Algorithm for Obtaining Cartesian Debiased Estimates of Target Coordinates from Range and Direction Measurements for an Arbitrary Radar Angular Orientation and Offset

Introduction . In order to increase the accuracy of estimating the coordinates of a target, it is necessary to compensate for systematic errors in the nonlinear transformation of coordinates from a spherical system to a Cartesian one. In this paper, we consider the generalization of the well-known coordinate transformation algorithm with compensation for systematic errors when the radar is positioned and oriented arbitrarily in the global Cartesian coordinate system. By applying the proposed algorithm, the coordinate vector and error correlation matrix can be obtained in the global Cartesian coordinate system in the presence of range measurements and angular positions in the local spherical coordinate system associated with the radar position. The proposed algorithm is discussed with respect to trajectory filtering. As a result of the compensation of systematic errors and the calculation of the correlation matrix of the coordinate vector, the accuracy of trajectory tracking is enhanced. Aim . To improve the accuracy of trajectory tracking when using the Kalman filter with converted measurements by means of the mathematical expressions obtained to estimate the coordinates of a target and the error correlation matrix in the global Cartesian coordinate system. Materials and methods . The problem was solved using the methods of mathematical statistics, statistical estimation theory, and computer simulation. Results. Mathematical expressions for calculating coordinates and the corresponding correlation matrix within the global Cartesian coordinate system were derived. Furthermore, comparative graphs illustrating trajectory tracking errors, associated with the use of various methodologies for constructing a Kalman filter based on transformed measurements, were created. Conclusion . The use of explicit expressions for coordinate transformation, accompanied by compensation for systematic errors, illustrates the potential for a substantial enhancement in accuracy when the errors of primary measurements increase. This improvement can be achieved when applying both direct and straightforward coordinate recalculation methods and a Kalman filter for transformed measurements within the global Cartesian coordinate system.