Analysis of the influence of the trajectory of motion of a dynamic controlled object on the accuracy of determining navigation parameters

Abstract

To implement the requirements of the International Civil Aviation Organization of increasing the capacity and use efficiency of airspace, an area navigation strategy and its component – free flight routing – have been developed. The aim of the research is to analyze the influence of the trajectory of a dynamic controlled object on the accuracy of determining coordinates in the course of area navigation and free flight routing. This article analyzes the influence of the chosen flight route on the accuracy of determining the navigation parameters within the framework of the Kalman’s extended filter algorithm. It is shown that there is an unambiguous dependence of the radial error, geometric factor, and observability measure on the trajectory rotation angle. Based on the analysis, it is proposed to use the observability measure to form an optimization criterion in the process of implementation of area navigation. The methods of statistical simulation have confirmed the unambiguous relationship between the geometric factor, the observability measure and the trace of the covariance matrix of filtering errors for various trajectories of movement of a dynamic controlled object. The proposed approach seems to be more rational in comparison with the calculation of the covariance matrix of the estimation errors while practically implementing optimal control algorithms in the navigation processor because of the reduction in the amount of computations. The results of the analysis allow us to consider the maximum of the observability measure as a decision rule in the problems of trajectory optimization, as well as in observation control algorithms.