MARINESHELF.COM: G P S (GLOBAL POSITIONING SYSTEM)

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Intoduction

GPS is a satellite navigation system designed to provide real time information anywhere, any time and in any weather of receiver’s:

1. Position

2. Velocity

3. Time

GPS comprises of three segments:

Control Segment

The Control Segment consists of a system of one master control station at Colorado Springs (USA) and 4 tracking and monitoring stations located around the world. (Ascension Island, Diego Garcia, Kwajalein & Hawai)
The monitor stations measure signals from the SVs which are incorporated into orbital models for each satellites. The models compute precise orbital data (ephemeris) and SV clock corrections for each satellite and sent to the Master Control Station.
The Master Control station estimates the satellites orbit and clock performance as well assesses the health of satellites and determines if any repositioning may be required.
The Master control station then uploads orbital parameters and clock data to the SV’s through 3 uploading stations co located at Ascension Islands, Diego Garcia and Kawajalien.
The SV’s then send subsets of the orbital ephemeris data to GPS receivers over radio signals.
Due to the worldwide spread of the control stations, all GPS satellites are tracked 92% of the time.

Space Segment

The Space Segment of the system consists of the GPS satellites. These space vehicles (SV’s) send radio signals from space.
The nominal GPS Operational Constellation consists of 24 satellites that orbit the earth in 12 sidereal hours. Minimum of 21 operating 98% of the time.
Orbiting in near circular orbits at a height of 20,200 Kms. above Earth’s surface.
6 orbital planes. 4 satellites in each orbit planes.
Each orbital plane inclined by 55* to the equatorial plane and separated in R.A. by 60*.
Each satellite visible for about 5hrs. above horizon.
Constellation of satellites is configured so that any receiver located anywhere on globe will have minimum of four satellites in view having elevation of more than 9.5*.
User Segment
- The GPS User Segment consists of the GPS receivers and the user community. GPS receivers convert SV signals into position, velocity, and time estimates. Four satellites are required to compute the four dimensions of X, Y, Z (position) and Time. GPS receivers are used for navigation, positioning, time dissemination, and other research.
- To decipher the GPS signals, the receiver must perform the following tasks:
1.      Locking to satellites in view

2.      Measure time interval

3.      Measuring and tracking of satellites

4.      Recovering navigational data

5.      Compute to give receiver position, velocity and GPS time.

What is the Principle of GPS? How is position fix obtained in GPS?

·         The principle used to obtain the position of the ship is by ranging.

      Range = C x T

      C is speed of electromagnetic waves = 300,000,000 m/s

T is time taken between transmission and reception.

·         The positions of the satellites in space are accurately known (from satellite messages, computed by control station through 4 monitoring station).

·         By knowing the positions of the satellites and measuring the time taken for a message to reach the receiver, the receiver gets a range, and thus a position spheroid.

·         Intersection of the position spheroid and earth’s surface is a small circle.

·         Simultaneous application of the second range measurement from second satellite gives a second small circle on Earth’s surface.

·         The two circles intersect at 2 point but as the two intersection points are significantly away from each other there will be no ambiguity.

·         Since the Clocks of the satellite and user clocks are different clocks with differing accuracy. The T time difference between time of transmission (Satellite clock) and reception (user clock) as measured by the receiver gives psuedo ranges.

·         3 psuedo ranges from 3 different satellites are measured to obtain fix on earth’s surface to resolve/ calculate user clock error and to get true range and hence the position of the receiver.

·         Let the coordinates of the known position of the three satellites be (x’,y’,z’), (x”,y”,z”), (x’’’,y’’’, z’’’) and of the receiver which to be found out be (x,y,z).

Time taken for the satellites message to reach user as measured by the user clock be T’,T’’, T’’’

Unknown Error of the user clock = Dt

Then we have three equations

PR’ = C x T’= C x ( t’± Dt) = sqr root √ (x’- x) ² + (y’-y) ² + (z’-z) ²

PR” = C x T”= C x ( t”± Dt) =   √ (x”- x) ² + (y”-y) ² + (z”-z) ²

PR”’ = C x T”’= C x ( t”’± Dt) =   √ (x”’- x) ² + (y”’-y) ² + (z”’-z) ²

For an observer on Earth’s surface Radius of earth r =   √x² + y² + z ²                          z can be found in terms of x and y.

As we have three simultaneous equations and three unknowns x, y, and Dt which can be computed and observer/receiver’s position can be computed.

For an observer in space 4 psuedo ranges from 4 satellites will be required as then unknowns will be 4( x, y, z, Dt).

What do you understand by pseudo range and true range? How the error due to user clock bias obviated (removed).

Since the Clocks of the satellite and user clocks are different clocks with differing accuracy. T the time difference between time of transmission (Satellite clock) and reception (user clock) as measured by the receiver gives psuedo range PR = C x T Pseudo range is false range because it includes range error due to user clock bias.

The time delay as measured by the receiver gives psuedo ranges.

The user clock bias (error) is computed by the processor of the receiver.

Since all pseudo ranges to different satellites have the same clock offset during one measurement epoch.

The receiver measures 4 psuedo ranges from 4 different satellites at the same instant. And we get 4 simultaneous equations and 4 unknowns ( x, y, z, Dt) which are computed to get user clock error.

Let the coordinates of the known position of the three satellites be (x’,y’,z’), (x”,y”,z”),

(x’’’,y’’’, z’’’), (x””, y””,z””) and of the receiver which to be found out be (x,y,z).

Time taken for the satellites message to reach user as measured by the user clock be T’,T’’, T’’’, T””

Unknown Error of the user clock = Dt

we have four equations

PR’ = C x T’= C x ( t’± Dt) = sqr root √ (x’- x) ² + (y’-y) ² + (z’-z) ²

PR” = C x T”= C x ( t”± Dt) =   √ (x”- x) ² + (y”-y) ² + (z”-z) ²

PR”’ = C x T”’= C x ( t”’± Dt) =   √ (x”’- x) ² + (y”’-y) ² + (z”’-z) ²

PR”” = C x T””= C x ( t””± Dt) =   √ (x””- x) ² + (y””-y) ² + (z””-z) ²

True Range(TR) is the actual range of the satellite from the receiver without any user clock error and ionospheric Dt’ and tropospheric Dt” delay errors.

TR = PR(as measured) ± C x Dt - C x Dt’(ionosphere) - C x Dt” (troposphere)

What Factors effect the accuracy of a GPS position?
1. Satellite vehicle clock error : Error of the satellite vehicle clocks is computed by the control stations and sent in the navigation data to be applied by the receiver.
1. Satellite Vehicle clock Error : The atomic clocks used on the satellites are very,    very precise but they're not perfect. Minute discrepancies can occur, and these translate into travel time measurement errors.
The satellite vehicle clock error is monitored by monitoring stations and is calculated & transmitted by the control station to the receiver in navigation message.
Error can be obviated by using DGPS.
2. Error in predicted ephemeris of satellite vehicles: Though the satellites positions are constantly monitored through monitoring stations but they can't be watched every second. So slight position or " ephemeris" errors can sneak in between monitoring times.
Error can be obviated by using DGPS.
3. Error due to Ionosphere : The ionosphere extends from a height of 70 to 1000 km above the Earth, as the signal propagates through the ionosphere, the carrier experiences a phase advance and the codes experience a group delay.
In other words, the GPS code information is delayed resulting in the pseudoranges being measured too long as compared to the geometric distance to the satellite.
The extent to which the measurements are delayed depends on the electron density along the signal path.
The electron density is dependent on three further factors: the geomagnetic latitude of the receiver, the time of day and the elevation of the satellite. Significantly larger delays occur for signals emitted from low elevation satellites (since they travel through a greater section of the ionosphere), peaking during the daytime and subsiding during the night (due to solar radiation). In regions near the geomagnetic equator or near the poles, the delays are also larger .

The ionospheric delay is frequency dependent and can therefore be eliminated using dual frequency GPS observations, hence the two carrier frequencies in the GPS design. Two frequency are used for transmission of P code.

The ionospheric delay can be obviated by using DGPS.

1.   Error due to Troposphere:

2.      The troposphere which from the ground level to 70 km, the troposphere causes a delay in the transmitted signals. Error due to troposphere is not frequency dependent (within the GPS L band range) it cannot be canceled out by using
dual frequency measurements.
This error is maximum when angle of incidence of transmitted waves is high, to avoid large errors in the positions ,the satellite vehicles having angle of elevation of less than 9.5* are not used in computation of user position.
The ionospheric delay can be obviated by using DGPS.

5. Multipath: Mutipath is the phenomena by which the GPS signal is reflected by some object or surface (mountains, buidings near the coast, funnel near the antenna) before being detected by the antenna. Mutipath is more commonly considered to be the reflections due to surfaces surrounding the antenna and can cause range errors as high as 15 cm for the L1 carrier and of the order of 15-20 m for the pseudoranges. The surface most prone to multipath is water, whilst sandy soil is the least .

This error can not be obviated by using DGPS.

This error can be minimized by using special antennas.
6.Receiver Noise: Errors which are due to the measurement processes used within the receiver are grouped together as receiver noise. These are dependent on the design of the antenna, the method used for the analogue to digital conversion, the correlation processes, and the tracking loops and bandwidths .
Better the receiver lesser the errors.
7. Geometric dilution of Precision : Basic geometry itself can magnify these other errors with a principle called "Geometric Dilution of Precision" or GDOP.
There are usually more satellites available than a receiver needs to fix a position, so the receiver picks a few and ignores the rest.
If it picks satellites that are close together in the sky the intersecting circles that define a position will cross at very shallow angles. That increases the gray area or error margin around a position.
If it picks satellites that are widely separated the circles intersect at almost right angles and that minimizes the error region.
Good receivers determine which satellites will give the lowest GDOP.
8. Error due to Selective Availability: GPS is funded and controlled by the U.S department of defense. Therefore they can intentionally degrade the gps signals and deny gps signals on regional basis. (selective availability discontinued since may 1, 2000)
9. Error due to perturbing forces on the GPS satellite.
Kepler's laws are for an idealised satellite orbit where the only attracting force is a spherical gravity field. For any satellite orbiting the Earth this is not the case and its Keplerian position will be affected by the following perturbing forces:
Earth not being true sphere and mass not equally distributed therefore gravitational forces different at equator and at pole.

Ø Gravitational forces of sun, moon and other planets.

Ø Solar radiation

Ø Atmospheric drag.
10. User Clock Bias: Explained above.
BLUNDERS

1.      Control segment mistakes due to computer or human error can cause errors from one metre to hundreds of kms.

2.   Datum Shift:Incorrect geodetic datum selection can cause errors from 1 to hundreds of meters.

3.

·         Receiver errors from software or hardware failures can cause blunder errors of any size.

·         Interference of other radio signals with GPS signals.

·         User mistakes like plotting a previous frozen position or not reading if the gps is giving DR or fix.

What are the various componenets of GPS signals and what is there significance?

Components of GPS signals are:

·         Carrier Signal (L1 & L2)

·         Code (P or C/A)

·         Navigation Data Message

Carrier Signal (L1 & L2)

GPS satellites transmit two L-Band signals that can be used for carrying the code and navigation data message from GPS satellites to the receiver.

The signals, which are generated from a standard frequency of 10.23 MHz, are L1 at 1575.42 MHz (10.23 * 154) and L2 at 1227.60 MHz(10.23 * 120) and are called the carriers. The frequencies are generated from the fundamental satellite clock frequency of fo =10.23 MHz.

The reason for using high frequency is because higher the frequency lower is the interference or attenuation thru the ionosphere.

The reason for using two different frequencies is so that errors introduced by ionospheric refraction can be eliminated.

Signal

Frequency (MHz)

Wavelength (cm)

L1

154fo = 1575.42

~19

L2

120fo =1227.60

~24

Code (P or C/A)

Since the carriers are pure sinusoids, they cannot be used easily for instantaneous recognition/identification of GPS satellites.

Therefore two binary codes are modulated onto them: the C/A (coarse acquisition) code and P (precise) code.

Also it is necessary to know the coordinates of the satellites and this information is sent within the broadcast data message which is also modulated onto the carriers.

For purposes of imposing the binary data onto the carriers, all of the codes are transferred from the 0 and 1 states to the -1 and 1 factors respectively.

The broadcast data message is then modulo-2 added to both the C/A code and the P code. This inverts the code and has the effect of also inverting the autocorrelation function.

Modulo-2 Addition

Binary biphase modulation (also known as binary phase shift keying [BPSK]) is the technique that is used to modulate the codes onto the initial carrier waves.

Binary Biphase Modulation

The codes are now directly multiplied with the carrier, which results in a 180 degree phase shift of the carrier every time the state of the code changes.

The modulation techniques also have the properties of widening the transmitted signal over a much wider frequency band than the minimum bandwidth required to transmit the information which is being sent (Pratt, 1992). This is known as spread spectrum modulation and has the benefits of developing processing gain in the de-spreading operation within the receiver, and it helps prevent possible signal jamming.

The L1 signal is modulated by both the C/A code and the P code, in such a way that the two codes do not interfere with each other. This is done by modulating one code in phase and the other in quadrature (ie they are at 90 degrees to each other).

L1 Signal Structure

The C/A code is also amplified so that it is between 3 and 6 dB stronger than the P code (Spilker, 1980).

For L2, it is stated that the signal is modulated by P code or the C/A code (Spilker, 1980) although normal operation has seen the P code being used. It should be noted that the precision obtained from P code measurements is thought not to be in the interests of US national security and therefore will be restricted for civilian users. This is the same for both the L1 and L2 frequencies.

C/A Code

The C/A code is a pseudo random (PN) binary code (states of 0 and 1) consisting of 1,023 elements, or chips, that repeats itself every millisecond.

The term pseudo random is used since the code is apparently random although it has been generated by means of a known process, hence the repeatability.

Due to the chipping rate (the rate at which each chip is modulated onto the carrier) of 1.023Mbps, the chip length corresponds to approximately 300m in length and due to the code length, the ambiguity is approximately 300km - ie the complete C/A code pattern repeats itself every 300km between the receiver and the satellite.

CA Code represenation

The C/A code can be thought of as a number of rulers extending from the satellite to the receiver. The length of each ruler is approximately 300km, and each graduation is 300m apart.

The code is generated by means of a linear feedback register which is a hardware device representing a mathematical PN algorithm.

The sequences that are used are known as Gold codes which have particularly good autocorrelation and cross correlation properties. The cross correlation properties of the Gold codes are such that the correlation function between two different sequences is low - this is how GPS receivers distinguish between signals transmitted from different satellites.

P Code

The P code, or precise code, is a long binary code that would repeat only every 38 weeks (Pratt, 1992).

Despite the code being shortened to a one week repeatability because each satellite transmits a different weekly section of the code, there is still no ambiguity between the satellite and receiver.

P code representation

The P code can be thought of as a ruler extending from the satellite to the receiver. The length of the ruler is approximately one week multiplied by the speed of light, and each graduation is 30m apart.

Rapid access to the relevant part of the code for a particular satellite is carried out by means of a hand-over-word obtained from the broadcast data message.

The chipping rate is at 10.23 MHz resulting in a chip length of approximately 30 m.

Navigation / Broadcast Data Message

The data message includes information describing the positions of the satellites, their health status, and the hand-over-word.

Each satellite sends a full description of its own orbit and clock data (within the ephemeris information) and an approximate guide to the orbits of the other satellites (contained within the almanac information).

The data is modulated at a much slower rate of 50 bps and thus it takes 12.5 minutes to transmit all of the information. To reduce the time it takes to obtain an initial position, the ephemeris and clock data is repeated every 30 seconds (Langley, 1990).

Parameters representing the delay caused by signal propagation through the ionosphere are also included within the data message.

Differential Global Positioning System (DGPS)
DGPS works by placing a high-performance GPS receiver (reference station) at a known location. Since the receiver knows its exact location, it can determine the errors in the satellite signals. It does this by measuring the ranges to each satellite using the signals received and comparing these measured ranges to the actual ranges calculated from its known position. The difference between the measured and calculated range is the total error. The error data for each tracked satellite is formatted into a correction message and transmitted to GPS users. The correction message format follows the standard established by the Radio Technical Commission for Maritime Services, Special Committee 104 (RTCM-SC104) These differential corrections are then applied to the GPS calculations, thus removing most of the satellite signal error and improving accuracy. The level of accuracy obtained is a function of the GPS receiver. Sophisticated receivers like the Starlink DNAV-212 and INVICTA 210 series can achieve accuracy on the order of 1 meter or less.

REFERENCE STATION:

The reference station GPS receiver knows exactly the position of its antenna, therefore it knows what each satellite range measurement should be. It measures the ranges to each satellite using the received signals just as if it was going to calculate position. The measured ranges are subtracted from the known ranges and the result is range error. The range error values for each satellite are formatted into messages in the RTCM SC104 format and transmitted continuously.

MODULATOR:

Depending on the transmission format, the modulator encodes the data as necessary for transmission. For example, in the free USCG system, the modulator creates a carrier signal which varies using MSK modulation. A "one" data bit is represented by a advancing carrier phase and a "zero" bit by a retarding carrier phase. The modulated carrier output from the modulator is connected to the transmitter.

TRANSMITTER:

The transmitter is basically a power amplifier which is connected to an antenna system. The modulated carrier is amplified and driven to the antenna. In the USCG system, the transmitter is 250-1000 Watts and operates in the 300KHz frequency range. The amplified signal is radiated via the antenna to remote DGPS receivers for real-time position correction.

DGPS CORRECTION RECEIVER:

A DGPS correction receiver decodes the signals received from a reference site. Data is formatted into a data stream and provided to the remote GPS receiver. There are many types of DGPS correction receivers.

GPS RECEIVER:

The GPS receiver measures ranges to each satellite, but before the measurements are used to calculate position, corrections received from the DGPS receiver are applied to the measurements. The position is then calculated using the corrected range measurements providing vastly increased accuracy.

NOTES:

GPS with SA has an accuracy of about 100 meters. GPS with corrections (DGPS) has an accuracy of between 1 and 5 meters depending on the quality (price) of the GPS receiver.

Accuracies that are guaranteed to the SPS user are better than, or equal to ... (DoD/DoT, 1995b)

100 m in horizontal position,

95% of the time

156 m in the vertical component

95% of the time

300 m in horizontal position

99.99% of the time

500 m in the vertical component

99.99% of the time

340 nanoseconds timing accuracy

95% of the time