Calculation of spatial target coordinates in range-difference passive radars by the Levenberg – Marquardt method

Abstract

This article studies and analyzes the results of applying numerical iterative methods for solving nonlinear equation systems (Newton, modified Newton's method, gradient descent, sequential iterations, Levenberg – Marquardt), compiled and used to calculate the rectangular spatial coordinates of radio emission sources in range-difference passive radars of various configurations (incorporating from 3 to 4 receiving points). The aim of the research was to determine the optimal number of receiving points and to select the most effective algorithm for coordinate transformations of the vector of observed parameters (a set of range difference estimates from radio emission sources to the corresponding pairs of receiving points) into the vector of measured parameters (rectangular spatial coordinates). The following parameters were used as comparison criteria: passive radar working area (a part of space where the deviation of target coordinate estimates from their true values does not exceed the maximum tolerable values); average error in calculating spatial coordinates in the working area; iterations number of coordinate calculation in the analyzed part of space. Upon completing a comparative analysis of obtained characteristics and dependencies, we concluded that it is optimal to include four receiving points in a range-difference passive radar and use the Levenberg – Marquardt method to calculate the spatial coordinates of radio emission sources.