Estimation of state of nonlinear stochastic dynamic systems with optimized extended Kalman filter

In this paper, we critically investigate the application of the Extended Kalman Filter (EKF) in the estimation of states of nonlinear stochastic dynamical systems. We apply an algorithmic approach to EKF and investigate its efficiency in state estimation under stochastic conditions. Through simulation example analysis, we provide detailed insights into the performance and advantages of the EKF compared to other national accounting methods. This paper contributes to the understanding and application of EKF in complex nonlinear systems and lays the foundation for further research in state estimation in dynamic systems using adaptive learning methods, algorithm is adjusted to dynamic changes in the system to ensure the best estimate of the situation. In addition, we develop and implement advanced fault detection and correction methods that ensure O-EKF stability and reliability even under adverse conditions through detailed analysis of O-EKF performance over various stochastic conditions, we demonstrate a significant improvement in the accuracy and speed of conditional estimation compared to traditional methods. Finally, we highlight the importance of innovation in the development of state accounting systems and the applicability of O-EKF in areas such as autonomous vehicles, robotics, and industrial logistics actually use it. This paper represents an important contribution to research on advanced state accounting methods and opens the way for further developments in real-world systems.