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# Beginner's guide to GPS

GPS (Global Positioning System) is a satellite-based positioning and navigation system owned and operated by the US Department of Defense. Access is free for all users and the service is available 24 hours a day, 365 days a year. GPS is an all weather system that works anywhere in the world. GPS can give an instantaneous, real-time position to within approximately 10m using a single handheld receiver.

## How GPS works

Your receiver scans for and then locks onto signals from a number of GPS satellites. Each one continuously transmits its position. By measuring the distance – or range –from itself to each satellite it finds, your receiver triangulates its position and then either or both gives a numerical read-out and/or shows where you are as a pin on a map. The more satellites used to calculate your position, the higher the degree of accuracy of your stated position.

## Measuring the range to a satellite

Each satellite contains a very accurate clock (actually four very accurate atomic clocks) and the clock is used to generate a unique coded signal for each satellite.

The receiver on the ground generates the same coded signal at the same time and compares the received code with the one being generated.

The time difference between the two codes gives the time of signal travel between the satellite and receiver and:

range to satellite (D) = signal travel time (dt) x speed of light

A range measured in this way is often called a pseudorange. This is because because not all the errors in the measurement are taken into account and therefore the range measured is not the true one.

## Positioning using pseudoranges (trilateration)

Each satellite generates a different coded signal and this enables pseudoranges to several satellites to be measured at the same time.

The satellite positions are known and if the pseudoranges of the receiver to at least four satellites are measured, the position of receiver can be computed.

One pseudorange narrows down the postition to the surface of a sphere.

The second pseudorange narrows it down to a circle.

The third pseudorange narrows it to just two points.

The fourth pseudorange confirms the correct point from the two possibilities identified by the third pseudorange.

## Accuracies using a single GPS receiver

Positional accuracy with a single receiver, to civilian users approximately equals 5m to 10m, 95% of the time, and the height accuracy is generally 15m to 20m 95% of the time. Military users receive a more accurate coded signal from the satellites.

The positional accuracy is affected by GPS satellite orbit errors, the atmosphere and receiver clock errors. To give better accuracy, the known errors must accounted for all of them.

Like the satellites, the receiver uses a clock to generate the codes used in measuring the ranges. This clock is not as accurate as the one in the satellite; if it was, GPS receivers would be unaffordable! The receiver clock is therefore assumed to contain an error. Fortunately receiver clock errors can easily be computed if distances to 4 or more satellites are measured.

The GPS satellite orbit errors and errors introduced into the signal travel time due to it travelling through the atmosphere, cannot be computed by a single receiver in real time. The real-time positional accuracy of a single receiver can, however, be greatly improved by using a technique known as differential GPS (DGPS).

DGPS involves the computation of corrections to the GPS signals. The corrections counteract the effect of the remaining errors in the GPS position (orbit and atmosphere). The corrections are combined with GPS signals at the receiver to improve the computed position.

The corrections are computed using another GPS receiver at a known point. The receiver at the known point compares its computed and known positions and uses the differences to compute the corrections to the GPS signal.

The corrections, which can be used over a wide area, are then transmitted to other receivers in the area.

## Differential GPS services and accuracies

There are a variety of delivery mechanisms for the correction signal.

The GLA service improves the positional accuracy of a single GPS receiver to the 1-2m level.

These systems use geostationary satellites to beam down a footprint of corrections covering a wide area (for example, the UK). One such system is OmniSTAR. This type of system is usually available by subscription and they are based on a network of GPS receivers. The broadcast corrections are valid across the whole footprint area. Accuracy does not tend to vary with distance from a network GPS receiver and is more uniform over whole of the correction footprint.

## Surveying with GPS

GPS can be used as a surveying tool as well as a positioning tool.

When surveying with GPS, rather than the absolute positions of the points being measured, the baseline (three-dimensional distance) between two points is computed instead.

The answer is generally not instantaneous. GPS data has to be simultaneously collected at both points and used later in computations to determine the baseline. This is generally known as Static GPS.

Some systems compute the baseline in real time to give an almost instantaneous answer. This technique is generally known as Real-Time Kinematic (RTK) GPS.

The measurement of the baseline between the two points can be very accurate (cm level and better). This relative positioning of points with respect to each other is much more accurate than instant absolute positioning using one receiver.

At least two receivers are required. To get accurate absolute positions one receiver has to be on a known point. The Ordnance Survey active GPS Network provides a network of GPS receivers on known points that can be used for surveying with GPS.

The amount of data needed increases with baseline length and required accuracy.

The carrier wave of the coded signal is used rather than the coded signal itself.

The carrier wave can be used as an accurate ruler to measure the range to the satellite because 1 wavelength approximately equals 20 cm. This gives a more accurate range than a code derived pseudorange.

The range to the satellite is computed by calculating the whole number of wavelengths between the receiver and the satellite. Computation requires a time span of GPS data.

The final result of the data processing is a computation of the baseline between the two receivers. Due to this combination of data, many of the errors in the data cancel out, giving an accurate baseline result.

Two carrier waves (L1 and L2) of different wavelength are recorded. This requires a dual frequency receiver.

Using two wavelengths enables the atmospheric errors to be accurately modelled.

## Real-time surveying with GPS

The real-time technique is often called RTK (real-time kinematic) GPS. The set-up is exactly the same as static GPS except that the receiver at the known point (the base station) transmits its GPS data to other receiver (the rover) in real-time.

The baseline between the two points is computed in real time at the rover.

The baseline and the known coordinates of the base station are combined to give an instant position of the rover.

## The OS Active GPS Network

Static and RTK techniques are the most accurate forms of GPS. With high order static techniques, relative positions of a few millimetres are possible over hundreds of kilometres.

The highest accuracy requires a lot of data, geodetic equipment and specialist processing software.

Centimetre accuracy is possible with small amounts of data, standard equipment and software. RTK also gives centimetre accuracy.

Accurate positions require accurate known points. The OS Active GPS Network provides a network of GPS receivers on known points that can be used for surveying with GPS.