Surveying Capter-3: Surveying Instruments: Theodolite

Theodolite: It was invented by Roemer, a Danish astronomer in 1690. The instrument was used to observe the passage (transit) of stars across any portion of the celestial meridian. About a century later it was modified to suit the surveying requirements.

It is a most precise instrument designed for the measurement of horizontal and vertical angles and has wide applicability in surveying such as laying of horizontal angles, locating points on line, prolonging survey lines, establishing grades, etc.

Figure shows three assemblies of theodolite

Following three axis of theodolite should always be perfectly perpendicular to each other, and by considering this permanent adjustment of theodolite carried out.

1.       Vertical axis

2.       Horizontal axis

3.       Line of sight

Theodolite may be classified as:

1.       Transit theodolite

2.       Non-transit theodolite

Transit theodolite is one in which the line of sight can be reversed by revolving the telescope through 180◦ in the vertical plane.

Non-transit theodolite are either plain theodolites or Y-theodolite in which the telescope cannot be transited. The transit theodolite is mainly used and Y-theodolites have now become obsolete.

Purposes for which a theodolite can be used:

1.       Measuring the horizontal angles

2.       Measuring the vertical angles

3.       Measuring the deflection angles

4.       Measuring the magnetic bearings

5.       Finding the vertical height of an object

6.       Measuring the horizontal distance between two points

7.       Finding the difference of elevation between various points

8.       Ranging a line

Terms used in Theodolite surveying:

1.       Centering: it involves setting the theodolite such that its vertical axis passes through the station mark on the ground. It is done by means of a plumb line attached to a hook below the instrument, or by optical plummet, if available. (Optical plummet substitutes for a plumb bob when centering the instrument.)

2.       Levelling: The operation of levelling involves the plates being made horizontal with the aid of bubble tubes or plate levels attached to them.

3.       Transiting (or plunging or reversing): It is a process of turning the telescope over the horizontal axis through 180◦ in a vertical plane, making its upside down and pointing in the opposite direction.

4.       Face left (bubble up): if the vertical circle is to the left of the observer when sighting from the eyepiece end. The angle measured in this position is called a face left observation. The bubble tube attached to the instrument lie above it.

5.       Face right (bubble down): if the vertical circle is to the right of the observer when sighting from the eyepiece end. The angle measured in this position is called a face right observation. The bubble tube attached to the instrument lie below it.

6.       Changing face: it is the process of changing face from right to left. The face of theodolite is changed by transiting the telescope first and then turning it through 180◦.

7.       Right swing: it is made by turning the telescope to the right (or clockwise) in the horizontal plane. The reading on the horizontal circle then increases.

8.       Left swing: it is made by turning the telescope to the left (or anti clockwise) in the horizontal plane. The reading on the horizontal circle then decreases.

Figure: The essential components of a transit theodolite

Figure: The essential components of transit theodolite

Some important terms:

Vertical axis: It is the axis of rotation of telescope in horizontal plane.

Horizontal axis: It is the axis of rotation of telescope in vertical plane. It is also known as turnnion axis.

Ques. What are the permanent adjustment of theodolite?

Ans. A theodolite is said to be in permanent adjustment if the the following requirements are fulfilled:

1.       The plate level axis is perpendicular to vertical axis.

2.       The horizontal axis is perpendicular to vertical axis.

3.       The line of sight coincide with optical axis of the telescope.

4.       The axis of the altitude level is parallel to the line of sight.

5.       When the line of sight is horizontal vertical circle Vernier reads zero.

First four requirements are the requirements among five fundamental axis and the fifth one is about the vertical circle index.

Ques. What is the procedure to check the plate level axis is perpendicular to vertical axis?

Ans. Following procedure is adopted:

1.       Set up the theodolite on a firm ground and complete all temporary adjustment. See that the plate bubble is exactly in the centre when the telescope is parallel to the two screws.

2.       Revolve the telescope by 180◦,

3.       If the instrument is in adjustment, bubble remains in the centre, otherwise note down the number of divisions by which the bubble has moved out.

Oues. Define for vertical axis, bubble axis, collimation axis, horizontal axis?

Ans.  Vertical axis: It is the axis of rotation of telescope in horizontal plane.

Horizontal axis: It is the axis of rotation of telescope in vertical plane. It is also known as turnnion axis.

Collimation axis: it is a line joining the optical centres of objective lens and eyepiece.

Ques. What relationship exist among the above principal axes of theodolite??

Ans. Principal axises of theodolite are perfectly perpendicular to each other to maintain the permanent adjustment.

Ques. What are the fundamental lines of a transit?

Ans. Following are the fundamental lines of theodolite:

1.       Vertical axis

2.       Horizontal axis

3.       Line of sight or line of collimation

Ques. How is the principal of reversal applied while adjusting the axis of plate bubble of a theodolite??

Ans. The principle of reversal sates that if there is any error in a certain part of instrument, then it will be doubled by reversing i.e. by revolving the telescope through 180◦. Thus apparent error becomes twice the actual error on reversing.

Using the Principle of Reversal following steps can be adopted:

1.       Set up the theodolite on a firm ground and complete all temporary adjustment. See that the plate bubble is exactly in the centre when the telescope is parallel to the two screws.

2.       Revolve the telescope by 180◦,

3.       If the instrument is in adjustment, bubble remains in the centre, otherwise note down the number of divisions by which the bubble has moved out.

Ques. Under what situation can there be difference between the Vernier readings of horizontal circles of a theodolite? How will you eliminate the error in one or both of them?

Ans. Difference in Vernier readings can occur

1.       If the centre of graduated horizontal circle does not coincide with the centre of the Vernier plate. Reading against Vernier will be incorrect. This can be eliminated by taking average of two readings.

2.       If there is imperfect graduations of the horizontal circle. This can be minimized by taking mean of several readings distributed over different portions of the horizontal circle.

3.       If the zeroes of the Vernier are not at the end of the same diameter, this can be eliminated by taking mean of the two readings.                                                                                                                         

Ques. Bring out the difference in theodolite, if any, between the

a.       Horizontal axis and trunnion axis

b.      Line of collimation and line of sight.

Ans. Trunnion axis of a theodolite is the axis about which the telescope and vertical circle rotate. It is the line passing through the journals which fit into the bearings at the top of the standards. When this line is horizontal, it becomes the horizontal axis of the instrument.

Line of sight is any line passing through the eyepiece and the optical centre of the objective of telescope. Line of collimation is an imaginary particular line joining the intersection of the crosshair of the diaphragm and the optical centre of the objective. This line should be perpendicular to the horizontal axis and should also be truly horizontal when the reading on the vertical circle is zero and the bubble on the telescope or on the Vernier frame is at the centre of its run.

Ques. What is the basic difference between temporary and permanent adjustments of a theodolite?

Ans. Temporary adjustment are required to be made at each station before taking readings. Permanent adjustments which usually last for a long time etc. in proper relation to one another.

References:

Surveying, Volume 1 By Dr. B.C. Punmia, Ashok Kumar Jain, Ashok Kr. Jain, Arun Kr. Jain

Surveying And Levelling By Basak

Surveying, Volume 1 By Duggal

The Surveying Handbook By Russell Charles Brinker

Surveying and Levelling, Volume 1 By S. S. Bhavikatti

Textbook of Surveying By C Venkatramaiah

Surveying: Capter-2: Station Dependent Errors in GPS signals

Multipath: when a GPS receiver is operated in any field survey measurements, it becomes an essential requirement of any measurement that the signal propagation from the satellite to the receiver should be straight through the atmosphere, but in real world this ideal condition no longer exists due to wide range of obstacles present on ground terrain, these obstruction or obstacles assembles the multipath issues with GPS signals.

GPS signals are highly vulnerable to the path of propagation from source of emission (satellite) to the receiver, it means that GPS signals also have multipath issued and GPS measurements are highly affected by multipath. The multipath errors induced by the refraction or deflection of GPS signals from their actual path of signal propagation, due to the reflection of radio signals from surrounding terrain, buildings, hard profile of ground, canyon walls, big trees and high slops etc.

Fig: Multipath Effect due to building and terrain profile

 Delay in the signal propagation through atmosphere due to these obstacles, causes GPS measurement errors which are different for different GPS signals, because of signal dependency on the wavelength. When GPS measurements are carried out in field both direct signals and indirect signals (reflected) may be received by the receiver. The path of the received signals highly dependent on the reflecting surface and the satellite position, as the satellite moves in orbit multipath effect will also be get affected by time means it is time variable. For evaluating the position of any object GPS receivers make pseudo-range measurements using ranging codes, transmitted by satellites. A multipath error in measurements are responsible for creating a false position of any objet measured by GPS receiver, due to the distortion of resulting cross correlation function and a shift in the peak of function displayed from its correct position. The shift introduced here in the correlation function causes pseudo range error. The multipath error is also dependent of the architect of the receiver. Multipath may introduced an error of positioning approximately 150m for C/A code and 15m for P code.

How to reduce or eliminate the multipath error: A very efficient way of eliminating the multipath error in GPS measurement is to set the GPS receiver at a multipath free position, means where there are no obstacles are present. But in real world it is a very hard to found a survey sight which is obstacle free because of the varying ground profile and natural obstruction.  But in case of measurements we can keep our GPS antenna far from the obstacles whenever taking observations in the field but it is not always possible. 

Narrow correlator spacing are there to mitigate the multipath error. If long delay multipath error is associated with a signal, receiver itself can encounter with this error and discard it. But for shorter delays from ground reflection in signals, special type of antennas can be used like Choke ring antenna. The shorter delays in signals are very hard to filter out by receiver because of their resemblances to routine fluctuations in atmospheric delays, so they interfere with true signals.

Station coordinates:  The ambiguity associated with station coordinates, also introduce errors in the GPS measurements thus the resolution of ambiguity becomes very important for determination of accurate and precise station coordinates. Ambiguity resolution is essential for converting biased phase observables into the unbiased range observables with the same degree of precision. It has been suggested that an improvement of 2.5 can be achieved in baseline precision of eastern component due to an ambiguity resolution of baselines having length up to 500m. A perfect station network design plays a vital role in ambiguity resolution. When talking about the confidence limit of ambiguity resolution, the baseline distance between the two receiver stations has prime concern that form double difference.  After every ambiguity resolution in station coordinates, covariance matrix is updated with new information and after resolving few ambiguities, automatically may resolve the ambiguity of entire network and got ambiguity free. High quality and dual frequency pseudo-range is helpful in successful ambiguity resolution.

Geometry dependent (Dilution of Precision: DOP):  Dilution of precision represents the satellite geometry in the sky, which is very important parameter in result accuracy assessment in the GPS measurements. Basically DOP value is a qualitative and quantitative measure of the satellite position in the sky. It is affected by the number of satellites in the receiver range and separation between them. The visible satellites grouped together closely in the space, are said to be in weak geometry and introduces high DOP values whereas if the separation is large among the satellites then it said to be in strong geometry and DOP value associates with, is low. Thus the lower DOP value causes a better GPS positioning accuracy because of the large separation between the satellites, used for calculating the GPS unit’s position.

Fig: Satellite Geometric Dilution Precision (GDOP)

The presence of obstacles such as buildings, nearby mountains can also alter the effective DOP value. It can also be represented as HDOP, VDOP, PDOP and TDOP respectively for horizontal, vertical positional (3D) and temporal dilution of precision. GPS receiver is able to obtain the DOP value when taking measurements. 

Fig: Good GDOP with obstacles

 Thus the higher DOP values introduces error in  measured coordinates, and represents the weak satellite geometry thus the weak signals, also closely spaced satellites have low coverage of area under observation so may introduce positional error too in DGPS surveys.

The geometry of satellites introduces the positional errors, which called geometric dilution of precision and it can be denoted as

GDOP= positional error/ range error

For assessing the error introduced by satellite geometry let us take an example of 4satellite geometry which forms the tetrahedron. The larger the volume acquired by tetrahedron the better will be the GDOP value obtained. If the volume is small then the GDOP value get worse. Similarly larger the no of satellites better will be the obtained GDOP.

The description of some DOP values given below;

DOP=1; Ideal DOP value, gives highest possible confidence level

DOP=1 to 2; Excellent DOP value, used in highly sensitive position measurements

DOP=2 to 5; Good DOP,

DOP=5 to 10; Moderate DOP,

DOP=10 to 20; Fair DOP,

DOP>20; Poor DOP,

User Equivalent Range Error (UERE):  

User equivalent range error is a commutative effect of various errors associated with the receiver and satellites, which is contributing in the total error budget. It can be define as a equivalent error in the range between the satellite and receiver. It can be introduced by different sources thus independent of each other.  The UERE can be calculated by taking square root of the sum of the squares of all the errors. Their errors can be listed as their descending order of contribution to the total error budget, as follow:

1.      Satellite clock error: actually receivers are used in calculating the distance between satellite and receiver position as function of time difference in signals, when signal transmitted from satellite to receiver on ground. NAVSTAR satellite clocks (atomic clocks) are very accurate, the possibility of their stray-up from standard GPS time is negligible or of the order of milliseconds. And the amount of satellite drift is calculated in the GPS control segment, generally called monitoring station.  Satellites which are able to make clock correction, reduces the satellite clock errors significantly. 

2.      Upper atmosphere (Ionospheric error): the atmosphere has varying density by latitude all through the length of 50km to 1000km in atmosphere above the earth surface, seasonally and with time also, due to these variation in density signals propagating through atmosphere undergo various interference like delay in signal propagation from satellite to receiver and also signal may get deflected through their actual path. Satellite orbited vary close to the horizon, has tendency to transmit a signal by taking a long route through the ionosphere than the satellites overhead, so these signals greatly affected by interference.  The ionosphere's density in response to the Sun's ultraviolet radiation, solar storms and maximums, and the stratification of the ionosphere itself. The GPS Control Segment is able to model ionospheric biases, however. Monitoring stations transmit corrections to the NAVSTAR satellites, which then broadcast the corrections along with the GPS signal. Such corrections eliminate only about three-quarters of the bias, however, leaving the ionosphere the second largest contributor to the GPS error budget.

3.      Receiver clock error: Surveying receivers are equipped with the quartz crystal clock whereas, NAVSTAR satellites have atomic clock. Quartz crystal clocks are less stable than that of atomic clocks, thus due to the un-stability in time measurement by the quartz clock some error introduced in the receiver co-ordinates observed.

4.      Satellite orbit: the shape of orbit of satellite is greatly affected by the gravitational attraction of earth, sun and moon, the monitoring station calculates the deviation in the in satellite eccentricities by observing the satellite location in orbit and calculating the eccentricities of orbits. The deviations are documented as ephemerids. An ephemeris is compiled for each satellite and broadcast with the satellite signal. GPS receivers that are able to process ephemerides can compensate for some orbital errors.

5.      Lower atmosphere (Topospheric error): The atmospheric delays in GPS signals are also adding slightly to the calculated distances between satellites and receivers. Satellites close to the horizon transmit signals having mostly delayed, since they pass through more atmosphere than signals from satellites overhead.

6.      Multipath error: physical bodies obstruct the signals propagating through atmosphere, thus introduces the error of multipath.

Surveying: Capter-1: Satellite Dependent Errors In GPS Signals

Satellite dependent: Ephemeris errors and orbit perturbations, Forces on GPS satellites, Effects of orbital bias, Types of satellite ephemerides, Satellite clock bias, Selective availability, Receiver dependent: Receiver clock bias, Cycle slip, Selective availability (SA), Observation.

Types of satellite ephemerides:

Ephemeris is generally refers to a table or computerized records of the position of naturally occurring astronomical objects, as well as artificially satellites in space in a time. The satellites in their orbits slightly get shifted from their theoretical positions due to some gravitational influences by solar bodies in solar system. These shifts are very difficult to predict, and are generally fall in the range of 0.5m. These astronomical satellite positions basically derived from the timings of their eclipses in the shadow of Jupiter.

The satellite orbital information can be collected in two different classes

1.      Broadcast ephemerides, which are based on the previous tracking information, available to all users at the time of GPS observations. This ephemeris information is available in satellite navigation message, computation are made in the master control station by having use of tracing data obtained from 5 monitoring stations.

Regarded to this ephemeris’s accuracy, some effects can be seen

1. Effect of accuracy of procedure adopted in orbit computation; P-code seudo-range data is used in the computation, although signal tracking geometry is not so strong to provide best results.
2. Errors associated with the unpredictable satellite orbital motion during upload.
3. Effect of selective availability, included the intentional degradation in related broadcast ephemeris parameters within the navigation message. The error induced has high variability in magnitude as possible as 100m or more.  

The accuracy provided by broadcast ephemeris data is below 10m for single navigation message, and better then 5m when daily 3 updates has performed.

2.      Post processed ephemerides, which representation data of orbit, valid only for period of time for which tracking data covered. More accurate than the broadcast ephemerides, having an accuracy level below the meter level.  To get these high accuracy ephemerides there are two requirement 

1. Network of tracking stations and
2. An orbit processing facility.

After the mid 1980’s it become easier to establish a bigger tracking network, because since then there have been tracking networks organized on regional, continental and global bases. These networks were operated for scientific, private and/or government initiatives, as well as military purposes. Some networks have operated intermittently, for specific geodetic applications; others were organized on a semi-permanent basis. Several of these networks were the first examples of international civilian cooperation in the field of GPS ground infrastructure.

Ephemeris errors and orbit perturbations:

Ephemeris errors and orbit perturbations are the inconsistency or difference between the true position of satellite or its orbit and its broadcast ephemeris. These positions are recorded as a function of time in broadcast navigation message. The prediction of these positions, are done on the basis of the previous GPS observations at ground control stations. This ephemeris information for determining GPS satellite positions is produced from the tracking data collected by five monitoring stations of satellite control segment. Data obtained, is processed at MCS (Master Control Station) and navigation satellite information is uploaded to every satellite. The associated errors in satellite position prediction are transmitted to the user in the satellite data message and are available to the GPS users at the time of the observation.

This discrepancy can be parameterized in a number of ways, but a common way is via the three orbit components: along-track, cross-track and radial.  In the case of GPS satellites the along-track component is the one with the largest error.

Figure 1: Satellite ephemeris bias

Reference: http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap6/623.htm

The ephemeris errors and perturbation are very much influence because of the influence of the some forces, which can be listed as below:

1.      Central gravitational attraction forces

2.      Non-central gravitational forces (perturbing forces)

These forces are very difficult to calculate, and thus the ephemeris errors are very tough to eliminate. The first force is very large in magnitude (about 3order larger) in comparison of all other perturbation forces in solar system.

Ephemeris error are basically satellite dependent and are most difficult to model, correct and eliminate because of failure in prediction of effect of above mention force directly and magnitude on the predicted orbit of satellite.

Forces on GPS satellites:

Mainly acing forces on GPS satellites are classified as below;

1. Central gravitational attraction force
2. Non-central gravitational forces (perturbing forces)

Perturbing force is a combined effect of various solar forces caused by various solar bodies and effects that can further be summarized as;

1. Non central gravitational forces
2. Third body effects like gravitational attration of sun, moon, and other solar planes near and farther to satellite location
3. Atmospheric drag force
4. Solar radiation pressure force
5. Magnetic forcesVariable part of earth gravitational field arising from tidal and other deformations of solid earth and ocean.

Figure 2: Forces on satellite

Some of the forces mention above are significantly affect the theoretical position of satellite in their predicted orbit and influences the shift in location orbit and satellite position. Pre described satellite motion is mainly function of the central gravitational force, hence it is very much concerned of it.

Effects of orbital bias:

These are the effects which are

1.      Associated with computational accuracy of procedure which is used to calculate the orbital location and associated velocity using P-code pseudo-range data, with a weaker tracking geometry because of tracking station located in equatorial belt. In this case accuracies better than 5m can be achieved.

2.      Resulted from the unpredictability in the orbital motion during the period since uploaded. These are essentially prediction errors, which has varying magnitude from meter level to some tens of meters.

3.      Introduction of selective availability caused intentional degradation of broadcast ephemeris parameters; inducing highly variable orbital errors.

4.      Dependent on the ephemerides errors which are influence by

a.      Location and number of tracking stations

b.      Orbital force model

c.       Geometry of satellites in space

5.      Ephemeris errors are uncorrelated between satellites and affect both code and phase measurements. Ephemeris errors are liable to introduce equal error shift in calculated absolute positions.

6.      High measurement is less accurate because there is no satellite below the horizon. Means large error in vertical component of position. The vertical component is accurate and this amount is of the order of 2 to 3 times lesser than horizontal component accuracy.

7.      Each satellite has identical ephemeris errors associated for all users, but different users have different view angles when locating the same satellite, so its effect on range measurement a position is different.

8.      Surveys conducted by using at least 2 receivers at a time gives accurate results then the single one; both receiver have the same amount of error due to effect of orbital bias which is mainly dependent on the distance between the receivers.  If receivers are located more closely than the amount of error will have more similarity. Hence the differential GPS surveys are more reliable to give more accurate point positions.

Satellite clock bias:

For determining the accurate position of objects GPS receiver clock and satellite clock must be in the same time frame. The GPS receiver clocks are generally lacking in precise synchronization with atomic clocks (very stable and expensive clocks) of satellites.  Even these clocks are not so stable enough on their own, so cause some drift or shift of time. Thus there is a time lack in between both the clocks which introduces positional error. The ground segment continuously measures these drifts and keeps them synchronized with the system time scale within a permissible limit. The satellite clocks are not corrected physically for these drifts or shifts in time, rather some satellite broadcast correction made to compensate these drifts between satellite time and system time.  These corrections must include satellite time drifts and its derivatives, which are predicted for some time period over satellites. The corrections made here are then broadcasted within the navigation message to the user.

We can easily classified the problems related to satellites in

a.      Clock drift

b.      Relativistic effect

Clock drift: As mansion above that clock in the satellites and receiver are differ very much in their accuracy as well as materialistic character. Every atomic clock in satellite has high quality, each GPS block 2 and 2A satellites have four atomic clocks, two of them are of cesium and other two of rubidium atomic clocks. One of two cesium clocks is used for time keeping and signal synchronization because they behave better in compare of rubidium clocks, rest of two clocks are for backup.  Stability of GPS clocks basically dependence on the type of clock used in GPS bock satellite both 2 and 2A

a)     Rubidium clock: 1 to 2 parts in 10¹³ over a period of one day or about 8.64 to 17.28 ns per day

b)    Cesium clock: stability improves to 1 to 2 parts in 10¹⁴ over 10 days

c)     Hydrogen maser: 1 part in 10¹⁴

These temporally variant clock errors, which are unavoidable, are the source of significant biases. These biases are monitored by the control segment during tracking data analysis. To reduce these errors in satellite clock, corrections are made, which reduces them up to 1ms of satellite clock error to around 30ns of GPS time.

Realistic effect:  The realistic effect actually accounts for two conditions, which measuredly affect the satellite clocks’ functionality;

Firstly, the time dilation before satellite is sent to orbit; this is basically to ensure the fundament frequency. The fundamental frequency is set to little below than 10.23MHz before launch,  and it is necessary to achieve the fundamental frequency when successfully located in orbit.

Secondly, this effect attributes to eccentricity (0.02) of orbit causing time error of 45.8ns. this error automatically corrected in GPS receiver, by avoiding an error of about 14m.

Selective availability:

Selective availability is a way of the introducing positional random error in the GPS signals for the security purpose. This is a function in GPS navigation system for civilian GPS receivers. 

Each satellite is uniquely located in an orbit in space; the signals broadcasted by a satellite are unique in nature which provides time information of satellite in space.  The position of satellites at a time is recorded in GPS receivers by knowing the all information about signal propagation from satellite to receiver. Using the 4 satellite (at least 4) messages, GPS receiver calculates the time of signal propagation via atmosphere satellite to receiver and having known positions of 4 satellites it estimates the latitude, longitude and elevation of a point. Having use of selective availability on GPS receiver some un-certainties are introduced in the time measurement at the satellite, because selective availability forced to satellite to send wrong time. Although the time sent by satellite is pretty close to the real time, but not that accurate. So this inaccuracy in time makes receiver to estimate the wrong coordinates or position of object which has tried to measure. Thus the positional accuracy goes down due to the interference of selective availability.

The selective availability introduces the error in position up to 100m to the civilian navigation signals. Pseudorandom error are introduced by selective availability uses, which is produced by cryptographic algorithm from a classified seed key available only with some authorized users like government, military, etc. which uses a special type of military GPS receiver with a very controlled key system.

Before it was turned off on May 2, 2000, typical SA errors were about 50 m (164 ft) horizontally and about 100 m (328 ft) vertically.^[10] Because SA affects every GPS receiver in a given area almost equally, a fixed station with an accurately known position can measure the SA error values and transmit them to the local GPS receivers so they may correct their position fixes. This is called Differential GPS or DGPS.

Figure 3: The images compare the accuracy of GPS with and without selective availability

DGPS also corrects for several other important sources of GPS errors, particularly ionospheric delay, so it continues to be widely used even though SA has been turned off. The ineffectiveness of SA in the face of widely available DGPS was a common argument for turning off SA, and this was finally done by order of President Clinton in 2000.

DGPS services are widely available from both commercial and government sources. The latter include WAAS and the U.S. coast guard network of LF marine navigation beacons. The accuracy of the corrections depends on the distance between the user and the DGPS receiver. As the distance increases, the errors at the two sites will not correlate as well, resulting in less precise differential corrections.

( Reference: http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System )