ERROR EFFECT IN GPS
Selected and re-edited by FauSham from many resources as Informative sources for MFM Reader.Atmospheric effects
Inconsistencies of atmospheric conditions affect the speed of the GPS signals as they pass through the Earth's atmosphere, especially the ionosphere. Correcting these errors is a significant challenge to improving GPS position accuracy. These effects are smallest when the satellite is directly overhead and become greater for satellites nearer the horizon since the path through the atmosphere is longer (see airmass). Once the receiver's approximate location is known, a mathematical model can be used to estimate and compensate for these errors.
Because ionospheric delay affects the speed of microwave signals differently depending on their frequency — a characteristic known as dispersion - delays measured on two or more frequency bands can be used to measure dispersion, and this measurement can then be used to estimate the delay at each frequency. Some military and expensive survey-grade civilian receivers measure the different delays in the L1 and L2 frequencies to measure atmospheric dispersion, and apply a more precise correction. This can be done in civilian receivers without decrypting the P(Y) signal carried on L2, by tracking the carrier wave instead of the modulated code. To facilitate this on lower cost receivers, a new civilian code signal on L2, called L2C, was added to the Block IIR-M satellites, which was first launched in 2005. It allows a direct comparison of the L1 and L2 signals using the coded signal instead of the carrier wave. (see Atmospheric Effects in "Sources of Errors in GPS")
The effects of the ionosphere generally change slowly, and can be averaged over time. The effects for any particular geographical area can be easily calculated by comparing the GPS-measured position to a known surveyed location. This correction is also valid for other receivers in the same general location. Several systems send this information over radio or other links to allow L1-only receivers to make ionospheric corrections. The ionospheric data are transmitted via satellite in Satellite Based Augmentation Systems (SBAS) such as WAAS (available in North America and Hawaii), EGNOS (Europe and Asia) or MSAS (Japan), which transmits it on the GPS frequency using a special pseudo-random noise sequence (PRN), so only one receiver and antenna are required.
Humidity also causes a variable delay, resulting in errors similar to ionospheric delay, but occurring in the troposphere. This effect both is more localized and changes more quickly than ionospheric effects, and is not frequency dependent. These traits make precise measurement and compensation of humidity errors more difficult than ionospheric effects.
Changes in receiver altitude also change the amount of delay, due to the signal passing through less of the atmosphere at higher elevations. Since the GPS receiver computes its approximate altitude, this error is relatively simple to correct, either by applying a function regression or correlating margin of atmospheric error to ambient pressure using a barometric altimeter.Multipath effects
GPS signals can also be affected by multipath issues, where the radio signals reflect off surrounding terrain; buildings, canyon walls, hard ground, etc. These delayed signals can cause inaccuracy. A variety of techniques, most notably narrow correlator spacing, have been developed to mitigate multipath errors. For long delay multipath, the receiver itself can recognize the wayward signal and discard it. To address shorter delay multipath from the signal reflecting off the ground, specialized antennas (e.g. a choke ring antenna) may be used to reduce the signal power as received by the antenna. Short delay reflections are harder to filter out because they interfere with the true signal, causing effects almost indistinguishable from routine fluctuations in atmospheric delay.
Multipath effects are much less severe in moving vehicles. When the GPS antenna is moving, the false solutions using reflected signals quickly fail to converge and only the direct signals result in stable solutions.Ephemeris and clock errors
While the ephemeris data is transmitted every 30 seconds, the information itself may be up to two hours old. Data up to four hours old is considered valid for calculating positions, but may not indicate the satellite's actual position. If a fast Time To First Fix (TTFF) is needed, it is possible to upload valid ephemeris to a receiver, and in addition to setting the time, a position fix can be obtained in under ten seconds. It is feasible to put such ephemeris data on the web so it can be loaded into mobile GPS devices. See also Assisted GPS.
The satellite's atomic clocks experience noise and clock drift errors. The navigation message contains corrections for these errors and estimates of the accuracy of the atomic clock. However, they are based on observations and may not indicate the clock's current state.
These problems tend to be very small, but may add up to a few meters (10s of feet) of inaccuracy.Selective availability
GPS includes a (currently disabled) feature called Selective Availability (SA) that can introduce intentional, slowly changing random errors of up to a hundred meters (328 ft) into the publicly available navigation signals to confound, for example, the guidance of long range missiles to precise targets. When enabled, the accuracy is still available in the signal, but in an encrypted form that is only available to the United States military, its allies and a few others, mostly government users. Even those who have managed to acquire military GPS receivers would still need to obtain the daily key, whose dissemination is tightly controlled.
Prior to being turned off, SA typically added signal errors of up to about 10 meters (32 ft) horizontally and 30 meters (98 ft) vertically. The inaccuracy of the civilian signal was deliberately encoded so as not to change very quickly. For instance, the entire eastern U.S. area might read 30 m off, but 30 m off everywhere and in the same direction. To improve the usefulness of GPS for civilian navigation, Differential GPS was used by many civilian GPS receivers to greatly improve accuracy.
During the Gulf War, the shortage of military GPS units and the ready availability of civilian ones caused many troops to buy their own civilian GPS units: their wide use among personnel resulted in a decision to disable Selective Availability. This was ironic, as SA had been introduced specifically for these situations, allowing friendly troops to use the signal for accurate navigation, while at the same time denying it to the enemy—but the assumption underlying this policy was that all U.S. troops and enemy troops would have military-specification GPS receivers and that civilian receivers would not exist in war zones. But since many American soldiers were using civilian devices, SA was also denying the same accuracy to thousands of friendly troops; turning it off (by removing the added-in error) presented a clear benefit to friendly troops.
In the 1990s, the FAA started pressuring the military to turn off SA permanently. This would save the FAA millions of dollars every year in maintenance of their own radio navigation systems. The amount of error added was "set to zero" at midnight on May 1, 2000 following an announcement by U.S. President Bill Clinton, allowing users access to the error-free L1 signal. Per the directive, the induced error of SA was changed to add no error to the public signals (C/A code). Clinton's executive order required SA to be set to zero by 2006; it happened in 2000 once the US military developed a new system that provides the ability to deny GPS (and other navigation services) to hostile forces in a specific area of crisis without affecting the rest of the world or its own military systems.
Selective Availability is still a system capability of GPS, and error could, in theory, be reintroduced at any time. In practice, in view of the hazards and costs this would induce for US and foreign shipping, it is unlikely to be reintroduced, and various government agencies, including the FAA, have stated that it is not intended to be reintroduced.
One interesting side effect of the Selective Availability hardware is the capability to correct the frequency of the GPS cesium and rubidium atomic clocks to an accuracy of approximately 2 × 10-13 (one in five trillion). This represented a significant improvement over the raw accuracy of the clocks.
On 19 September 2007, the United States Department of Defense announced that future GPS III satellites will not be capable of implementing SA, eventually making the policy permanent.
The following two graphs show the improvement of position determination after deactivation of SA. The edge length of the diagrams is 200 m, the data were collected on May 1, 2000 and May 3, 2000 over a period of 24 h each. While with SA 95 % of all points are located within a radius of 45 m, without SA 95 % of all points are within a radius of 6.3 m.
Without SA (deactivation of SA)
Satellite clocks are slowed by its orbital speed but sped up by its distance out of the earth's gravitational well.
According to the theory of relativity, due to their constant movement and height relative to the Earth-centered inertial reference frame, the clocks on the satellites are affected by their speed (special relativity) as well as their gravitational potential (general relativity). For the GPS satellites, general relativity predicts that the atomic clocks at GPS orbital altitudes will tick more rapidly, by about 45.9 microseconds (μs) per day, because they have a higher gravitational potential than atomic clocks on Earth's surface. Special relativity predicts that atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by about 7.2 μs per day. When combined, the discrepancy is about 38 microseconds per day; a difference of 4.465 parts in 1010. To account for this, the frequency standard on board each satellite is given a rate offset prior to launch, making it run slightly slower than the desired frequency on Earth; specifically, at 10.22999999543 MHz instead of 10.23 MHz. Since the atomic clocks on board the GPS satellites are precisely tuned, it makes the system a practical engineering application of the scientific theory of relativity in a real-world environment. To put atomic clocks on artificial satellites as a means to test Einstein's general theory was first proposed by Winterberg in 1955.Sagnac distortion
GPS observation processing must also compensate for the Sagnac effect. The GPS time scale is defined in an inertial system but observations are processed in an Earth-centered, Earth-fixed (co-rotating) system, a system in which simultaneity is not uniquely defined. A Lorentz transformation is thus applied to convert from the inertial system to the ECEF system. The resulting signal run time correction has opposite algebraic signs for satellites in the Eastern and Western celestial hemispheres. Ignoring this effect will produce an east-west error on the order of hundreds of nanoseconds, or tens of meters in position.Satellite Geometry
Another factor influencing the accuracy of the position determination is the "satellite geometry". Simplified, satellite geometry describes the position of the satellites to each other from the view of the receiver.
If a receiver sees 4 satellites and all are arranged for example in the north-west, this leads to a “bad” geometry. In the worst case, no position determination is possible at all, when all distance determinations point to the same direction. Even if a position is determined, the error of the positions may be up to 100 – 150 m. If, on the other hand, the 4 satellites are well distributed over the whole firmament the determined position will be much more accurate. Let’s assume the satellites are positioned in the north, east, south and west in 90° steps. Distances can then be measured in four different directions, reflecting a „good“ satellite geometry.
The following graph shows this for the two-dimensional case.
Good geometrical alignment of two satellites Good geometrical alignment of two satellites
If the two satellites are in an advantageous position, from the view of the receiver they can be seen in an angle of approximately 90° to each other. The signal runtime can not be determined absolutely precise as explained earlier. The possible positions are therefore marked by the grey circles. The point of intersection A of the two circles is a rather small, more or less quadratic field (blue), the determined position will be rather accurate.
Bad geometrical alignment of two satellites Bad geometrical alignment of two satellites
If the satellites are more or less positioned in one line from the view of the receiver, the plane of intersection of possible positions is considerably larger and elongated- The determination of the position is less accurate.
The satellite geometry is also relevant when the receiver is used in vehicles or close to high buildings. If some of the signals are blocked off, the remaining satellites determine the quality of the position determination and if a position fix is possible at all. This can be observed in buildings close to the windows. If a position determination is possible, mostly it is not very accurate. The larger the obscured part of the sky, the more difficult the position determination gets.
Most GPS receivers do not only indicate the number of received satellites, but also their position on the firmament. This enables the user to judge, if a relevant satellite is obscured by an obstacle and if changing the position for a couple of meters might improve the accuracy. Many instruments provide a statement of the accuracy of the measured values, mostly based on a combination of different factors (which manufacturer do not willingly reveal).
To indicate the quality of the satellite geometry, the DOP values (dilution of precision) are commonly used. Based on which factors are used for the calculation of the DOP values, different variants are distinguished:
* GDOP (Geometric Dilution Of Precision); Overall-accuracy; 3D-coordinates and time
* PDOP (Positional Dilution Of Precision) ; Position accuracy; 3D-coordinates
* HDOP (Horizontal Dilution Of Precision); horizontal accuracy; 2D-coordinates
* VDOP (Vertical Dilution Of Precision); vertical accuracy; height
* TDOP (Time Dilution Of Precision); time accuracy; time
HDOP-values below 4 are good, above 8 bad. HDOP values become worse if the received satellites are high on the firmament. VDOP values on the other hand become worse the closer the satellites are to the horizon and PDOP values are best if one satellite is positions vertically above and three are evenly distributed close to the horizon. For an accurate position determination, the GDOP value should not be smaller than 5. The PDOP, HDOP and VDOP values are part of the NMEA data sentence $GPGSA.
The satellite geometry does not cause inaccuracies in the position determination that can be measured in meters. In fact the DOP values amplify other inaccuracies. High DOP values just amplify other errors more than low DOP values.
The error in the position determination caused by the satellite geometry also depends on the latitude of the receiver. This is shown below in the two diagrams. The diagram on the left side shows the inaccuracy of the height (at the beginning of the curve with SA), recorded in Wuhan (China). Wuhan is situated on 30.5° northern latitude were ideal satellite constellation can be found at all time. The graph on the right side shows the same interval recorded by the Casey-Station in the Antarctica (66.3° southern latitude). Due to the satellite constellation from time to time the error is much larger. Additionally the falsification by the atmospheric effect gets more significant the closer the position is to the poles (for an explanation see “atmospheric effects”).