# How The Gps Works Principles Computer Science Essay

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As Global Positioning System may be used either as a positioning tool or as a survey tool, archaeologists are introducing this technique to many of their survey tasks on site. This guide outlines the basic principles of GPS and its use in archaeological work.

The GPS system consists of 24 satellites. The number may vary slightly as new ones are launched and old ones are retired. Each satellite is in an 11,000 mile orbit and transmits a very weak signal. The system is monitored and maintained by the U.S. Military. The satellites only broadcast to the user and the user only receives. There is no charge for use.

To start with, assume that all of the satellites and the receiver have a perfect internal clock. This is not the case, but it makes a good starting point. Each satellite transmits a coded signal. Consider this signal to be like the peaks and ridges along the edge of a super long key. This code is generated as a function of time. The receiver is also able to generate the same code. The receiver

matches the incoming code to the internally generated code except that there is a delay caused by the signal's travel time between the satellite and the receiver.

The receiver measures how much it has had to shift the timing of its code to match the incoming code. Since the receiver knows how much time it took the signal to reach the receiver and the speed of travel of the signal, it can then calculate the distance from the satellite.

If you know how far you are from one satellite then you know that you are somewhere along an imaginary sphere around that satellite. If you know how far you are from two satellites, then you are somewhere along the intersection of where these two spheres, which is a circle. If you add another satellite, then you are somewhere where this third sphere intercepts the circle created by the intersection of the other two spheres. The sphere will most likely intercept the previous circle at two points. One of these points is where you are, and the other is not a reasonable solution - somewhere in outer space. Thus by knowing where you are relative to these three satellites the receiver with a perfect clock can know where it is.

Although no clock is perfect, the satellites have atomic clocks-pretty close. The clock in the GPS receiver is closer in technology to an inexpensive digital watch. Light travels at 186,000 miles per second. If the receiver time was off by 1/100 of a second the calculated distance would be off by 1,860 miles.

For each receiver to have its own cesium clock would make GPS technology prohibitively expensive and non-portable. What the GPS receiver does is to use a cheap clock similar to a digital watch and add one more satellite to the calculation to correct the time in the receiver. The receiver shifts the time calculation back and forth so that all of the imaginary spheres around the satellites intercept at one point.

For three-dimensional navigation you need to receive four satellites. Think of it as one satellite for each dimension and one for the time. For two-dimensional navigation you can scrape by with only receiving three satellites. If you know your altitude, the GPS can treat the center of the earth as a satellite reducing the number of required satellites by one. Your distance from the center of the earth is the radius of the earth plus your altitude. This is why aviation GPS models have barometric altimeter input and you may occasionally see a handheld GPS ask for your altitude during poor reception conditions.

Newer GPS receivers use the extra signals above the minimum that is required to further refine the position for increased accuracy. This is known as an over determined solution.

The use of GPS may appear at first complicated, but the principle is quite simple.

GPS stands for Global Positioning System -a shorted term for NAVSTAR GPS (NAVigation Satellite Timing and Ranging) -a system for locating ourselves on earth. It is a satellite-based system created and controlled by the US Department of Defense, initially for military purposes but extended later for civilian usage. It consists of a constellation of 24 satellites (4 satellites in 6 orbital planes) orbiting at an approximate altitude of 20200 km every 12 hours.

Each satellite broadcasts two carrier waves in L-Band (used for radio) that travel to earth at the speed of light. The L1 channel produces a Carrier Phase signal at 575.42 MHz as well as a C/A and P Code. The L2 channel produces a Carrier Phase signal of 1227.6 MHz, but only P Code.

These codes are binary data modulated on the carrier signal. The C/A or Coarse/Acquisition Code (also known as the civilian code), is modulated and repeated every millisecond; the P-Code, or Precise Code, is modulated is repeated every seven days.

The GPS system works with a receiver (essentially a radio receiver) that acquires signal from satellites in order to locate its position geographically. The GPS receiver simply calculates the distance to the satellite by measuring the travel time of the signals transmitted from the satellite and multiplying it by the velocity.

Distance = velocity (speed of light) x Time

The GPS receiver computes its position and time by making simultaneous measurements to the satellites. A signal from three satellites will sort out a 2-dimensional position or horizontal position. In order to get a 3 dimensional position (latitude, longitude and height) at least four satellites are needed within signal range.

## 2. Accuracy

There has been a misconception over the past years about the accuracy of GPS. It is true that for many years the US Department of Defense maintained intentional degradation of accuracy called Select Availability (S/A), a system for randomly degrading the accuracy of the signals being transmitted to civilian GPS receivers. However, the S/A was removed in May 2000.

Therefore, the accuracy of GPS should be a discussion based on the type of system (device) and its ability to eliminate error sources and not on the availability of reliable satellite signals.

Error sources are variable; here are some of the more commonly occurring:

Ionospheric delays. The ionosphere is the upper layer of the atmosphere ranging in altitude from 50 to 500 km. It consists largely of ionized particles which cause a disturbing effect on the GPS signals. Since the density of the ionosphere is affected by the sun there is less ionospheric influence during night time. The ionosphere has also a cyclical period of 11 years which reaches a maximum and a minimum of the magnitude of its effect. For the current cycle, it reached its maximum in 1998 and its minimum in 2004.

In addition, low elevation satellite signals (anywhere between the horizon and up to 15 degrees above it) will be affected by a longer ionospheric delay as the distance the signal has to travel further and generally "noisier". In the more sophisticated GPS receivers an "elevation mask" can be set so that satellites below the mask are not used in computing position.

Satellite and receiver clock errors. Each satellite is equipped with a very accurate clock which is continuously monitored by ground stations (US Department of Defense). Despite this, errors of precision can be up to one metre.

Each receiver also has a clock but less accurate than the satellite's clock (its cost - around \$50000- and weight -20kg- would not be suitable for a land GPS).

ï‚• Multipath error. This is where more than one signal is received due to a reflection on other objects nearby (tall buildings or lakes) causing erroneous measurements.

ï‚• Satellite geometry. This means the relative position of the satellites at a specific moment. When satellites are located at wide angles relative to each other, the possible error margin is small. On the contrary, when satellites are grouped together or located in a line the geometry will be poor. The effect of the geometry of the satellites on the position error is called Geometric Dilution of Precision (GDOP). GDOP comprises the components shown below, which can be individually computed but are not independent of each other:

PDOP - Position Dilution of Precision (3-D)

HDOP - Horizontal Dilution of Precision (Latitude, Longitude)

VDOP - Vertical Dilution of Precision (Height)

TDOP - Time Dilution of Precision (Time)

## 3. Types of GPS

Broadly speaking, there are three types of GPS, depending on the level of acquired accuracy.

Hand-held GPS or Navigational (> c. 10m) Differential Code-Phase GPS (DGPS) (< 1m) Carrier-Phase GPS (< cm)

## Hand-held GPS

The Navigational or hand-held GPS consists of a single receiver, as easy to use as a mobile phone and around the same cost. It is the simpler technique of GPS but also the least accurate. The position calculated from the satellites' signal is frequently distorted by sources of error, which can degrade its accuracy by several metres (about 15 to 100 m).

Figure 3: Hand-held GPS

## 3.2 Differential Code-Phase GPS (DGPS)

This differential measurement technique eliminates most of source errors, achieving results of sub-metre accuracy. It is obviously a more complex system than hand-held GPS - which is reflected in its substantially higher cost.

It consists of a base station and a rover receiver connected by a radio link. The base station or reference receiver when located at a known point can estimate what the ranges to the satellites should be and work out the differences between the computed and calculated range values. These differences are known as corrections. The base station transmits these real time differential corrections to the rover receiver (through the radio) so they can be used to correct its measurements. The DGPS corrections are transmitted in a standard format specified by the Radio Technical Commission Marine (RTCM).

One of the powerful radio transmitters is the Radio Beacon. Set up around the coastline of many countries, these transmitters are located at old Radio Beacon stations, and have ranges of 100-150 miles. The DGPS signals are radiated on frequencies in the old MF (medium frequency) Beacon band, around 300 kHz. (For a detailed table with Radio Beacons available in the UK consult the Northern Light-House Board at:

http://www.nlb.org.uk/dgps/dgpschart.htm

The users of these transmitters were mainly marine craft navigators, but in some countries such as the UK -where the system transmitters cover the inland territories, they are now being operated by other users.

Another radio transmitter is the OmniSTAR Inc, working in a similar way to the beacons. It consists of a network of GPS base receivers around the world, which broadcast corrections to user receivers. Access to these corrections is available by subscription. For more information consult:

www.omnistar.com

There are also new satellite-based differential systems, free of charge, such as WAAS, EGNOS and MSAS. The Wide Area Augmentation System (WAAS) is designed to provide a higher confidence level in autonomous GPS positioning for use in aviation. Unlike radio and satellite differential, WAAS corrects the atmospheric and orbital data so that autonomous calculations can better determine true position. But as the system is designed for aircraft, there are still some limitations for non aviation users.

The European Geostationary Navigation Overlay Service (EGNOS) is Europe's first step into satellite navigation, an initiative of the European Space Agency (ESA), the European Commission and Eurocontrol. For more information consult: http://www.esa.int/export/esaNA/egnos.html

The Japanese Multi-function Transport Satellite Augmentation System (MSAS), sponsored by the Japanese Civil Aviation Bureau, is designed to provide a satellite-system in some of the Far Eastern areas.

## 3.3 Carrier-Phase GPS

This differential system achieves accuracy ranging from centimetre to millimetre, depending on the measuring technique. The Carrier-Phase GPS uses a minimum of two receivers simultaneously.

## 4. Co-ordinate systems

It is essential to mention some elements of geodesy as the study of the Earth's shape and its representation, for a better understanding of GPS survey and its relation to local mapping. The

Earth is represented by various co-ordinate systems made to fit specific areas of its surface. Each mapping system is based on a local ellipsoid, designed to match the geoid. The ellipsoid is a mathematical surface that approximates the shape of the earth and the geoid is a theoretical surface which most closely matches mean sea level, both created to ease the representation of the Earth.

Figure 6: Geoid, ellipsoid and surface of the Earth (after Ordnance

To provide grid co-ordinates, each local co-ordinate system will have been projected onto a plane surface, using the projection that better suits the area to be represented. A projection is the method used to represent the 3 dimensional curved surface of the spheroid on a plane surface.

## 4.1 OSGB36

In Great Britain, the National Grid is based on a Transverse Mercator Map projection. This projection is based on a cylinder that is slightly smaller the spheroid and is then flattened out. The Easting and Northing axes are given a false origin just south-west of the Scilly Isles to ensure that all co-ordinates in Britain are positive. The false origin is 400 km west and 100 km north of the true origin on the central meridian at 49Â° N 2Â° W. To reduce the number of figures needed to give a National Grid reference, the grid is divided into 100 km squares which each have a two-letter code. National Grid positions can be given with this code followed by an Easting between 0 and 100 000 m and a Northing between 0 and 100 000 m.

All Great Britain height values above sea level are related to ODN, Ordnance Datum Newlyn, a traditional vertical co-ordinate system based on mean sea level tidal observations at Newlyn in Cornwall between 1915 and 1921.

Figure 7: Representation of ellipsoidal height in relation to the ODN (after Ordnance Survey

For a detailed explanation to Great Britain co-ordinate system consult: http://www.gps.gov.uk/guidecontents.asp

## 4.2 GPS co-ordinates systems: WGS84 and ETRS89

Data received from GPS is related to a global co-ordinate system known as WGS84 or World Geodetic System 1984. GPS position will be expressed in latitude, longitude and ellipsoid height.

However, the WGS84 co-ordinate system will become unacceptable when using fixed points for land surveying. This is caused by the constant motion of continents with

respect to the WGS84 co-ordinate system: in Great Britain, it moves on a rate of 25mm per year away from the WGS84, meaning that in reality there are no fixed points.

For this reason, the European Terrestrial Reference System 1989 (ETRS89) is used as the standard precise GPS co-ordinate system throughout Europe. The ETRS89 is tied to the European continent, and hence it is steadily moving away from the WGS84 co-ordinate system.

If co-ordinates are required in a local mapping system, a transformation from GPS WGS84 or ETRS89 is needed.

For Great Britain, the most accurate transformations are the Ordnance Survey's OSTN02 and OSGM02 (available free from their website www.gps.gov.uk). The OSGM02 geoid model will transform the ellipsoid height onto orthometric height, above sea level.

Furthermore, Great Britain's Ordnance Survey enables GPS users to tie their positions with the National Grid through the use of the National GPS network. The Ordnance Survey active GPS network consists of 32 permanently installed geodetic quality GPS receivers throughout Great Britain. Most locations in Great Britain are within 75 km of at least one active station, and several serve major urban areas. These active stations record dual-frequency GPS data 24 hours a day and their position is in relation to the ETRS89 co-ordinate system.

Additionally, there are 900 passive stations but with the disadvantage of having to be occupied e by the user's own GPS receiver.

ETRS89 co-ordinates and full information from both active and passive stations are supplied by Ordnance Survey through their website ready to use for post-processing.