GPS Accuracy, Errors & Precision

- notes and details about GPS accuracy, errors and precision with details of CEP, SEP, DRMS & DOP as well as sources of GPS errors.

One of the key points and advantages of GPS is its accuracy. The GPS errors can be reduced to a sufficiently small level that the system provides excellent results in commercial applications as well as the much higher level of accuracy obtainable by US military users.

GPS accuracy is far greater than anything that was previously available, and it is sufficiently accurate for most applications. However there are GPS errors that have been significant for some applications, and much work has been undertaken to reduce the level of GPS errors to a level where they are insignificant.

It is found that if GPS positions are logged over a period of time, the positions indicated will be scattered over an area as a result of the measurement errors. The plot of the dispersion of the indicated points is called a scatter plot, and it is this indication that manufacturers of GPS receivers use to determine the accuracy of the GPS equipment. The scatter plot is then analysed statistically to provide an indication of the GPS accuracy performance for the receiver.

GPS accuracy & precision

The term GPS accuracy is a rather over-used term. However it can be said that the levels of GPS accuracy are extremely high these days, even for civilian use GPS units.

It is also worth defining the difference between accuracy and precision:

  • GPS accuracy:   The accuracy refers to the degree of closeness the indicated readings are to the actual position.
  • GPS precision:   Is the degree to which the readings can be made. The smaller the circle of unknown the higher the precision.

The difference between accuracy and precision is described visually in the diagram below.

GPS accuracy and precision
GPS accuracy and precision

Prior to the de-activation of the Selective Availability accuracies to within around 100 metres could be obtained. Afterwards, accuracies to within 15 metres could typically be obtained. This depended on many factors including the number and position of the satellites as well as the design of the receiver - parallel multi-channel receivers are able to provide significant improvements over earlier systems.

Understanding GPS accuracy specifications

Specification of the GPS accuracy for various receivers is subject to much marketing terminology as each manufacturer is trying to show their equipment to its best. Also GPS accuracy is difficult to describe, especially in simple terms and in data sheets where space is at a premium. However for the typical SatNavs used in automobiles, the accuracy is sufficient to enable the receiver to track the position against the known map stored in the SatNav.

In addition to this it is necessary to remember that GPS accuracy specifications are determined under ideal conditions - in an open sky with more than sufficient satellites to gain a good fix, and in open country where there is no possibility of reflections that could give rise to inaccuracies. Real operating conditions are rarely this good.

As the errors are subject to statistical spreads they are often expressed in terms of the 95th percentile, i.e. 95% of the data generated will be better than the stated value, and 5% outside it, or as the 50th percentile where 50% of the data is inside the specified value, and 50% outside.

On top of this, there are two common terms associated with GPS accuracy specifications:

  • CEP - Circular Error Probability:   GPS accuracies specified as CEP refer only to the horizontal plane, i.e. position on a map. CEP is defined as the radius of a circle centred on the true value that contains 50% of the actual GPS measurements. So a receiver with 10 metre CEP accuracy will be within ten metres of the true position 50% of the time. The circle of radius indicating the 95% probability is often referred to as R95, i.e. R95 is the CEP with the radius of the 95% probability circle.
  • SEP - Spherical Error Probability:   GPS accuracies specified as SEP refer to both horizontal and vertical planes. For a 50th percentile, half the data points or positions would fall within a sphere of this radius.

When viewing the accuracy specifications of a consumer GPS receiver, accuracy specifications in the form "Real-Time Accuracy <10 Metre CEP" may be seen. This means that under ideal conditions (which may be specified in the spec sheet), the GPS receiver will indicate the location to within 10 metres of the true location 50% of the time. This specification is for the horizontal accuracy as SEP was not quoted. Typically the vertical accuracy will be 2 to 3 times worse than the horizontal accuracy.

2D GPS accuracy, i.e. horizontal accuracy may also be specified in terms of DRMS, Distance Root Mean Square this is a single number that can express the GPS equipment. This is the square root of the average of the squared horizontal position errors. There is a 65% probability of the position being within the actual probability circle.

GPS DRMS formula

The concept of RMS accuracy can be taken further. It is possible to change the DRMS formula to give twice the DRMS of the horizontal position errors. In other words the circle defined gives the 95% probability of the real position falling within the circle defined. The 2DRMS circle is twice the radius of the DRMS circle. Similarly the 3DRMS circle gives the 97.5% probability and is three time the radios of the DRMS circle.

GPS 2DRMS & 3DRMS formulae

GPS error sources

There are a number of ways in which errors can creep in to the overall GPS system. These are well known and documented.

  • Propagation errors:   There are errors introduced as the signal slows as it passes through the ionosphere and troposphere. However it is only possible to estimate the average errors that are likely to be encountered. Any local conditions may alter the validity of these calculations.

    It is found that the ionised particles in the ionosphere will tend to slow radio signals travelling through it. This will alter the triangulation calculations for the GPS receiver. Also refractive index changes in the troposphere will have a similar, if small, effect.
  • Signal multipath:   Errors can be introduced when signals are reflected of buildings of geographical entities such as large rocks, etc. As the less direct path will be longer and take extra time, this can add errors into the system if the receiver recognises the reflected signal.
  • Receiver clock errors:   As the clock inside the receiver will be nowhere near as accurate as the four atomic clocks on board the satellite, this can introduce some small errors.
  • GPS satellite orbit errors:   Holding the satellite in an exact orbit is a real challenge. Deviations from the positions given in the ephemeris data - ephemeris errors will translate into GPS receiver position errors.
  • Number of satellites visible:   Obviously the more satellites that can be seen and can be used to provide readings, the more triangulation points are obtained and the greater the level of certainty and accuracy.
  • Satellite position geometry:   The geometry of the satellite positions can have an impact on the GPS errors. The optimum situations occur when the satellites have wider angles relative to each other. Poorer readings are obtained when the satellites have small angels between them. A measure of this known as DOP or Dilution of Precision is explained below.

Dilution of Precision, DOP

The dilution of precision or DOPP figure is used to give a simple characterisation of the geometry of the satellites being used for a fix. As the satellite geometry has an impact on the accuracy of the reading the DOP figure provides a useful guide. When using triangulation techniques, the distance from known points is used to determine the position of the target point. The distance from the known points forms a circle around each known point, and where the circles intersect, there is the target. The optimum accuracy is achieved when the angles to the known points are near right angles to each other. The same is true for the triangulation techniques used with satellites.

Triangulation Accuracy and GPS DOP
Triangulation Accuracy and GPS DOP

It can be seen that where the satellites are well separated, the distance lines from the satellite intersect at right angles giving a clear point of intersection. Where the satellites are close together, the distance lines intersect with a small angle and it is more difficult to determine the exact point of intersection.

The dilution of precision, DOP is related to the volume formed by the intersection of the points of the user satellite vectors, with the user at the centre of the sphere.

Larger volumes of cones, the better the intersection of the distance lines and this gives smaller DOP values which in turn generally relate to better position accuracy. Conversely smaller volumes of cones where the satellites are closer together give smaller cone volumes and larger DOP values which indicates poorer accuracy.

Although the DOP is a useful estimate of the likely accuracy and precision related to the satellite positions, this is not the only source of error as can be seen from the list above.

DOP Value Rating Comment
1 Ideal Highest possible confidence level
1 - 2 Excellent At this level of DOP, all but the most exacting measurements should be met
2 - 5 Good This level represents the lowest level of confidence for making business decisions
5 - 10 Moderate Measurements made would be adequate for most applications but could be improved
10 - 20 Fair Represents a low confidence level. Any measurements should be treated with caution
> 20 Poor At this level of DOP there will be significant levels of inaccuracy and error.

Sometimes other abbreviations may be seen: HDOP, VDOP, PDOP, and TDOP are abbreviations for Horizontal, Vertical, Positional (3D), and Time Dilution of Precision.

Summary of typical GPS accuracy levels

The accuracy expected to be obtained using a GPS receiver will vary according to the overall system used. While accuracy level actually achieved will depend upon many factors, typical estimations of the level of GPS accuracy can be given.

GPS system Expected GPS accuracy (metres)
GPS with S/A activated ±100
GPS without S/A activated ±15
GPS with WAAS ±3
Differential GPS ±5

By Ian Poole

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