Abstract
The problem of determining the location of radio emission sources by means of the time difference of arrival method is considered. The advantages and disadvantages of this method are analyzed. When solving equation systems, it is used Newton's iterative method. In this case, there are cases where Newton's method diverges, and the solution cannot be found. Jacobean is close to zero, if the radio emission source coordinates are located on the segment connecting the observation stations. The method of parameterization of the calculation system for increasing the convergence of the Newton method is considered. The efficiency of the proposed parameterization with different mutual arrangement of the passive radar system and the source of radio emission is analyzed, and proved for greater accuracy calculations should be chosen that hyperboloid, the angle at the top of which is the smallest. It was shown the conditions by that the hyperboloid parameterization allows object coordinates determining with rather high accuracy.
Highlights
Coordinates determination of the radio emission source (RES) by the multi-position complexes of a passive location is based on the time differential and range-metering method, which in foreign literature is called in abbreviated form as TDOA method (Time Difference of Arrival)
The system of mathematical equations expressing the distances and geometry structure of the stations and RES relative positioning consists of the unknown coordinates set at the minimum quantity of measurements, and the equations should not be linearly dependent
Analytical methods of the solution of the nonlinear equations systems guaranteeing receiving an acceptable result does not exist, systems of equations are solved by approximate iterative methods
Summary
Execution to the nonlinear equations properties Newton's method is as well the most effective. For n of points of observation (one of them is a central station of reception) the n-1 system of the nonlinear hyperbolic equations is necessary to solve In this case, the system of mathematical equations expressing the distances and geometry structure of the stations and RES relative positioning consists of the unknown coordinates set at the minimum quantity of measurements, and the equations should not be linearly dependent. The most common coordinates determination method in the passive location systems is the measurement of relative signal delays. The first attempts of the passive systems use came down to use of direction finding channels of radar station with the subsequent combination of information in the central station This method of determination of coordinates received the name triangular (direction finding, goniometric). Its essence consists in measurement by several RS, being at some distance from each other, the temporary arrival difference of the signal radiated by the source
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