Sensor: GPS Transmitter

Description

The GPS transmitter is a component specific to the Spacecraft initialized within a GPS constellation. The purpose of the module is to compile the orbital properties required for a GPS message of the GPS satellite in question.

Example Use Cases

• GPS Constellation: Creating and transmitting the GPS navigation message of each GPS satellite.

Module Implementation

The message created in the GPS transmitter has three major sections which are the time properties, orbital properties and correction factors.

Time Properties

The Time properties for the GPS message are handled by the Spice Interface which it calculates the required GPS time properties with respect to the GPS starting epoch of 00:00:00h 6th January 1980.

Orbital Properties

The orbital properties required for the GPS navigation message are derived directly from the Classical Orbital Elements. The Mean Anomaly is derived using the following equation obtained from Kepler’s Equation using the eccentricity (e) and true anomaly (f).

\[ M=\tan^{-1}\bigg(-\frac{\sqrt{1-e^2}\sin(f)}{-e - \cos(f)}\bigg)+\pi-e\frac{(\sqrt{1-e^2})\sin(f)}{1+e\cos(f)} \]

The time-dependent variables such as the rate of inclination and the rate of Right Ascension of the Ascending Node (RAAN) are computed numerically using the method of finite differences across the previous time step and the present time. The following is a representation of the inclination and RAAN.

Correction Factors

The correction factors for the GPS message are currently user-defined and would be required to feed in correction factors for each GPS satellite defined in the constellation.

Assumptions/Limitations

• The time components namely the Time of Clock and Time of Ephemeris are assumed to be perfectly in sync with one another and across the entire simulation.

References

[1] Danby, John M.; Burkardt, Thomas M. (1983). "The solution of Kepler's equation. I". Celestial Mechanics

[2] Griffiths, D.V. and Smith, I.M. (2019) Numerical Methods for Engineers. Boca Raton: Chapman & Hall/CRC.