Planning a GPS Survey Part 2 – Dilution of Precision Errors

Figure 1

Professor Chinmaya S Rathore

You can might also like to read Part 1 of this article series titled Understanding the GPS navigation Message, Almanac and Ephemeris. Please click on figures to enlarge.

The accuracy of the position (latitude, longitude and altitude) displayed by the GPS receiver is subject to many factors. The signals transmitted by the GPS satellites and received by the GPS receiver are delayed as they pass through the earth’s atmosphere. Significant contributions come from the ionosphere, which has free electrons and ions (measured as Total Electron Content or TEC) and the troposphere, which is associated with much of the weather phenomena (Figure 1). Other sources of error include satellite and receiver clock errors, orbital or ephemeris errors, multipath errors and receiver noise.  Typical contributions of these errors are usually presented as the GPS error budget shown in Table 1. 

Rather than look at errors individually, all the above errors can be conveniently summarised in one value called the User Equivalent Range Error or UERE. UERE is a distance figure and is sometimes abbreviated as User Range Error or URE. If we assume that errors for all satellites are identical and independent, UERE can be calculated by taking the square root of the sum of squares of individual errors in the error budget. In Table 1 for example, the UERE value of 6.09 has been arrived at as follows:

 

As can be inferred from Table 1, there is not much that a user can do to control UERE as most sources of error are beyond the user's control. However, the story of positional accuracy is not complete yet and there is one thing that the user can definitely control that has a pronounced effect on the accuracy of GPS measurements – choosing the time of the day (or night) when a GPS survey is conducted.  The geometry of satellites in the sky at the time of the GPS survey has a significant impact on positional accuracy. Errors contributed by bad satellite geometry called Dilution of Precision or DOP can amplify UERE leading to a decrease in positional accuracy. Before moving ahead, let us therefore briefly discuss DOP. 

The DOP idea is summarised in Figure 2. When satellites are far apart in the sky, a large tetrahedron (or polyhedron) volume is created minimising the area of positioning uncertainty which leads to good DOP (Small DOP values). On the other hand, when visible satellites are clumped together in one part of the sky, the polyhedron volume is less which leads to bad DOP (Large DOP values). Therefore, you want to be out collecting GPS coordinates at that time of the day or night when satellites that your receiver will lock onto are spread far apart in the sky (Figure 2b) and not when they are clustered close together (Figure 2a).

 

Figure 2

DOP, by itself, is a rather generic term. Specifically, there are five commonly used DOPs. These are: (a) HDOP or Horizontal Dilution of Precision (b) VDOP or Vertical Dilution of Precision (c) PDOP or Position Dilution of Precision (d) TDOP or Time Dilution of Precision and (e) GDOP or Geometric Dilution of Precision.  Table 2 provides a brief explanation of what these terms mean and what values are acceptable. 

Out of the above, two DOPs that we are quite interested in for GPS survey planning purposes are the Position Dilution of Precision or PDOP and the Horizontal Dilution of Precision or HDOP. As satellite geometry is dynamic and keeps changing at different times ( different GPS satellites keep coming in view in the sky above and going out of view), it is important that we choose that time of the day to conduct our GPS Survey which has the least PDOP or HDOP.   

It is important to note how PDOP or other DOPs described above effect position accuracy. The thing is that if there were no geometry related DOP issues involved, the accuracy that you would get from your GPS receiver would be close to the UERE. However, as we know that satellite geometry is indeed an issue, the positioning accuracy that you actually end up getting is UERE x PDOP or UERE x HDOP ( or VDOP etc). For example, if the UERE was 5.1 meters and the PDOP was 3 meters, the positioning accuracy will be 5.1 x 3 = 15.3 meters indicating that you may be 15.3 meters off from the actual position. From a practical viewpoint, it is important to note that DOPs – which are unitless numbers – act as multipliers amplifying UERE (Milbert, 2009). The larger the DOP value (HDOP, VDOP, PDOP), the more UERE is amplified resulting in increased positional inaccuracy.  

In summary, it is important to plan your GPS survey at that time of the day or night when you not only have the maximum number of satellites overhead but also when the satellite geometry is such that DOP values are at the lowest (see Table 2 for good and acceptable values). If you are interested in 3D positioning i.e. accurate latitude, longitude and elevation, you must particularly focus on PDOP values ensuring that you choose a time window for your survey when the PDOP values are likely to be less than 4. If you are primarily interested in horizontal positions and not elevation per se, you should choose a time window when the HDOP values are likely to be less than 2. By doing so, you increase the chances of getting better positional accuracy in your surveys than what you have got otherwise.

Part 3 of this article series discusses skyplots and how to practically determine HDOP and PDOP value scenarios in advance, such that you can plan your GPS surveys on a future date and time that offers the lowest DOPs. 

References 

Milbert, D. (2009): A Companion Measure of Systematic Effects in GPS World - Innovation: Improving Dilution of Precision coordinated by Prof. Richard Langley [ http://gpsworld.com/gnss-systemalgorithms-methodsinnovation-improving-dilution-precision-9100/ ]

US Government, 2008: Global Positioning System Standard Positioning Service Performance Standard, 4^th Edition [ http://www.gps.gov/technical/ps/2008-SPS-performance-standard.pdf ]

Supplementary Notes 

1. Official GPS accuracy as stated by the US Government is <=7.8 meters (95%). We can considerably improve this using Differential Positioning or Satellite-Based Augmentation System (SBAS) like WAAS (USA), EGNOS(Europe) or GAGAN (India). I will be covering this in a separate article.  

2. It is possible for the reader to come across a slightly different typical error budget in some literature sources. Some GPS error budgets might also include error component for Selective Availability (an intentional signal degradation) which was turned off by the US Government in May 2000.  More information on GPS Error sources and a differently expressed error budget can be found here. The used of error budget in this article is to primarily explain the idea of UERE and illustrate its relation with DOP. 

3. Many GPS receivers mention some additional terms to describe positioning accuracy.   These are (a) Circular Error Probable or CEP – a figure in meters that refers to a circle of that radius (= the CEP value) within which 50% of the measurements that you take are likely to fall. If the CEP for a GPS receiver is 5 meters and you collect 20 coordinates, 10 out of those 20 waypoints (2D Latitude, Longitude position) will be within 5 meters of the true latitude and longitude for that point. This called CEP 50. CEP 95 means that 95% observations will fall within the CEP 95 distance radius.  This illustration describes the CEP 50 and CEP 95 concept (b) SEP  or Spherical Error Probable is the same as CEP except that instead of a circle, we take a sphere (latitude, longitude, altitude i.e. 3D position).

4. SNR is Satellite Signal to Noise ratio and it is an indicator of signal strength. Generally, weak signals can lead to degradation in position computation. Forest canopies degrade signal strength. In addition, satellites at low elevation have poor signal strengths. Your GPS receiver’s Skyplot usually shows the signal strength from each satellite as a signal bar. Some GPS receivers permit you to set an SNR mask value ensuring that only those satellites which have a strong signal are used by the GPS receiver for computing positioning solution. Some GPS receivers permit users to set an SNR mask to ensure that only those satellites that have a good signal strength can be used for positioning solution.

5. The aim of this article is to simplify positioning concepts from a field GPS users point of view and therefore many fine details that do not concern an average GPS user have been left out of these explanations.