| GPS Q&A: Industry experts answer reader's GPS questions Q. What is the best way to determine the accuracy of differentially corrected GPS data? I have several research sites at which I took GPS readings. The majority of them are 3D. Because my project is based on spatial relationships, I would like to be able to say that my sites are at x and y locations, within s amount of error. Can I use the standard deviations given to me by the differential correction program to represent s? Or is there another standard method of determining accuracy? Also, what, if anything, can be done with the few points where I was only able to get 2D data? - K.M. [email protected] A. Michel Bourdon, Leica Canada Inc.: The accuracy of differentially corrected GPS position data is determined by the measurement accuracy of the receiver. For example, a P-code receiver such as the SR399 can provide position accuracy between 0.3 to 0.5 meters RMS with a GDOP below 5. The standard deviation S given by the differential correction program represents precision estimates of positions, not the accuracy. The statistics are too optimistic and you should multiply these sigma values by two or three times which will give you a more realistic accuracy estimate.
There are other ways to determine accuracy estimates. One of them is to redetermine the same points at different times (four hours apart) under adequate geometric conditions using different satellites. Differences between the individual determinations will give a better estimate of position accuracy. Ultimately, best accuracy estimates are obtained from GPS Vector Network Adjustment where two or more known points are being held fixed within a set of GPS vectors forming a closed figure pattern.
For the few points where we are able to get only 2D data, the height must be known within a few meters of error and held fixed to be able to use the 2D data. If the vertical is not known, the 2D data is useless. Simon Newby, NovAtel Communications Ltd.: The issue of accuracy in differential GPS applications is an extremely complex one. Are we talking about real-time or post-processed? Are we using code observations or a combination of code and phase observations? In the latter case, is it a floating ambiguity solution or a fixed ambiguity solution? Clearly there are many permutations and many variables to consider, and to fully address the topic would require a hugely complicated text which falls outside the scope of this column. Instead, I attempt to give a generic description which makes no assumptions about real-time vs. post-processed, or code vs. phase.
GPS receivers give estimated position accuracies whether being used in stand-alone, differential, 2D, or 3D modes of operation. These estimated accuracies, or standard deviations, are based upon a number of variables including: the geometrical strength of the GPS satellite constellation; the signal-to-noise ratio of the observations; the quality of the observations (e.g., Standard Correlator vs. Narrow Correlator); estimated multipath environment; the elevation angle of the satellites; and in some instances, the baseline length.
Left to their own devices, GPS observations would yield inherently optimistic accuracy estimates. Therefore, most receiver manufacturers have devised weighting schemes which offer more realistic estimates of accuracy. In other words, if the GPS receiver or post-processing software says that the estimated position accuracy is xx cm or xx meters, then we can probably trust that this is the case. However, remember that multipath remains one of the nastiest error sources in GPS measurements and caution must be exercised if a poor multipath environment is suspected.
The real confidence builder comes when a network of known points is at the disposal of the user. In this case you can use GPS to measure the baselines and then compare the GPS solution with the known solution. This technique is conceptually very simple, it also gives an independent, and reliable estimate of the GPS solution's accuracy. I wouldn't necessarily recommend doing this all the time, but as an initial confidence builder in the technology and your receiver's accuracy estimates it's probably a good approach.
If you were only tracking three satellites your receiver would first assume some knowledge of the z coordinate - only then would it be able to output a 2D position. Any errors in the assumed z coordinate would be propagated into the 2D position, and you could expect to see larger standard deviations than usual. You would have standard deviations for the x and y coordinates and could estimate the standard deviation of the horizontal position only. You would know nothing about the vertical component, and would not have the entire picture of your spatial relationship. Unfortunately, there's no way of working around this. Samuel Shaw, Trimble Navigation: This is a good question because the answer is not what people will want it to be. I wouldn't recommend accepting a critical level of liability based on the standard deviation you described because you may have a very tight position distribution around a point that is terribly inaccurate due to biases such as multipath. The answer involves two phases of hard work. The first is to collect the data in a way that enhances accuracy. There are many factors involved here such as the ability to use all of the satellites in view instead of just four, using only satellites that are at least 15 degrees in elevation, using a post-processing program that is known for its outstanding results, being cognizant of the distance between the occupied site and the base station and using a superior antenna. You should also keep your DOP mask down to at least four to ensure that stray positions are never accepted in the first place. If you are collecting phase data the outcome can sometimes be enhanced by occupying the site for some time but this technique is not always necessary or desirable.
The second phase is to crosscheck. This is essentially what survey networking software will do. The idea is to ask, "How does your point compare in when measured from one place as opposed to another?" This variety in positions is the real measure of the accuracy of the point. About the participants:
Michel Bourdon, Q.L.S., is a GPS specialist at Leica Canada Inc in Ontario, Canada, and may be reached at 613-226-1105 (phone), 613-226-5163 (fax), or Compuserve: 75112; 2513 Samuel Shaw is a technical services engineer for GIS Data Capture at Trimble Navigation in Sunnyvale, Calif. He may be reached at 408-481-8704 (phone) or at [email protected] Simon Newby is the dealer support coordinator for NovAtel Communications Ltd. in Calgary, Alberta, Canada. He may be reached at 403-295-4636 (phone), 403-295-4901 (fax), or e-mail: [email protected] Back |
