position, as well as its velocity and orientation are estimated with the use of smoothing algorithms. For off-line estimation, a fixed-interval smoothing algorithm has been applied. On-line estimation has been accomplished with the use of a fixed-lag smoothing algorithm. The paper includes chosen results of simulations demonstrating improvements of accuracy of UAV position estimation with the use of smoothing algorithms in comparison with the use of a Kalman filter.

This paper considers the problem of applying the Kalman filters to nonlinear systems. The Kalman filter (KF) is an optimal linear estimator when the process noise and the measurement noise can be modeled by white Gaussian noise. The KF only utilizes the first two moments of the state (mean and covariance) in its update rule. 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 linearization of the state transition matrix and the observation matrix with Taylor series expansions. Exploiting the assumption that all transformations are quasi-linear, the EKF simply makes linear all nonlinear transformations and substitutes Jacobian matrices for the linear transformations in the KF equations. The linearization can lead to poor performance and divergence of the filter for highly non-linear problems. An improvement to the extended Kalman filter is the unscented Kalman filter (UKF). The UKF approximates the probability density resulting from the nonlinear transformation of a random variable. It is done by evaluating the nonlinear function with a minimal set of carefully chosen sample points. The posterior mean and covariance estimated from the sample points are accurate to the second order for any nonlinearity. The 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).