documento - desconocido - introduction to gps

8/6/2019 Documento - Desconocido - Introduction to GPS

1/19

Introduction to GPS

GPS is a satellite navigation system designed to provide instantaneous position, velocity and time

information almost anywhere on the globe at any time, and in any weather.

GPS is a utility awaiting applications. It can provide positioning accuracies ranging from 100 metres (95%

of the time), to 5 meters, to relative accuracies at the sub-centimeter level. Naturally the higher accuracies

involve a greater infrastructure and thus greater cost.

Present usage of GPS for positioning includes personal navigation (yachts, cars etc), aircraft navigation,

offshore survey and seismic vessel navigation, fleet tracking, mechanical control systems, civilengineering, land surveying, deformation analysis, geophysical studies ... The list is almost endless.

The day-to-day running of the GPS program and operation of the system rests with the US Department ofDefense (DoD). Management is performed by the US Air Force with guidance from the DoD

Positioning/Navigation executive Committee. This committee receives input from a similar committee

within the Department of Transportation (DoT) who act as the civilian voice for GPS policy matters

(NAPA, 1995).

Originally designed by the US Department of Defense (DoD), GPS comprises three main components: the

control segment, the space segment, and the user segment.

GPS Control Segment

The control segment comprises five stations located at Falcon Air Force Base, Colorado Springs, Hawaii,

Ascension Island, Diego Garcia and Kwajalein.These stations are the eyes and ears of GPS, monitoring the satellites as they pass overhead by measuring

distances to them every 1.5 seconds. This data is then smoothed using ionospheric and meteorological

information before 15 minute normal points are generated and sent to the Master Control Station at the US

Air Force's Space Command facilities at Colorado Springs.

It is here that parameters describing the satellites' orbit and clock performance are estimated, as well asassessing the health status of the satellites and determining if any re-positioning may be required. This

information is then returned to three uplink stations (collocated at the Ascension Island, Diego Garcia and

Kwajalein monitor stations) which transmit the information to the satellites.

Due to the worldwide spread of the control stations, all GPS satellites are tracked 92% of the time.

GPS Space Segment

The space segment comprises a network of satellites in near circular orbits at a nominal height of 20,183

km above the Earth and with a period of 12 sidereal hours. The original constellation was for 24 satellites,in 3 orbital planes and inclined to the equator by (Spilker, 1980), but these plans have since been changed

and the satellites are currently placed into six different planes and have a inclination.

There are four categories of GPS satellite, of which two types have been currently launched (as of July

1995).

The first prototype Block I satellite was launched in February 1978 from the Vandenberg Air Force Base in

California. Since then a further 10 satellites have been launched until 1985. All of the Block I satellites are

now non-operational, although one is still intermittently switched between on and off. These satellites havea design life of 4.5 years and were placed in the original inclination. The main difference between these

and the later generation satellites is that there was no ability to degrade the transmitted signals thus

providing the civilian users of GPS with a reduction in the achievable positioning accuracy.

The second category of GPS satellite is the operational Block II which were first launched in 1985. Thesehave the capability to degrade the signal, have a design life of 7.5 years, and are in an inclination of .

Originally they were to be put into orbit from the Space Shuttle, but due to the 1986 disaster, they were re-

enforced and are now launched using the Delta II rocket; a process that delayed the whole GPS program.

The Block IIA satellites are a slight modification of the original design.


2/19

The Block IIR satellites (R for replenishment) are designed to have a longer life (10 years), being capable

of satellite to satellite communications, and will be launched from 1996 in order to maintain the full

constellation. A further follow-on category Block IIF has also been planned.

Initial operational capability was declared on 8 December, 1993, when there were 24 working Block I, II,

and IIA satellites in orbit.

Full operational capability was declared after testing on 17 July, 1995. Click here for the official pressrelease.

GPS User Segment

The user segment comprises the receivers that have been designed to decode the signals transmitted from

the satellites for the purposes of determining position, velocity or time. To decipher the GPS signals, the

receiver must perform the following tasks:

selecting one or more satellites in view acquiring GPS signals measuring and tracking recovering navigational dataThere are two types of service available to GPS users - the SPS and the PPS.

The Standard Positioning System

The US Government defines the GPS Standard Positioning Service as follows:

SPS is a positioning and timing service, and is provided on the GPS L1 frequency. The GPS L1 frequency,

transmitted by all GPS satellites, contains a coarse acquisition (C/A) code and a navigation data message.

The SPS is therefore the capability provided to a user with one basic C/A code receiver. The P-code and

the L2 frequency has been made unavailable to SPS users.

Accuracies that are guaranteed to the SPS user are better than, or equal to ...

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 timeIn order to maintain (or limit) these accuracies the US DoD implemented SA to reduce horizontal

positioning capabilities from approximately 20 m to 100m and AS to deny the P code.

So what does this mean?

If you're lost, or have one receiver, you can always obtain your position to 100 m - not bad if you're lost! If

you want better accuracies then you must use other techniques which usually require the use to two

receivers - see differential GPS or phase differencing techniques. Even without the intentional accuracydenial of SA, the best you can get is approximately 15 m. If you want better, you still must use other

techniques.

For the most precise positioning using the carrier phase observable, it is preferable to have four different

types of observation - two carrier phase and two pseudorange measurements, one of each on each GPS

frequency.


3/19

The Precise Positioning Service

The PPS is the service available to authorised military users. This consists of the SPS signal plus the P

code on L1 and L2 and the carrier phase measurements on L2.

Horizontal accuracy is guaranteed to better that 22 m and vertical accuracy 27.7 m 95% of the time. If you

want better, you still must use other techniques - see differential GPS or phase differencing techniques.

How does it Work?

Positions are determined by intersecting distances between the GPS satellites and the receiver.Traditionally, the technique is called trilateration.

Distances between the GPS satellites and the receiver are not measured directly and therefore must be

derived. Typically the distances are derived from two fundamental GPS measurements:

There are two types of service available to GPS users - the SPS and the PPS.

Pseudorange Measurement

The Pseudorange measurement is the basic GPS observable that all types of receiver can make. It utilises

the C/A and/or P codes modulated onto the carrier signals.

The measurement records the actual time taken for the relevant code to travel from the satellite to thereceiver. This time is then multiplied by the speed of light to convert it into a distance.The process works something like this...... At a certain instant in time, codes (the C/A codes, for example)

are generated within the satellite and the receiver. The satellite's code is then transmitted and is picked up

by the receiver. The receiver then compares the state of the incoming code with its own code - thedifference is the time of flight.

However, there are two problems with this:

The receiver and satellite clocks are not perfectly synchronised - unless a very expensive clock is usedwithin the receiver. This introduces a clock, or timing, offset which acts as an error on the distance to

the satellite - hence the term pseudorange. This error must be computed and this is easily done since

all pseudoranges to different satellites have the same clock offset during one measurement epoch.

This is why 4 satellites are required for a position fix - to determine 3 coordinates (eg latitude,

longitude and height, or X, Y and Z, or Easting, Northing and Height) + 1 for the clock offset.

The C/A code is approximately 300 km long, and therefore raw observation can only range between 0 -300 km. But the distance to the satellite is around 20,000 km. The observation must therefore becorrected and the actual pseudorange is some multiple of 300 km plus the raw observation.

This is called an integer ambiguity and, for the C/A code at least, is very easy to resolve - if it's wrong,

you'll soon know about it! The P code does not have any ambiguity since its length is the distance traveledby light in one week - approximately 181 440 000 000 km!


4/19

The Carrier Phase Measurement

The carrier phase measurement can be thought of as the same as the pseudorange measurement in that it isa measurement of the time taken for a signal to travel from the satellite to the receiver.

This time the L1 and/or the L2 carrier signals are utilised. Since these have wavelengths of 19 and 24 cm

respectively, the measurements can only be up to these values - the distance is some multiple (the integerambiguity) of 19 or 24 cm plus the observed quantity. Often four different measurements are made to eachsatellite.

The receiver does, however, give the user a helping hand to allow for the ambiguities to be computed.

When the receiver locks on to a satellite signal it assigns some arbitrary value to the ambiguity. From then

on, the receiver counts how many complete cycles have occurred since lock on. In other words, the integer

ambiguity needs to be computed only when each satellite is locked on by the receiver - subsequent

measurements are correct relative to the initial one.

Terms often associated with the carrier phase measurement are loss of lock and cycle slip. Loss of lock is

as it sounds and the receiver must lock on to the satellite again and assign a new arbitrary value to theinteger ambiguity. A cycle slip is when the receiver loses count of the complete number of wavelengths

and therefore measurements are no longer correct relative to the initial one.

Very high accuracies are achievable when using the carrier phase. These require the use of two geodetic

standard receivers, although a recent technique has been developed allowing point positioning to thecentimetre level.

There are a number of processing strategies and observing techniques associated with carrier phase GPS

positioning.

Cross Correlation

Under anti-spoofing, the P code is denied to all SPS users by mixing this with a so-called W code to

produce a Y code, which is transmitted from the satellite. PPS users have a key to undo all this and convert

the signal back to the original P code.

So what about SPS users?

Most geodetic GPS receivers are capable of recording a pseudorange measurement on the second

frequency. One such technique for doing this is called cross correlation.Cross correlation uses the fact that the Y codes transmitted by a satellite are the same on both frequencies.

Therefore by correlating the two incoming Y codes on L1 and L2, the difference between their respectivetimes of flight can be ascertained. This difference is equal to the time delays that the frequencies sufferwhen they pass through the ionosphere. Adding the difference in the time delays to the L1 C/A code

measurement results in a pseudorange measurement containing the same information as an actual P code

measurement on L2.

The GPS Positioning Signals

GPS satellites transmit two L-Band signals which can be used for positioning purposes. The reasoning

behind transmitting using two different frequencies is so that errors introduced by ionospheric refraction

can be eliminated.

The signals, which are generated from a standard frequency of 10.23 MHz, are L1 at 1575.42 MHz and L2

at 1227.60 MHz and are often called the carriers.


5/19

Since the carriers are pure sinusoids, they cannot be used easily for instantaneous positioning purposes and

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

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.

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.

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

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

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.

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 1states 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.

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.The codes are now directly multiplied with the carrier, which results in a 180o phase shift of the carrierevery 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.

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 notinterfere 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).

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

For L2, it is stated that the signal is modulated by P code or the C/A code 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.

The GPS Receiver's Role

A GPS receiver has to detect and convert the signals transmitted from all of the satellites into useful

measurements. During the propagation of the signals through the atmosphere, a loss in signal strength

occurs and it is because of this that the spread spectrum and correlation properties of the signals arerequired. The processing steps for the L1 signal will be briefly described.


6/19

Antenna

The antenna is usually designed to be omni-directional with a gain of 3 dB, meaning that 50% of all

surrounding signal is ignored (those coming from below the horizon, or antenna ground plane). The

antenna is connected to the receiver by a coaxial cable through which a voltage is sent from the receiver to

a pre-amplifier at the antenna end. This pre-amplifier increases the power of the detected signal so that it

can be sent along the cable into the receiver.

Converting Noise to Signal

The signal is immediately passed through a high-pass filter that rejects all parts of the signal which are notwithin the L1 bandwidths (typically a filter with a central frequency of 1575.42 Mhz and bandwidth of 20

MHz) and this results in the radio frequency (RF) signal. The signal is then modulated with a sinusoid

generated by the local oscillator, resulting in the generation of a signal with two different frequency

components.

The frequency produced by the local oscillator is selected so that a signal at a low frequency

(approximately 40 KHz) will be created. This lower frequency is then separated by passing the signalthrough a low-pass filter which will also eliminate some further noise. The bandwidth of this filter is

dependent on the type of measurements that are required. If the P code is required, the bandwidth will be

set to approximately 20 MHz (the distance between the first two nulls) and will be around 2 MHz if only

the C/A code is tracked. The remaining analogue signal (known as the IF, or intermediate frequency

signal) is then sampled as fast as possible to convert it to a digital form. An in-phase (I) and quadrature (Q)sample of the signal is generated by further sampling with an in-phase and a delayed (by 90o) frequencyfrom the local oscillator.

Making Measurements on the Signal

In order to perform the de-spreading operation the IF signal is mixed down to zero frequency and copies of

the signal are sent into separate channels, each of which extract the code and carrier information for a

particular satellite. A replica of the C/A or P code is generated by the numerically controlled oscillator

(NCO) and this is correlated with the noisy IF signal. The correlation process also de-spreads the signal,

moving it to above the noise floor. The pseudorange is measured as the time shift required to align the

internally generated signal with the IF signal, scaled by the speed of light. Three replica codes are in fact

used for the correlation purposes - one is directly aligned with the IF signal (punctual), one is delayed (late)and one is advanced (early). The early and late codes lie on the slope of the autocorrelation function either

side of the peak and are used to aid the continuous tracking of the code, and to reduce the tracking error.

New advances in receiver design have reduced the spacing between the early and late correlators whichresults in the cancellation of much of the noise inherent in the measurement process.

The signal is then processed for the data modulation and the carrier phase measurements. A locally

generated carrier is generated by the carrier NCO and is correlated with the IF signal within a unit called

the Costas loop. Once the two signals have been correlated, the data message bits can be decoded by

detecting the shift in phase. The continuous phase observable is obtained by counting the elapsed cycles

and by measuring the fractional part of the phase of the correlated locally generated signal. Cycle slips

occur within this measurement when the elapsed cycles are not correctly counted, and loss of lock when the

two signals are no longer continuously correlated.

Differential GPS

Differential GPS (DGPS) relies on the concept that the errors in the position at one location are similar tothose for all locations within a given area. By recording GPS measurements at a point with knowncoordinates, these errors can be quantified and corrections can be applied to the other locations. By

applying these corrections in real-time, the accuracy of GPS for instantaneous positioning is reduced from100 m (95%) to typically 5m (95%). DGPS is now a well practiced technique for areas such as navigation,

offshore surveying and seismic surveying.

The DGPS infrastructure consists of three main components: the reference station, the mobile station, and

the connecting medium - the data link.


7/19

Other issues applicable to DGPS are height aiding, integrity monitoring and the use of multiple reference

stations.

DGPS Reference Station

Under DGPS operations a station is established at a known location with its role being to generatecorrections which will later be applied at the unknown stations. The reference station consists of a GPS

receiver and antenna and a data link (modulator and antenna).

The corrections that are generated could be of two different types: 3D positional errors or individualpseudorange errors. Both of these approaches give identical results if, and only if, the same satellites are

observed at the reference station and the unknown mobile station(s). There are several reasons why this

may not always be the case:

The receiver criterion for selecting satellites may be different (eg 12-channel vrs 5-channel receivers). The satellite geometry at the two stations may be different due to the distance between them, resulting

in differing rise and set times for the individual satellites.

Terrain obstructions may exist at either station The receivers at both stations may not necessarily use all observed satellites to determine its position.Because of these reasons, the pseudorange corrections are generated at the reference station which usually

adopts an all-in-view policy. By transmitting individual corrections for all satellites, the mobile station

uses the corrections for the satellites observed at that station thus avoiding any errors that may beintroduced. As well as a pseudorange correction for each satellite, its rate of change is also computed and

transmitted to the mobile station and is used to model the time varying characteristics of the correctionsover the period in which the corrections are generated at the reference station and applied at the mobilestation (the age of correction).


8/19

A central processor (a dedicated PC linked to the GPS receiver) is often used to generate the corrections,

although many of today's receivers can generate the corrections in the "box". The processor also converts

the corrections into a standard binary format (RTCM SC-104) which is then sent to the data link equipment

and modulated onto a carrier frequency which is subsequently transmitted to the mobile station. the

corrections into a standard binary format (RTCM SC-104) which is then sent to the data link equipment and

modulated onto a carrier frequency which is subsequently transmitted to the mobile station.

DGPS Mobile Station

The mobile station consists of a GPS receiver and antenna, a data link receiver and demodulator, and

usually a PC acting as a central processor. The pseudorange and range rate corrections are received via the

data link equipment, demodulated, and the binary message is then sent to the PC. The corrections are then

translated and applied to the individual pseudorange corrections observed by the mobile station's GPS

receiver which is also connected to the PC. The final correction is added to the observed pseudoranges and

is derived from:

PRC(t) = PRC(t0) + RRC(t1-t0)

where PRC(t) is the correction to be applied to the appropriate mobile pseudorange,

PRC(t0) is the correction generated at the reference station,

RRC is the range rate correction,t0 is the time at which the correction was generated at the reference station, and

t1 is the time at which the mobile pseudorange data was observed.

Occasionally a further correction (the delta correction) needs to be applied if the reference station has used

different ephemeris data to generate the pseudorange corrections than is available at the mobile station. All

satellites that have been "corrected" are then used within a position computation in which the position and

appropriate statistics for the mobile station are derived.

DGPS Data Links

The data link provides the connection between the reference and mobile station, and the medium that isused must be such that it can transmit over the required reference-mobile separation, the binary data can be

modulated fast enough to provide a certain age of correction, and it must be reliable in terms of probabilityof good reception (Barboux, 1993). The choices that are available can be divided into land based andsatellite based links.

The land based data links are predominantly radio transmitters operating at various frequencies dependent

on application. Low frequency (LF) links can be used which provide a wide coverage due to good surface

wave propagation. However, these systems require substantial antenna and power, and provide a relatively

slow age of correction (Barboux, 1993) due to their long wavelengths. Choosing higher frequencies

generally reduces the power consumption, requires simpler hardware, reduces the age of correction, but

also leads to a reduction in the distance over which the signal can be transmitted. Alternatives to the LF

option that are in operation include the medium (MF), high (HF), and ultra-/very-high (UHF/VHF)

frequencies. Other options for land based data links use existing radio transmissions which avoids the needto establish a dedicated link and the necessity to obtain frequency allocation permission. These include theuse of existing radiolocation systems (for example Pulse-8 and Hyper Fix), local FM radio broadcasts,

cellular telephones, and marine radiobeacons. The latter uses a existing network of direction findingradiobeacons which, although no longer used for positioning purposes, are well maintained, have frequency

allocation and a range of several hundred kilometres.

One final option for ground based transmissions is for the use of pseudolites which are designed to transmit

the data at the GPS frequencies. The advantage of these is that the standard GPS antenna can be used to

receive the corrections, and the signal has the possibility of being used as a additional pseudorange

measurement. However, over land, the signal range is poor and this along with expense issues, has meant

that the option is seldom viable.


9/19

The satellite based data links are now common place and provide a near global coverage with a fast age of

correction (less than 5 seconds) and use the INMARSAT Standard-A telephone and telex link.

INMARSAT is an internationally owned cooperative set up to meet the communication needs of the world

shipping industry and operates geostationary satellites in four ocean region areas: the Atlantic Ocean

Region West, the Atlantic Ocean Region East, the Indian Ocean Region and the Pacific Ocean Region.

Information is uploaded to the satellites from Coast Earth Stations (CES) which is usually operated by thelocal signatory - in the UK this is British Telecom and the CES is located at Goonhilly in Cornwall. A Ship

Earth Station (SES) is required to receive the signals from the geostationary satellites. For DGPS

operations, the correction message is sent from the reference station to the CES via leased land lines, is

uploaded to the satellites and subsequently transmitted for the use of the mobile.

GPS Integrity Monitoring

Integrity - the ability of a system to provide timely warnings to users when the system should not be used

for navigation.

Monitoring the GPS system and assessing its quality in real- (or near real-) time must therefore be carried

out and action taken appropriately. Unhealthy satellites, incorrect pseudoranges, poor DGPS corrections,

excessive atmospheric interference and problems at particular reference stations must be detected and the

mobile stations must be informed. There are three main approaches that are being used to perform thesetasks.

Monitor stations A monitor station acts as a mobile station in that it receives the DGPS corrections from a

reference station and computes its position. The difference is that the monitor is at a known location and

can therefore assess the quality of the solution. Any abnormal occurrences are then sent back to the

reference station and are then transmitted to the mobile users via the RTCM SC-104 ascii message.

RAIM Receiver autonomous integrity monitoring (RAIM) is a technique whereby the performance of the

GPS system is determined within the receiver itself. Four pseudoranges are needed to compute a position

at any particular instance. If five are available then five different position solutions can be computed by

using all combinations of four satellites (Al-Nakib, 1992). By examining these five solutions, ones whichare using an erroneous pseudorange will be similar, and different from the remaining solution. In this way

poor ranges can be isolated, but the technique obviously relies on a full geometry to be able to detect

multiple errors.

GIC The GPS integrity channel (GIC) uses satellites to transmit the warnings which are detected by

monitor stations. Geostationary satellites are used to transmit the integrity data to the mobiles, and two

different signal formats have been considered. Wideband GIC transmits a signal very similar to the C/A

code measurements at the same frequency as L1. This has the advantages that the GPS antenna can be usedto receive the signal, the data can be demodulated within the receiver, and the signal from the geostationary

satellite could be used as an additional pseudorange to augment the GPS coverage. The next generation of

INMARSAT satellites (INMARSAT 3), which was launched in late 1994, has this capability. The secondsignal format is the narrowband GIC which uses the telephone and telex communication bands to transmit

the message. This requires separate receiving antenna and is merely an extension of the space-based DGPS

correction services.

Multiple Reference Stations

Due the extensive network of DGPS reference stations that have been established, it is possible to receive

valid corrections from a number of stations. If this is the case, the operator will usually choose which

reference station to receive the corrections from and this is usually the closest. Within a multiple reference

station solution all pseudorange corrections received from pre-selected reference stations are used to

position the mobile station. There are a number of different approaches to provide such a solution.


10/19

Centroid approach The pseudorange corrections

from all reference stations are combined to form one

correction for each satellite in view. These

corrections should now fit the centroid of the area

defined by the reference stations that are used.

Additional directional corrections can also bedeveloped by examining the correlation between the

composite centroid corrections and those at particular

reference stations. The pseudorange corrections for

the centroid can be generated either at a land-based

hub or at the mobile station itself. The advantage ofthe former is that the mobile station needs only to

receive one set of pseudorange corrections.

All-in-view approach All the pseudorange

corrections received from the reference stations are

incorporated into one positioning solution with no

pre-processing (except for validity checks). Forinstance, the correction for satellite PRN 12 may be

received from 4 different reference stations and will

be used separately to correct the pseudorange observed at the mobile station from PRN 12 - thus adding 4observations to the system.

Position domain approach This is the simplest

approach which computes an independent position

using each reference station that corrections are

received from. The resultant positions are later

combined by taking a weighted average.

Wide area DGPS (WADGPS) This is a different

approach which no longer uses the concept of

pseudorange corrections and can provide positioning

accuracies of below 5 m (95%) of vast areas of several

thousand kilometres. The technique uses a network of

reference stations which transmit their GPS

observations to a processing hub location. The hub

performs the task of breaking down the pseudorange

errors into their different component parts (see section2) which are modeled in real-time. Orbital and

atmospheric corrections for each satellite are then

periodically transmitted to the mobile station as these

do not change frequently with time - the epsilon

component of SA can only change once per hour asthis is the frequency that the ephemeris messages are

updated for each satellite. The satellite clock errors are also modeled and transmitted to the mobile station

on a frequent basis as these need to counteract the effects of SA dither.


11/19

Measures of Accuracy

There have been many different measures used for describing the accuracies obtainable from GPS. The

most common two terms are CEP and 2drms, although the DOP values are also often (incorrectly) used.

Most Differential GPS systems now produce precision and reliability measures that conform to the

UKOOA Guidelines.

CEP

CEP is an acronym for Circular Error Probability and refers to the radius of a circle in which 50% of thevalues occur, i.e. if a CEP of 100 metres is quoted then 50%

of absolute horizontal point positions should be within 100

metres of the true position. For most offshore positioning

applications 50% is rather too small a probability to be

useful and a higher percentage is more valuable, typically

95% is often quoted and the term R95 used (with thisnotation CEP is R50). R95 (or CEP) could be determined as

follows. Simply plot the results from a large number of GPS

fixes and draw a circle, centred on the mean (or known

position) that contained 95% (or 50%) of the results. The

radius of the circle would be the R95 (or CEP) value. Ofcourse the disadvantage of using this measure is that it saysnothing about the remaining 5% (or 50%) of the data (unless

the probability density function of the errors is known or assumed) and may hence hide the possibility of

there sometimes being some very large outages.

2drms

2drms is now the more commonly used term, and is often seen within previous Federal Radionavigation

Plans. It refers to twice the drms (distance root mean square error) and not, as many people seem to

believe, to the two-dimensional rms. In order to compute the drms from a set of data it is simply necessary

to compute the rms of the radial errors, i.e. the linear

distances between the measure and known (or mean)

positions. It can be predicted using covariance analysis bymultiplying the HDOP, a measure of the satellite geometry, by

the standard deviation of the observed pseudoranges and it islargely this predictability that makes it a much more

convenient measure in practice.

A disadvantage of the 2drms measure is that is does not have a

constant probability attached to it. This point is rathercomplex and has been analysed in detail by Chin (1987).

Essentially the associated probability is a function of the

ellipticity of the relevant error ellipse resulting from a

particular satellite geometry. On the assumption that the

pseudorange errors are normally distributed this probability will be in the range 95.4% to 98.2%.

DOP

The dilution of precision (DOP) is an indication of the quality of the results that can be expected from a

GPS point position. It is a measure based solely on the geometry of the satellites and therefore can be

computed without any pseudorange observations being recorded.

DOP values are often expressed in different terms relating to the propagation of the satellite configurationinto the position fix in its different components. The usual figures are:


12/19

GDOP geometrical dilution of precision

PDOP positional dilution of precision

TDOP time dilution of precision

HDOP horizontal dilution of precision

VDOP vertical dilution of precision

It is most critical that DOP values should be used as an indication of when GPS is likely not to produce

good positioning results, and equally should not be used as a measure that describes the quality of

positioning that has actually taken place. There are a number of reasons why a DOP value, measuring

geometry, may be misleading if used to describe resultant positions:

There may be outliers in the pseudorange observations resulting in a poor fix. This would not bepicked up by a DOP value.

Low elevation satellites will improve the geometrical configuration. However, ranges observed tothese satellites will have large atmospheric errors and again will lead to poor positioning.

There is no indication of the level and rate of SA which introduces errors on all observations.A more appropriate measure of precision is the standard deviation of the different components which is

taken from the covariance matrix of the parameters.

The UKOOA Quality Measures

he United Kingdom Operators' Association "Guidelines for the use of Differential GPS in Offshore

Surveying" (UKOOA, 1994) contain an extensive description of recommended measures and test statistics

to be used in assessing the quality of a DGPS position fix. These are summarised below.

The measures to describe positional quality:

The a posteriori horizontal error ellipse (at the 95% level) as a precision measure The largest horizontal position vector resulting from a marginally detectable error as a measure of

external reliability

The statistics to detect for outliers and test for modeling errors:

The w-test, or normalised residual test, to detect for outliers (blunders/spikes) using a 99% confidencelevel

The F-test, or unit variance test, to verify the validity of the stochastic and functional models beingused

The purpose of the test statistics is to ensure that the data being used within the position fix is free from any

outliers and that the procedures used in computing position are being carried out correctly. They do notdescribe the quality of the resulting position, and therefore can be regarded as a background process used

within the position estimation routines.

Of more importance to the offshore surveyor, or system operator, is the horizontal error ellipse which is

describing the estimated quality of the position coming from the fix. The ellipse, itself, is used as anapproximation of the true precision measures in all directions and the pedal curve represents the correct

shape. The physical meaning of the 95% horizontal error ellipse is as follows. If the ellipse is centred on

the true position, then there is a 95% chance of the estimated position lying within the boundary of the

ellipse.

The size, shape and orientation of the a posteriori error ellipses depend on the particular satellite geometry

and the stochastic modeling strategy that has been adopted. In practice they will vary slowly with time(with satellite geometry) with small changes being seen mainly at times of satellites entering, or leaving,the configuration.


13/19

w-test

The w-test is used to identify outliers in the data, or observations. It is called a data snooping or outlier

detection technique and is widely used for traditional surveying as well as for GPS.

When simplified, the w-test is obtained by dividing a residual by its standard deviation, and is therefore

often called the normalised residual.

The w-test statistic is said to come from a Normal distribution with a mean of zero and standard deviationof one.

The confidence level of 99% is suggested that means there is a 1% chance of rejecting an observation that

should have been accepted.

The critical value, determined from statistical tables, is 2.576. Therefore if a w-test statistic falls outsidethe range -2.576 to + 2.576, the observation should be rejected.

If one, or more, observations fail the test, the one with the largest (positive or negative) w-test statistic

should be removed from the system and the least squares estimation should be repeated with the remaining

data.

Notes

w-test statistics can be positive or negative Over time, an average w-test statistic should be zero Histograms of w-test statistics must be like the Normal distribution pdf With only one degree of freedom, all w-test statistics are identical - ie you cannot distinguish which

observation contains an error. There must be more than one degree of freedom before the w-test

becomes effective. This means there must be at least six satellites in a four parameter GPS positionfix.

F-test

The F-test, or unit variance test, statistic is used to check whether the correct stochastic and functional

models are being used.

The unit variance test statistic is driven largely by the sum of the squares of the weighted residuals.

Remembern is the number of observations

m is the number of parameters

The unit variance itself follows a Chi-squared distribution. When testing the unit variance, it is compared

against another Chi-squared distribution - therefore the tests use a F distribution.

The unit variance is tested against a Chi-squared distributed quantity whose variance is one.

The critical value comes from a F distribution and depends upon the degrees of freedom.

Notes

Unit variance test statistics are always positive Over time, an average statistic should be one Histograms of unit variance must be like the Chi-squared distribution pdf Occasional very small values of the unit variance are not a cause for concern - they just mean that the

residuals are small.

Occasional large unit variance values indicate outliers in the data. These should have been picked upby the w-test statistic.

Long-term averages significantly greater, or less, than one indicate model errors. It is usually assumedthat the functional model is correct and that the problem is with the stochastic model. If the unit

variance average is below one, the stochastic model is pessimistic which also means that position


14/19

fixing will be to better precisions than indicated. If the unit variance is above one the opposite is true -

precisions are worse than indicated.

Statistical Testing: A General Approach

Statistical testing is used to verify that everything is OK. It can be used to test for errors in the data or the

models used to represent that data.

All types of statistical test follow these steps:

1 State a null HO and alternative HA hypothesis

2 Define and compute a test statistic (t) that is sensitive to the hypotheses

3 Define on a level of significance (a) of the test

4 Compute the value of the test statistic (tO) that corresponds to the level of significance

5 If t < tO, accept HO and reject HA

If t >= tO, reject HO and accept HA

6 Specify a power of the test (1-b) and compute the size of the marginally detectable error in the test

statistic

In this example a quantity (data, for example) is being tested.

HO states that the quantity belongs to a normal distribution.

HA states that the quantity belongs to another normal distribution.

There are four possible outcomes:

Accept HO Reject HO

HO True correct decision (a) type 1 error (b)

HO False type 2 error (c) correct decision (d)

The correct decision can be made twice: the data belongs to the correct distribution and is accepted (a), andthe data belongs to the wrong distribution and has been rejected (d).

Two incorrectdecisions can also be made.

The data belongs to the correct distribution but is rejected (b). This is a Type One error and dependson the level of significance of the test - the higher the level of significance, the less chance of making

this type of error. a is the probability of a type one error.

The data belongs to the wrong distribution but, due to its size and direction, it has been accepted (c).This is a Type Two error and depends on the power of the test. b is the probability of a type two error.


15/19

Errors do not have to be large - they can be any size. Very small errors will always be accepted (a type 2

error) and some judgment must be made on the percentage of errors we wish to accept. This is the power

of the test.

Likewise, good data may have a very large random error component and falls in the tails of the distribution.

We don't really want to use this, and again some judgment must be made on how much good data should

we accept - this is the level of significance.The difference between the two mean locations of the null and alternative hypotheses is referred to as theupper bound. It governs the maximum size of test statistic error that can be detected with the probabilities

and .

Error Sources

Single receiver GPS positioning is capable of horizontal accuracies of, at best, 22m (95%) simply due to

the effect of hardware, environmental and atmospheric error sources. However, due to US national security

concerns, much larger intentional errors have been placed on the GPS system thus limiting accuracies

obtainable from civilian users. This has reduced the GPS accuracy to 100 m (95%) but has had the effect

of rapidly advancing DGPS techniques. The two aspects of this degradation are known as selective

availability (SA) and anti-spoofing (AS).

Receiver Noise

Errors which are due to the measurement processes used within the

receiver are typically grouped together as receiver noise. These aredependent on the design of the antenna, the method used for the

analogue to digital conversion, the correlation processes, and thetracking loops and bandwidths. Noise within the pseudorange

measurements can be reduced by a factor of 50% by combining with

the more precise carrier phase observations.

Selective Availability

SA essentially consists of two different components, known

as dither and epsilon. Dither is an intentional manipulation

of the satellite clock frequency resulting in the generation of

the carrier waves and the codes with varying wavelengths.In other words, under SA, the distance between each C/A

code chip will be variable, and no longer the designed 293m.

The replica code generated within the receiver will still

assume the chip length to be 293m and pseudorange

measurements are based on this. Typical pseudorange errorsfor satellites with SA imposed are +/-100m - see SPS.

The epsilon component of SA refers to errors imposed

within the description of the satellite orbit in the ephemeris

data sent in the broadcast message. For positioningpurposes, the coordinates of the satellites are derived using

this incorrect information, and errors in these coordinatespropagate into the position of the receiver.


16/19

Atmospheric Propagation Errors

The satellite signals propagate through atmospheric layers as they travel from the satellite to the receiver.

Two layers are generally considered when dealing with GPS: the ionosphere which extends from a height

of 70 to 1000 km above the Earth, and the troposphere which from the ground level to 70 km.

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 thepseudoranges being measured too long as compared to the geometric distance to the satellite. The extent to

which the measurements are delayed depends on the Total Electron Count (TEC) along the signal path

which is a measure of the electron density. This 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 occurfor 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. Single frequency users, however, can

partially model the effect of the ionosphere using the Klobuchar model. Eight parameters for this model

are transmitted with the broadcast data for the satellites, and are used as the coefficients for two third order

polynomial expansions which are also dependent on the time of day and the geomagnetic latitude of the

receiver. These polynomials result in an estimate of the vertical ionospheric delay, which is then combinedwith an obliquity factor, dependent on satellite elevation, producing a delay for the receiver-satellite line of

sight. The final value provides an estimate within 50% of the true delay and produces delays ranging from5m (night) to 30m (day) for low elevation satellites and 3-5m for high elevation satellites at mid latitudes.

The troposphere causes a delay in both the code and carrier observations. Since it is not frequency

dependent (within the GPS L band range) it cannot be canceled out by using dual frequency measurements

but it can, however, be successfully modeled. The troposphere is split into two parts: the dry component

which constitutes about 90% of the total refraction, and the wet part which constitutes the remaining 10%.

Values for temperature, pressure and relative humidity are required to model the vertical delay due to the

wet and dry part, along with the satellite elevation angle which is used with an obliquity/mapping function.

Models are all successful in predicting the dry part delay to approximately 1 cm and the wet part to 5 cm.

Satellite Errors

Further unintentional errors within the space system still exist and will propagate into a position solution.

These include errors in the modeling of the satellite clock offset and drift using a second order polynomial,

and also errors that exist within the Keplerian representation of the satellite ephemeris information. The

cause of these errors is primarily due to the manner in which the satellite ephemeris and clock is monitored.

Tracking data for all observed satellites recorded at the GPS Monitor Stations is sent to the Master ControlStation which then uses this data to predict the parameters for the future. These predictions are then

returned to the uplink stations where they are transmitted to the satellites. The latency of the tracking data

and the prediction routines used at the Air Force Base therefore directly effect the satellite system errors.

Although similar to the SA errors, these are much smaller in magnitude.

Multipath

Mutipath is the phenomena by which the GPS signal is reflected by some object or surface before beingdetected by the antenna. The signal can be reflected off a part of the satellite (for instance the solar panels)

although this is usually ignored as there is nothing that can be done by the user to prevent this. 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 (abid.).


17/19

QA/QC of DGPS Data

Number of Satellites

The number of satellites used in a position fix is of great importance as this drives the performance of the

test statistics.

The redundancy is the number of extra observations than is actually required within the position fix. For a

GPS and DGPS pseudorange position fix, there are four parameters to solve (three coordinate components

and the receiver clock offset).

Redundancy = Number of Satellites Used - 4

# Satellites


18/19

UDRE/URA Age of DGPS (RTCM SC-104) correction Distance to reference station (especially in a multiple reference station network) Code/carrier filter performance Estimated multipath error Estimated atmospheric errors Vehicle dynamicsSignal to Noise Ratio

The signal to noise ratio (SNR) is an indication of how precise a measurement can be made to a particular

satellite.

Values range from 0 - 34 and the SNR is linearly correlated with the elevation angle of the satellite. This

further supports the use of an elevation angle driven weighting strategy.

URA and UDRE

The User Range Accuracy (URA) and the User Defined/Differential Range Error (UDRE) are indicationsof the standard deviation of a range measurement to a satellite.

The URA indicates the error size on a pseudorange measurement to a particular satellite and refers to stand-

alone, single receiver, positioning. The URA takes values between 0 and 15 and a value of 7 typically

indicates that SA is activated on that satellite. URAs are transmitted as part of the navigation/data message

and are pre-determined by the GPS Control Segment.

The UDRE is a similar measure but is applicable to DGPS. It is an indication of the precision of adifferentially corrected pseudorange. The UDRE is generated by the DGPS reference station and is

transmitted as part of the RTCM SC-104 message.

DGPS Age of Correction / Latency

The time difference between when a pseudorange correction is generated at a reference station and when it

is applied within the position fix at the mobile station is called the age of correction (AOC).

The longer this time difference the less applicable the DGPS corrections, mainly due to SA. There is nodeterioration in position (at the R95 level) using AOCs of 9 seconds far all satellites under the current

levels of SA.. After 25 seconds a 3-fold error is introduced.

Differential latency is the time difference between the reception of successive DGPS corrections at the

mobile station. This is a component of the AOC.


19/19

IODE

The Issue of Date of Ephemeris (IODE) is an identification stamp of the ephemeris/navigation message

used to compute the coordinates of the satellites for a position fix.

The IODE should be the same at a DGPS reference and mobile station. If this is not the case a RTCM SC-104 Type 2 message must be used to correct the satellite coordinates within the mobile stations position fix.

documento - desconocido - introduction to gps

Documents