The Principles of Satellite Position Estimation

The Principles of Satellite Position Estimation

The military designed GPS as a one-way ranging system to enable the user to be ‘passive’ and make no electronic noise.  Therefore, the radio signal only has to travel in one direction from the satellite to the receiver.  To enable the user to calculate an accurate range, the time of transmission of that signal must be accurately known at the receiver terminal to be able to estimate the range.  Therefore, two clocks are required and, most importantly, the clock at the point of transmission (the satellite) and the clock at the point of reception (the user’s receiver) must be precisely aligned.

This ranging technique is known asynchronous one-way ranging as the receiver clock is normally not aligned to GPS time.  To be able to range, the first action for the receiver to undertake is to calculate the time offset of the receiver clock to the time held by the satellites (GPS time); this is known as trilateration.

If the receiver clock is not precisely aligned then the range estimation will be too large (over range) or too small (under range).  An extremely simple analogy for one-way ranging is to consider your childhood and reflect how you calculated your distance from a thunderstorm.  When you saw a lightning flash you would start counting until you heard the noise of the thunder.  From this, you were able to estimate the range from that lightning strike based on the knowledge that that light travels at approximately 300,000 km/sec (almost instantaneously for a child) and that sound travels at 330 m/sec.  However, consider that if your internal count (your ‘local clock’) did not start at zero but started earlier (-1 sec) or later (+1 sec), what would the impact have been on your range estimation.  In our lightning example, for every second our timing was out that would be an error by - or + 330 m in the range estimation.

In the case of GPS timing, a 1 nanosecond error is approximately 30 cm and a 1 millisecond error is the equivalent of a 300 km range error.

Accurate ‘one way’ ranging can only be achieved if the time at the transmission point and at the receiver is precisely aligned.

Satellite navigation works along the following principles:

  • The satellite continuously broadcasts a timing pulse and onto that pulse information about the satellite and the constellation will be superimposed.
  • This information is in the form of a navigation message and this will tell the end user the time (Time T) when the next message will leave the satellite and where the satellite is estimated to be at that time (T).
  • The satellite continuously moves around its orbit (obeying the Kepler Orbital Laws).
  • At precisely Time (T), the satellite transmits the ranging signal.The receiver receives the signal with a delay that depends on its range (distance) to the satellite.  Provided the two clocks are synchronised, the time delay multiplied with the speed of light enables the receiver to calculate an estimated range from the satellite.
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