|
Have you ever stared out of your wheelhouse window and wondered how your satnav GPS works? How it accurately calculates
where you are located in the World? Well, global positioning systems, GPS, use a relatively simple method called Trilateration.
For example, if you knew you were 50 miles from Portland Bill, you could draw a circle on the chart and know you were located
somewhere on that circle. If you also knew you were 15 miles from Brixham, you could draw another circle on the chart, with
a radius of 15 miles, centred on Brixham and know that where the 50 and 15 mile circles intersected or crossed each other,
that that would be your position. But as the circles intersected at TWO points, you would require a third range, say
from Berry Head at 5 miles, in order to determine your OP - observed position. By receiving more information, your position
is refined and its accuracy increased. The same principal is applied to GPS - but in three dimensions and on a much larger
scale.
Twenty-seven satellites currently make up the GPS network, and the more satellites you are getting a signal from, the more
accurate your position will be. Each GPS satellite sends out high-frequency, low-powered radio signals. Your receiver calculates
how far each signal has travelled - by knowing the altitude of the satellite and the time the signal took to reach you. The
system then calculates your Latitude, Longitude and Altitude, and displays your position with an accuracy of less than
15 metres.
A more elaborate explanation, based on the diagram above, would be:-
1- Satellite's position is detemined relative to the Earth.
2- Location on Earth is located relative to the satellite.
3- THEN the Location's position on the Earth can be determined from the VECTOR sum
of the other two measurements. All measurements must are done to such a precision that the location on the Earth is known
to within 15 m.
METHODS
How are each of the two measurements Determined?
- The satellite's position is determined by high resolution radar observations, then
precision orbital parameters are determined to prepare accurate ephemerii. Many small perturbations must be included in the
preparation of the ephemerii.
- Non-spherical shape of the Earth (causes precession of the orbit)
- Tidal attraction
- Solar Radiation and Winds
- Air Drag
- Relativistic Effects
- Solar and Earth Magnetic Fields
- The distance from the satellite is determined by the time it takes for a radio wave
to reach the site from the satellite.
distance = (speed of light) x (time of flight)This is very simple but there are a few difficulties:
- The receiver clock is not exactly synchronized with the satellite clock so the time
of flight will be imprecise.
- The satellite and receiver are in different velocity reference frames and gravitational
regimes so there are relativistic differences (both special and general)
- The speed of light is 300,000 km/s in a vaccum. However, while travelling through
the Earth Ionosphere and Troposphere, the radio waves travel at slightly slower speeds.
- Radio signals travelling through the atmosphere travel differents paths depending
on the location of the receiver.
- The location is a vector and must also include direction.
In order to do this, distances from several satellites are required. This is called trilateration.
We wish to find our latitude, longitude and height above
the center of the Earth. These are three different
numbers and would require distances to at least three different satellites.
|
