Analytical methods for determining the navigation parameters of aircraft based on signals from ground-based radio beacons


Аuthors

Airapetov A. M.1, Pimenov V. A.2*

1. School «World – Intelligence – Discovery – Education», Moscow, Russia
2. National Radio Technical Bureau, Moscow, Russia

*e-mail: va.pimenov@yandex.ru

Abstract

Ground-based radio beacon systems can provide redundant local or regional navigation. Such systems may include geographically dispersed radio beacons (RB) that simultaneously (simultaneously or in a known sequence) emit navigation signals into the surrounding space to be used by air and ground objects. Aircraft both manned and unmanned, are among the most promising consumers of radio signals of ground navigation systems (GNS), due to their high-altitude flight, which ensures an extended reception range. The article presents analytical methods of solving navigation problems for pseudo-range and difference-range methods of determining the coordinates of the aircraft from the data of passive onboard terminals receiving the signals of radio beacons, which are part of the ground navigation system. Algorithms for solving navigation problems for minimal and redundant number of beacons included in the system are considered. The results of modeling the process of determining the navigation parameters of aircraft in the presence of measurements errors are provided.
To determine the coordinates of the aircraft by pseudo-rangefinder method, the minimum number of beacons in the GNS, emitting radio signals, should be equal to four, according to the number of unknowns. The system of equations contains three linear and one nonlinear equation. The analytical method of its solution is defined. When solving the nonlinear equation with respect to the discrepancy between the onboard and ground time scales, an extraneous root appears. An effective method of its elimination is found.
It is shown that, when using radio signals from five radio beacons, the determination of the aircraft coordinates and the temporal inconsistency of the scales by the pseudo-rangefinder method is reduced to the solution of a linear system of four equations. In this case there is no problem of finding an extraneous root.
When finding the aircrafts coordinates by the differential-rangefinder method, the minimum number of radio beacons in the GNS is four However, in order to exclude the influence of extraneous solution of the nonlinear equation at large measurement errors occurring at a distance from the location of the RB5, it may be reasonable to use five RBs, in this case the determination of the coordinates of the aircraft is reduced to the solution of a linear system of three equations, and the solutions are tied to the onboard time scale. In the presence of pseudo-ranges from the equations it is also possible to find the inconsistency of onboard and ground time scales. In a particular case, when all beacons are in the horizontal plane, four radio-beacons are enough, and analytical solutions of the equations have a more compact form. The results of modeling the process of determining the parameters of aircraft motion when flying over the airfield at an altitude of 1000 m with simulated pseudo-range measurement errors are presented.
A generalization of the linear algorithm for the estimation of Aircraft coordinates from the relative ranges measured by the differential-rangefinder method for the redundant group of RBs is carried out. A significant change in the contribution of individual partial solutions to the overall solution during the aircrafts motion is shown by modeling. The proposed approach for a redundant number of RBs can also be used for the pseudo-rangefinder method of determining navigation parameters.
To improve the accuracy of coordinate determination by the considered methods, it is advisable to smooth both input and output data using the least squares method.

Keywords:

navigation, ground radio navigation system, radio beacon, aircraft, pseudo-rangefinder and differential-rangefinder methods, analytical solution

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