Global Positioning System

Chris Angove is familiar with the principles of the NAVSTAR system constellation and how they operate and he is currently improving his knowledge of the European equivalent, the Galileo System. He has supported the design and development of a GPS receiver for a military application, complete with many of the particular requirements of hardware intended for military end users.

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  1. Satellite Orbits
  2. The Navstar System of Global Positioning Satellites
  3. Theory of Operation
  4. Accuracy
  5. GPS and Precision Timing Applications

  1. Orbiting Satellites in General
  2. The orbits of satellites around the earth obey Kepler's Laws:

    1. The Law of Orbits. Orbits follow elliptical paths with one of the foci at the Earth's centre. (Recall that this includes circular orbits, since a circle is an ellipse with both foci coincident.)
    2. The Law of Areas. Within the orbit plane, a line joining the focus and the satellite will sweep out equal areas in equal periods of time.
    3. The Law of Periods. The square of the period of the satellite about the Earth is proportional to the cube of the satellite's mean distance from the Earth.

    Several factors influence the choice of GPS satellite orbits including coverage of the most populated areas of the Earth's surface, 'visibility', Doppler correction and availability. There is also a limit to the number of satellites it is economical to deploy, the result of a kind of diminishing returns.

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  3. The Navstar System of Global Positioning Satellites
  4. This is the American managed constellation of satellites currently used for the majority of global positioning systems. These are the main parameters:

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  5. Theory of Operation
  6. Each satellite transmits 2 'L' band signals centered at:

    L1 is modulated with 2 pseudo-random noise signals, known as:

    L2 carries only the P code.

    The data carried includes the time of departure of the signal and an identity of the satellite. Each satellite contains a highly accurate atomic clock. We have to assume that every satellite's clock is accurately set and the satellite's position is known accurately at any instant. Each receiver also has a clock, but of limited accuracy due to the obvious size/cost constraints to be widely available. Fortunately the absolute accuracy of the receiver clock does not need to be particularly high, it just needs to maintain stability over a short time, perhaps a few seconds, whilst a measurement is being made. Sometimes this is known as a flywheel clock, a good analogy to the mechanical equivalent.

    The whole principle depends on measuring how long the signal takes to travel from the satellite to the receiver antenna. We know the velocity of electromagnetic radiation accurately so, once this is known for each satellite we can define a sphere, centered at the satellite itself, which would include the receiver antenna somewhere on its surface. It only requires three similar measurements to determine the position of the receiving antenna in three dimensions. However, as with any measurements, the more measurements that are made and averaged, the more accurate will be the final result, and generally a minimum of 4 are made. If you want to measure a fixed point on the Earth's surface, for example a mountain peak, this is fine. Just set up the antenna accurately, switch on the receiver and let it number crunch for a perhaps a few hours and you will get a very accurate result. However this is not practical if you are using GPS to drive from Marble Arch to The Elephant and Castle.

    I would not pretend to know a great deal about GPS, but I can see that the receiver needs to be quite intelligent to process the data it receives from the satellites. To obtain the greatest possible accuracy, all of the following and more need to be allowed for:

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  7. Accuracy
  8. The Navstar system has both civilian users and military users. We can probably all guess a number of interesting military applications but I will only tell you what I know about the civilian service.

    Horizontal Accuracy

    Some 20 m of horizontal accuracy is available to civilian users from the Standard Positioning Service (SPS). This is degraded to 100 m for 95% of the time due to selective availability (SA).

    Vertical Accuracy

    This is 1.5 times worse than the horizontal accuracy, on account of the satellites spending relatively short periods overhead.

    The accuracy can be monitored by high quality receivers fed from antennas at accurately known positions on the Earth's surface. Appropriate adjustments may be made to the satellites via uplink control signals.

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  9. GPS and Precision Timing Applications
  10. GPS and Precision Timing Applications is a very good HP Application Note.

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    Chris Angove
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