N.V. Baranovskiy1, S.B. Nelipa2, A.V. Kosolapov3, V.O. Gavrilyuk4, V.S. Panko5

1–4 JSC «SPE «Radiosvyaz» (Krasnoyarsk, Russia)
5 Siberian Federal University (Krasnoyarsk, Russia)

1 nik.bar.2001@mail.ru, 2 sb.nelipa@yandex.ru, 3 dwl@mail.ru, 4 ejiick@bk.ru, 5 vpanko@sfu-kras.ru

Achieving high accuracy in determining the coordinates of objects is one of the most important goals when working with radio navigation equipment. An incorrect choice of the initial approach point can affect the operation of the entire radio navigation system. Not for every relative location of the reference stations there is such an approximation point that can ensure the convergence of the algorithm with the initial approximation for the entire area of operation of the system.

To perform such a study, a program has been developed to evaluate the influence of the approximation point on the convergence of the least-squares method (LSM). With the help of this program, a simulation has been carried out and the influence of the location of the approach point on the solution of the navigation problem has been investigated. The work uses LSM and the Levenberg-Marquardt method.

Based on the simulation results, it has been determined that it is better to place an approximation point between the axes. With this arrangement, although the size of the convergence zone is lower than when the point is located outside the triangle between the axes, there are no convergence zones. This gives a more predictable picture of the location of the coordinates, where full convergence of the algorithm will be achieved. That is, the diagram shows smooth transitions from areas of complete convergence to incomplete convergence, as well as the absence of areas of complete dissimilarity of the algorithm, which makes it possible to make predictable adjustments when the antenna-probe moves.

Baranovskiy N.V., Nelipa S.B., Kosolapov A.V., Gavrilyuk V.O., Panko V.S. Investigation of the effect of the initial approximation of coordinates when determining the location of an object using the difference-range method. Achievements of modern radioelectronics. 2026. V. 80. № 2. P. 49–59. DOI: https://doi.org/10.18127/j20700784-202602-05 [in Russian]

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