The influence of wrong information about transition and measurement models on estimation quality has been presented in the paper. Two methods of a particle filter, with and without the Population Monte Carlo modification, and also the extended and unscented Kalman filters methods have been compared. A small 5-bus power system has been used in simulations, which have been performed based on one data set, and this data set has been chosen from among 100 different – to draw the most general conclusions. Based on the obtained results it has been found that for the particle filter methods the implementation of the slightly higher standard deviation than the true value, usually increases the estimation quality. For the Kalman filters methods it has been concluded that optimal values of variances are equal to the true values.

The key to fingerprint positioning algorithm is establishing effective fingerprint information database based on different reference nodes of received signal strength indicator (RSSI). Traditional method is to set the location area calibration multiple information sampling points, and collection of a large number sample data what is very time consuming. With Zigbee sensor networks as platform, considering the influence of positioning signal interference, we proposed an improved algorithm of getting virtual database based on polynomial interpolation, while the pre-estimated result was disposed by particle filter. Experimental result shows that this method can generate a quick, simple fine-grained localization information database, and improve the positioning accuracy at the same time.

An approach to power system state estimation using a particle filter has been proposed in the paper. Two problems have been taken into account during research, namely bad measurements data and a network structure modification with rapid changes of the state variables. For each case the modification of the algorithm has been proposed. It has also been observed that anti-zero bias modification has a very positive influence on the obtained results (few orders of magnitude, in comparison to the standard particle filter), and additional calculations are quite symbolic. In the second problem, used modification also improved estimation quality of the state variables. The obtained results have been compared to the extended Kalman filter method.

The article presents a comprehensive study of a visual-inertial simultaneous localization and mapping (SLAM) algorithm designed for aerial vehicles. The goal of the research is to propose an improvement to the particle filter SLAM system that allows for more accurate and robust navigation of unknown environments. The authors introduce a modification that utilizes a homography matrix decomposition calculated from the camera frame-to-frame relationships. This procedure aims to refine the particle filter proposal distribution of the estimated robot state. In addition, the authors implement a mechanism of calculating a homography matrix from robot displacement, which is utilized to eliminate outliers in the frame-to-frame feature detection procedure. The algorithm is evaluated using simulation and real-world datasets, and the results show that the proposed improvements make the algorithm more accurate and robust. Specifically, the use of homography matrix decomposition allows the algorithm to be more efficient, with a smaller number of particles, without sacrificing accuracy. Furthermore, the incorporation of robot displacement information helps improve the accuracy of the feature detection procedure, leading to more reliable and consistent results. The article concludes with a discussion of the implemented and tested SLAM solution, highlighting its strengths and limitations. Overall, the proposed algorithm is a promising approach for achieving accurate and robust autonomous navigation of unknown environments.