Targets Spatial Coordinates Calculation in Angle-Difference Rangefinder Passive Location Complexes by Numerical Iterative Methods

This paper presents the analysis results of the iterative numerical algorithms use for roots calculating of nonlinear equations systems (Levenberg-Marquardt, Newton’s algorithm, modified Newton’s algorithm, sequential iterations and gradient descent) describing the process of spatial rectangular coordinates calculating of radio emission sources in the angle-difference-rangefinder passive location complexes with different configurations (containing from 2 to 4 receivers). The main objectives of the work include determining optimal number of receiving points and choosing the most effective way to transform the coordinates of the observed parameters vector (a set of range differences and angular coordinates estimates of objects emitting radio signals in relation to the receiver spatial location of the system) into a measured parameters vector (spatial rectangular coordinates of the observation object). The criteria for further comparison of the using analyzed algorithms results were determined by the following characteristics: working area of the passive location complex (the part of the space within which the targets coordinates estimates deviation from their true values does not exceed the maximum allowable values); average error of calculating the target spatial coordinates in the working area; number of coordinate calculating stages of radio sources in the studied part of the space. The results of a comparative analysis of the obtained numerical values by the selected criteria allowed us to conclude that the optimal implementation is the implementation of the angle-difference-rangefinder passive location complexes consisting of four receiving points and the use of the Levenberg-Marquardt algorithm for calculating the spatial coordinates of radio emission sources. 

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