PowerPoint Presentation - Global Positioning System ( GPS )

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Global Positioning System (GPS)

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Introduction

• The current global positioning system (GPS) is the culmination of years of research and unknown millions of dollars.

• The current system is managed by the U.S Air Force for the Department of Defense (DOD). • The current system became fully operational June 26, 1993 when the 24th satellite was lunched.

http://www.trimble.com/gps_tutorial/ 2

Introduction--cont.

• GPS provides specially coded satellite signals that can be processed with a GPS receiver, enabling the receiver to compute position, velocity and time.

• A minimum of four GPS satellite signals are required to compute positions in three dimensions and the time offset in the receiver clock.

• Accuracy and precision of data increases with more satellites.

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• Space segment • Control segment • User segment

Three Parts

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Space Segment

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Space Segment--Information

• The GPS uses a constellation of 24 satellites that orbit the earth at about 11,000 nautical miles, once every 12 hours.

• The orbital position is constantly monitored and updated by the ground stations.

• Each satellite is identified by number and broadcasts a unique signal.

• The signal travels at the speed of light.

• Each satellite has a very accurate clock, 0.000000003 seconds 6

Space Segment--Satellite Signals

• Because the GPS receiver calculates its location by trilateration, he task of the receiver is to determine its distance from multiple satellites. • The GPS system uses two types of signals to calculate distance.

– Code-phase ranging – Carrier-phase ranging 7

Space Segment--Satellite Signals--Code-Phasing Ranging

• Each satellite has a unique signal.

• It continuously broadcasts its signal and also sends out a time stamp every time it starts.

• The receiver has a copy of each satellite signal and determines the distance by recording the time between when the satellite says it starts its signal and when the signal reaches the receiver.

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Space Segment--Satellite Signals--Code Phasing Ranging – cont.

• Distance is calculated using the velocity equation.

• Rearranging the equation for distance:

Velocity = Distance Time Distance = Velocity x Time

determined.

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

Distance Example —Code Phase Ranging

• The signals from the GPS satellites travel at the speed of light- 186,000 miles/second. • How far apart are the sender and the receiver if the signal travel time was 0.23 seconds?

Distance (ft) = Velocity (mi/sec) x Time (sec) mi = 186,000 sec x 5208 ft mi 0.23 sec = 2,257,8400 ft • It should be clear that this system requires very accurate measurement of time and synchronization of clocks.

• These time errors limit the precision of this system.

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Space Segment —Carrier-Phase Ranging

• Surveying quality receivers use the underlying carrier frequency.

• Easy to determine number of cycles.

• The proportion of a partial cycle is difficult to determine.

• This is called phase ambiguity.

• Phase ambiguity error is resolved by comparing multiple signals from multiple receivers.

• More precise system.

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Receiver Segment

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Receiver

• The receiver collects, decodes and processes the satellite signals.

• The basic receiver does not include a transmitter.

• Different levels of precision are available.

• The receiver determines its location by trilateration.

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GPS Trilateration

• Each satellite knows its position and its distance from the center of the earth.

• Each satellite constantly broadcasts this information.

• With this information and the calculated distance, the receiver calculates its position.

• Just knowing the distance to one satellite doesn’t provide enough information.

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GPS Trilateration--cont.

• When the receiver knows its distance from only one satellite, its location could be anywhere on the earths surface that is an equal distance from the satellite.

• Represented by the circle in the illustration.

• The receiver must have additional information.

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GPS Trilateration--cont.

With signals from two satellites, the receiver can narrow down its location to just two points on the earths surface.

Were the two circles intersect.

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GPS Trilateration--cont.

• Knowing its distance from three satellites, the receiver can determine its location because there is only two possible combinations and one of them is out in space.

• In this example, the receiver is located at b.

• The more satellite that are used, the greater the potential accuracy of the position location.

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Factors Influencing Position Accuracy

The number of satellites (channels) the receiver can track.

– The number of channels a receiver has is part of it’s design.

– The higher the number of channels---the greater the potential accuracy.

– The higher the number of channels---the greater the cost.

• The number of satellites that are available at the time.

– Because of the way the satellites orbit, the same number are not available at all times.

– When planning precise GPS measurements it is important to check for satellite availability for the location and time of measurement.

– If a larger number of channels are required (6-10), and at the time of measurement the number available was less than that, the data will be less accurate.

The number of different systems that the receiver can track.

– WAAS [Wide Area Augmentation System] FAA & DOT – GLONASS [GLObal'naya NAvigatsionnaya Sputnikovaya Sistema] Russian 18

Factors Influencing Position Accuracy--cont.

 The system errors that are occurring during the time the receiver is operating.

– The GPS system has several errors that have the potential to reduce the accuracy.

– To achieve high levels of precision, differential GPS must be used.

• Differential GPS uses one unit at a known location and a rover.

– The stationary unit compares its calculated GPS location with the actual location and computes the error.

– The rover data is adjusted for the error.

• Real Time Kinematic (RTK) • Post processing 19

Location

Once the GPS receiver has located its position it is usually displayed in one of two common formats: – Latitude and longitude – Universal transverse Mercator (UTM).

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Latitudes and longitudes are angles.

Latitude and Longitude

Both use the center of the earth as the vertex, but they use a different zero reference.

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Latitude

• Latitude gives the location of a place on the Earth north or south of the Equator. • Latitude is an angular measurement in degrees (marked with ° ) ranging from 0 ° the Equator to 90 ° at the poles (90 ° the North Pole or 90 ° N for S for the South Pole) at The earth’s circumference is approximately 24,859.82 miles around the poles.

Miles Degree = 24859.82 miles 360 degrees = 69.05 miles/degree  69 miles   Stillwater has a latitude of 36.026

o . This puts Stillwater 2,485.79 miles north of the equator.

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Latitude--Equator

   The Equator is an imaginary circle drawn around the planet at a distance halfway between the poles.

The equator divides the planet into a Northern Hemisphere and a Southern Hemisphere. The latitude of the equator is, by definition, 0 ° . 23

Latitude--cont.

Four lines of latitude are named because of the role they play in the geometrical relationship with the Earth and the Sun.

– Arctic Circle — 66 ° 33′ 39″ N – Tropic of Cancer — 23 ° 26′ 22″ N – Tropic of Capricorn — 23 ° 26′ 22″ S – Antarctic Circle — 66 ° 33′ 39″ S 24

Longitude

Longitude describes the location of a place on earth east or west of a north south line called the Prime Meridian. – Longitude is given as an angular measurement ranging from 0 ° Prime Meridian to +180 ° −180 ° westward.

at the eastward and – In 1884, the International Meridian Conference adopted the Greenwich meridian as the universal prime meridian or zero point of longitude.

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Longitude--cont.

The circumference of the earth at the equator is approximately 24,901.55 miles.

Miles Degree = 24901.55 miles 360 degrees = 69.17 Miles Degree

Each degree of longitude

69 miles

 Stillwater has a longitude of -97.086. This puts Stillwater 6,698.934 miles west of the prime meridian, at the equator.

 26

Longitude--cont.

• • • • There is an important difference between latitude and longitude.

The circumference of the earth declines as the latitude increase away from the equator.

This means the miles per degree of longitude changes with the latitude.

This makes determining the distance between two points identified by longitude more difficult.

Latitude ( o )

0 10 20 30 40 50 60 70 80

Miles/deg.

69.17

68.13

65.03

59.95

53.06

44.55

34.67

23.73

12.05

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Mercator Projection • A Mercator projection is a ‘pseudocylindrical’ conformal projection (it preserves shape).

• Points on the earth are transferred, on an angle from the center of the earth, to the surface of the cylinder. • What you often see on poster-size maps of the world is an equatorial Mercator projection that has relatively little distortion along the equator, but quite a bit of distortion toward the poles.

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Mercator Projection-cont.

• In this illustration it can be seen the the projected distance is greater than the earth distance.

• Within a few latitudes of the equator the distortion is very small, but the distortion increases as latitude increases.

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Transverse Mercator Projection

• Transverse Mercator projection rotates the earth 90 degrees with in the cylinder.

• In this projection a small increases in longitude are relatively undistorted. 30

Transverse Mercator Projection

• This illustration shows that when transverse Mercator is used, narrow vertical slices of the earth have little distortion. 31

UTM Zones

The world is divided into 60 zones of latitude, each 6 o wide at the equator, that extend from 84 o N to 80 o s.

These zones begin consecutively eastward.

at 180 o longitude and are numbered 32

UTM Zones--cont.

• • The conterminous United States is covered by 10 UTM grid zones. In the Northern Hemisphere each zone's northing coordinate begins at the equator as 0,000,000 and is numbered north in meters. The easting coordinates are measured from an artificial reference line drawn perpendicular to the equator and centered in the zone at the equator.

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UTM--cont.

• The UTM system uses a different grid for the polar regions.

• These areas are covered by a different conformal projection called the

Polar Stereographic

. • Since compass directions have little meaning at the poles, one direction on the grid is arbitrarily designated "north-south" and the other "east-west" regardless of the actual compass direction. • The UTM coordinates are called "false northing" and "false easting.” 34

Using Location Information

• • • Each system has its advantages and disadvantages.

Latitude and longitude

Advantages

With the proper instruments, a person can determine their position at the site without using GPS.

Used by most maps

Disadvantages

Difficult to determine distances between two or more points.

UTM

Advantages

Best method for determining distances between two points .

Disadvantages

Not as useful for finding a location.

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Determining UTM Zone

• Treat west longitude as negative and east as positive.

• Add 180 degrees; this converts the longitude to a number between zero and 360 degrees.

• Divide by 6 and round up to the next higher number.

• Example: – The location of the intersection of Hall of Fame and Virginia on OSU campus is 56 7 23.71 N and 97 05 16.079 W.

-97.088 + 180 = 82.912

82.192

6 = 13.8 = 14

 36

Determining a UTM Grid Value for a Map Point

• The UTM grid is shown on all quadrangle maps prepared by the U.S. Geological Survey (USGS). • On 7.5-minute quadrangle maps (1:24,000 and 1:25,000 scale) and 15-minute quadrangle maps (1:50,000, 1:62,500, and standard edition 1:63,360 scales), the UTM grid lines are indicated at intervals of 1,000 meters, either by blue ticks in the margins of the map or with full grid lines. • The 1,000-meter value of the ticks is shown for every tick or grid line.

http://erg.usgs.gov/isb/pubs/factsheets/fs07701.html

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Determining a UTM Grid Value for a Map Point--cont.

• To use the UTM grid, you can place a transparent grid overlay on the map to subdivide the grid, or you can draw lines on the map connecting corresponding ticks on opposite edges. • The distances can be measured in meters at the map scale between any map point and the nearest grid lines to the south and west. • The northing of the point is the value of the nearest grid line south of it plus its distance north of that line; its easting is the value of the nearest grid line west of it plus its distance east of that line.

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Determining Distance Using UTM

• In the illustration the UTM coordinates for two points are given.

• The distance can be determined using Pythagorean Theorem because UTM is a grid system.

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

UTM Example--cont.

• Subtracting the easting proved the length of the horizontal side: 208,000 meters.

• Subtracting the northing proves the length of the vertical side: 535,000 meters.

• The distance between the two points is: Distance = 535,000 2  208,000 2 = 574011.32... or 574,000 meters Note: this is the plane distance. To find surface distance a curve equation must be used.

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Ground Segment

The ground segment has one master control, one alternative master control station, 12 command and control antennas and 16 monitoring sites.

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GPS Errors

• • • • • Satellite geometry Satellite orbits Multipath Atmospheric effects Clock 42

Error-Satellite Geometry

• Describes the position of the satellites with each other.

• The best geometry, and least error, occurs when the satellites are equally distributed.

• Satellite geometry error occurs when the satellites are concentrated in on quadrant or in a line.

• The Positional Dilution of Precision (PDOP) is an indication of the quality of the 3D coordinate satellite geometry.

– General surveys PDOP’s should be less than 3.

• Satellite geometry error is not measureable, it tends to enhance other errors.

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Error-Orbits

• Even though the satellites are positioned in very precise orbits, slight shifts are possible do to the gravitational influences of the sun and moon.

• Orbit errors can be as high as 2 meters.

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Error-Multipath

• Multipath errors are caused by satellite signals reflecting off of objects.

• Increase chance of occurrence when around tall buildings.

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Error-Atmospheric

• Radio signals travel at the speed of light in space, but are slowed down by the atmosphere.

• The majority of this effect can be eliminated by the receiver.

– Lower frequency signals are slowed down more that high frequencies.

– The receiver can determine the difference in the arrival time of high and low frequency signals and calculate a correction.

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Error-Clock

• In spite of the synchronization of the satellite and receiver clocks, and small amount of inaccuracy in timing remains.

• This can result in errors up to 1 meter.

• To keep clock errors to 1 meter or less, the time error must be be limited to 20-30 nanoseconds.

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Using GPS

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Availability

• Because GPS satellites are not stationary above one point of the earth, like telecommunication satellites, the number of satellites available at any one time is not constant.

• • The satellite availability should be checked before scheduling a GPS survey. Especially when high precision is required and /or you know that some stations may be partially blocked.

One site is: http://www.calsky.com/cs.cgi

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Example of Satellite Availability 50

Global Navigation Satellite System (GNSS) Terms

• • • • • • As the size of the area increases the dilution of precision increases. The dilution of precision is given in multiple measurements.

GDOP – Geometric dilution of Precision – A combination of navigational position and time error PDOP – Positional Dilution of Precision – The spatial geometrical quality of the positional solution. HDOP – Horizontal Dilution of Precision – Measure of the quality of the horizontal position. VDOP – Vertical Dilution of Precision – Measure of the quality of the vertical position TDOP – Time Dilution of Precision – Mean error of the time estimation. 51

DOP

DOP

1 2 – 3 4 – 6 7 – 8 9-20 20 50 –

Rating

Ideal Excellent Good Moderate Fair Poor

Description

Highest possible. Required for surveys requiring the highest precision.

Positional measurements are sufficient for all but the most stringent surveys.

Minimum level appropriated for business decisions.

Sufficient for calculations, but a more open sky view is recommended.

Positional information should only be used to indicate rough locations.

Measurements are +- 150 feet and are probably useless.

Values below 2 will produce acceptable results for most surveys. Values over three should not be used. 52

Static Time

• Because the receiver continuously calculates its position, increasing the time it is stationary improves the precision.

• Static time can be divided into three categories.

– Static – Fast static – Kinematic 53

Static Surveys

• The recommended time is related to the distances being surveyed.

– Static times of 30 minutes to 2 hours are recommended for distances of 1 to 20 miles.

• To qualify for a static survey, both receivers must observe a minimum of the same four satellites for the duration of the time.

• Data is post processed.

• Static surveys have the highest precision and can be used for any surveys.

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Fast Static

• Uses the same procedures as static surveys, just shorter observation times.

– Five (5) to 10 minutes are usually sufficient for surveys that do not require the highest level of precision.

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RTK

• Requires two receivers recording observations simultaneously.

• RTK requires receivers that can use the dual frequency L1/L2 observations.

• Can lock onto satellites while on the move.

• Must have radio or other link to transfer data and calculate error in real time.

• Accuracy can be as good as 0.02 to 0.05 feet, 0.24 inches to 0.6 inches.

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Questions?

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