V.G. Markin – Leading Engineer, JSC SPE «PROTEK» (Voronezh)
One of the automated command and control system (ACCS) functions is localization of mobile ground targets. This function can be realized by different methods including distance measurements from an object with unknown coordinates to beacon stations of a ground-based local radio navigation system (GRNS) with known coordinates.
Distances between beacon stations and a target are connected with its coordinates by a system of linear and quadratic equations. The usual way to solve a system of nonlinear equations is linearization via Taylor series expansion and using a successive approximation method. However, this method requires initial approximation and is very sensitive to its choice. Furthermore, successive approximations are highly time-consuming due to multiple operations of the same type.
This paper proposes four direct non-iterative methods, in which a system of nonlinear equations is solved by transforming them into linear equations. These methods are based on different ways of removing the quadratic term in nonlinear equations and thus trans-forming them into linear equations.
Identical transformations of a system of nonlinear equations into a system of linear equations ensure no errors in the solution caused by linearization.
Furthermore, the computational cost of direct methods is negligible compared to the cost of iterative methods, which involve approx-imations.
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