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.

The paper presents a method of computational complexity reduction in Extended Kalman Filters dedicated for systems with non-linear measurement models. Extended Kalman filters are commonly used in radio-location and radio-navigation for estimating an object’s position and other parameters of motion, based on measurements, which are non-linearly related to the object’s position. This non-linearity forces designers to use non-linear filters, such as the Extended Kalman Filter mentioned, where linearization of the system’s model is performed in every run of the filter’s loop. The linearization, consisting of calculating Jacobian matrices for non-linear functions in the dynamics and/or observation models, significantly increases the number of operations in comparison to the linear Kalman filter. The method proposed in this paper consists of analyzing a variability of Jacobians and performing the model linearization only when expected changes of those Jacobians exceed a preset threshold. With a properly chosen threshold value, the proposed filter modification leads to a significant reduction of its computational burden and does not noticeably increase its estimation errors. The paper describes a practical simulation-based method of determining the threshold. The accuracy of the filter for various threshold values was tested for simplified models of radar systems.

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 presents a solution to the problem of simultaneous localization and mapping (SLAM), developed from a particle filter, utilizing a monocular camera as its main sensor. It implements a novel sample-weighting idea, based on the of sorting of particles into sets and separating those sets with an importance-factor offset. The grouping criteria for samples is the number of landmarks correctly matched by a given particle. This results in the stratification of samples and amplifies weighted differences. The proposed system is designed for a UAV, navigating outdoors, with a downward-pointed camera. To evaluate the proposed method, it is compared with different samples-weighting approaches, using simulated and real-world data. The conducted experiments show that the developed SLAM solution is more accurate and robust than other particle-filter methods, as it allows the employment of a smaller number of particles, lowering the overall computational complexity.

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.