TOA Localization with Polar Coordinates

Localization and positioning based on measured distances from user position to the network of reference stations could be classified as the most frequently used navigation method in a variety of applications. Time of Arrival (ToA) method uses measured time of radio signal traveling in space for distance measuring between user and nodes of reference stations. In the paper, we study using ToA localization in the polar coordinate system. As input data, we consider usage coordinates of reference network given in heading angles and ranges from the reference point. User coordinates are obtained in a polar reference frame also. Roots of navigation equations are obtained with a help of a numerical method of solution of nonlinear equations. Also, equations for standard deviation estimation are given in the paper. Results of numerical demonstration in the field of airplane localization by the ground stations network of distance measuring equipment indicate that benefits from application could be obtained only in case of polar coordinates systems used as a primary reference frame.