# The signal delay theory applied to GLONASS and GPS

### Mathematics. Physics. Mechanics

### Аuthors

Joint Stock Company “Russian Space Systems”, JSC “RSS”, 53, Aviamotornaya str., Moscow, 111250, Russia

e-mail: vovasov@list.ru

### Abstract

The objective of present paper is the method for computation of the location coordinates of GLONASS and GPS navigation satellites according to received ephemeris data and reasoning for the delays of gravitational interaction and electromagnetic signal being delivered from a satellite. Approach proposed in the paper is named the theory of a signal delay; it is based on the proper computation of the delays of signals and their derivatives. It was shown that the analogue of the electromagnetic signal delay proves to be a clock shift in one inertial coordinate system relative to another one – such data are stated in a special theory of relativity. When the radial range computed at the start moment of the gravitational interaction signal radiation, then the time delay could be interpreted as unaccounted time interval resulting in a calculation of the coordinates with errors based on the differential expression application.The intermediate results are the expressions to calculate the radial range during the signal radiation time interval as well as this interval to be computed. The expressions obtained are practically identical to the Lorentz transform as to coordinate and time in the case of small radial rates of the signal sources compared with the velocity of light. The results obtained are invoked to specify the calculations are related to the GLONASS and GPS coordinates computations and currently based on application of the general and special theories of relativity.

The theory of a signal delay is predicated on the classical representation of space and time and makes it possible to take into account the relativistic and gravitational effects and to explain them from the physically intelligible event – signals delay in the air.

### Keywords:

theory of delay of the signals, special theory of a relativity, GLONASS and GPS### References

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