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This is the third of three articles discussing the precision obtainable with the Online Positioning User Service (OPUS) offered by NOAA’s National Geodetic Survey (NGS). The first two articles appeared in preceding issues of this magazine. OPUS is a Web-based utility available at www.geodesy.noaa.gov/OPUS to which surveyors and others can submit a dual frequency GPS data set and quickly receive an email containing positional coordinates for the location where their data were collected. OPUS computes these coordinates by processing the submitted data together with GPS data from the U.S. Continuously Operating Reference Station (CORS) network and/or the International GNSS Service (IGS) network. Actually, there are two OPUS processing engines. One engine is called OPUS-S, where "S" stands for static, which is designed for use with GPS data spanning more than two hours. The second engine is called OPUS-RS, where "RS" stands for rapid static, which is designed for use with GPS data spanning between 15 minutes and two hours.
While the precision of OPUS-S and OPUS-RS were addressed in the first two articles, there is more to the story. Certainly precision is important, but other factors also serve to distinguish between OPUS-S and OPUS-RS. One factor is that OPUS-RS requires much more computational resources than OPUS-S. Also of particular importance is the success rate of each of these two utilities. While OPUS-S has successfully computed coordinates for over 90% of the data sets submitted to it, OPUS-RS has successfully computed coordinates for only approximately 67% of the data sets submitted to it. These success rates do not address the precision of the computed coordinates, just the ability to perform the computation.
To better understand why OPUS-RS experiences so many failures, NGS personnel studied the collection of error messages issued by failed OPUS-RS solutions during the 30-month period from January 2008 to June 2010. A total of 31 different types of error messages were encountered. Table 1 identifies the top ten types of error messages issued during this 30-month period. These ten error types account for approximately 86% of the failed OPUS-RS solutions.
According to Table 1, the most frequent cause of failure is users submitting more than two hours of GPS data to OPUS-RS. This two-hour limitation is indeed an artificial restriction imposed by NGS. For sure, OPUS-RS could process many more hours of data if NGS allowed it to do so. However, the code within OPUS-RS invokes some simplifying approximations. The most critical of these approximations is based on the assumption that the travel time delay due to the distribution of molecules in the neutral atmosphere (commonly referred to as tropospheric refraction) remains constant for the entire time span of the data. Hence, the longer the time span, the more likely the tropospheric refraction will vary significantly from a constant value. By way of contrast, OPUS-S partitions the data’s total time span into 30-minute segments and assumes that the tropospheric refraction remains constant for each of these segments, but allows this refraction to vary from segment to segment.
As an aside, the assumption that the tropospheric refraction remains constant for a period of time can be the downfall of both OPUS-S and OPUS-RS when trying to process GPS data collected when the weather changes abruptly such as during the onset of a thunderstorm. NGS has experienced many poor OPUS-S and OPUS-RS solutions when trying to process GPS data collected during summer months in subtropical regions like southern Florida.
As mentioned in the second article, NGS is planning to revise the code behind the OPUS Web page so that the new code will automatically direct submitted data that spans more than two hours to OPUS-S while directing data that spans less than two hours to OPUS-RS. This new code will thus eliminate the most frequent error type causing OPUS-RS to fail.
According to Table 1, the second most frequent cause of OPUS-RS failure is the unavailability of at least three CORS/IGS stations within 250 km of the rover. Without at least three CORS/IGS stations, OPUS-RS cannot effectively interpolate/extrapolate the effect of atmospheric refraction to the rover. Maps, such as Figure 1, can help users identify the geographic regions where OPUS-RS is doomed to failure due to a lack of CORS/IGS stations in those regions. NGS creates such maps on a weekly basis to reflect the latest distribution of available CORS/ IGS stations. Users may view these maps at www.geodesy.noaa.gov/OPUSI/ Plots/Gmap/OPUSRS_sigmap.shtml. These maps, however, do not show the temporary outages occasionally experienced by individual CORS/IGS stations. Such temporary outages may cause the number of available CORS/IGS stations to drop below the magic number of three during a particular observing session. The remedy to this type of failure is simple in concept: increase the number of CORS/IGS stations in the United States and its territories. Indeed, the CORS network has been growing rapidly at a rate of more than 200 new stations per year during the past few years, thanks to contributions from more than 200 organizations that have built these stations and allowed NGS to freely provide their GPS data to the public.
Further examination of Table 1 provides additional insights as to how to reduce the number of OPUS-RS failures. Some failures can be eliminated by improving OPUS-RS and others by improving the users’ understanding of how OPUS-RS works. Simply by reducing the top two error types, the success rate of OPUS-RS will improve significantly, because these two error types have accounted for approximately 38% of the OPUS-RS failures during recent times.
Coordinate precisions discussed in these two articles are contingent on obtaining a "good" OPUS solution. So it may be asked, what constitutes a good solution? In the case of OPUS-S, NGS has suggested the following criteria:
• correct antenna type and antenna height used
• precise or rapid orbit from IGS used
• > 90% observations used
• > 50% ambiguities fixed
• RMS of residuals < 3 cm
• peak-to-peak error < 5 cm in latitude, longitude, and ellipsoid height.
In the case of OPUS-RS, similar criteria apply with the following differences. OPUS-RS requires that ALL integer ambiguities be fixed to their correct value, and so this utility employs a numerical measure called the W-ratio. Tests indicate that it is highly likely that all ambiguities have been correctly fixed if the W-ratio exceeds 3.0 in value. Otherwise, one or more of the ambiguities may have been fixed to an incorrect value. The OPUS-RS output actually reports two W-ratio values (or two "quality indicators" as they are referred to in the OPUS-RS output). The first W-ratio is for the process involving only CORS/IGS data when estimating the ambiguities and the values for the atmospheric refraction at the CORS/ IGS stations. The other W-ratio is for the process that uses the rover’s data, together with the CORS/IGS data, to estimate the rover’s coordinates. Both W-ratios should be greater than 3.0 for a good OPUS-RS solution. Furthermore for OPUS-RS, the RMS difference of the computed coordinates (rather than the peak-to-peak error) should be less than 5 cm in each dimension (except the RMS difference should be less than 10 cm in ellipsoi
d height when the duration of the observing session is less than 30 minutes). Moreover for OPUS-RS, the RMS of the normalized residuals should be less than 1.0, rather than the RMS of the residuals being less than 3 cm as is the criterion for OPUS-S. OPUS-RS computes normalized residuals by dividing each residual by its assumed standard deviation. The OPUS-RS output reports the RMS of the normalized residuals because this utility uses both carrier phase data and pseudorange data (with the latter having much larger standard deviations). OPUS-S uses only carrier phase data.
In summary, the suggested criteria for a good OPUS-RS solution are as follows:
• correct antenna type and antenna height used
• precise or rapid orbit from IGS used
• > 90% observations used
• > 50% ambiguities fixed
• RMS of residuals < 3 cm
• peak-to-peak error < 5 cm in latitude, longitude, and ellipsoid height.
In the case of OPUS-RS, similar criteria apply with the following differences. OPUS-RS requires that ALL integer ambiguities be fixed to their correct value, and so this utility employs a numerical measure called the W-ratio. Tests indicate that it is highly likely that all ambiguities have been correctly fixed if the W-ratio exceeds 3.0 in value. Otherwise, one or more of the ambiguities may have been fixed to an incorrect value. The OPUS-RS output actually reports two W-ratio values (or two “quality indicators” as they are referred to in the OPUS-RS output). The first W-ratio is for the process involving only CORS/IGS data when estimating the ambiguities and the values for the atmospheric refraction at the CORS/ IGS stations. The other W-ratio is for the process that uses the rover’s data, together with the CORS/IGS data, to estimate the rover’s coordinates. Both W-ratios should be greater than 3.0 for a good OPUS-RS solution. Furthermore for OPUS-RS, the RMS difference of the computed coordinates (rather than the peak-to-peak error) should be less than 5 cm in each dimension (except the RMS difference should be less than 10 cm in ellipsoid height when the duration of the observing session is less than 30 minutes). Moreover for OPUS-RS, the RMS of the normalized residuals should be less than 1.0, rather than the RMS of the residuals being less than 3 cm as is the criterion for OPUS-S. OPUS-RS computes normalized residuals by dividing each residual by its assumed standard deviation. The OPUS-RS output reports the RMS of the normalized residuals because this utility uses both carrier phase data and pseudorange data (with the latter having much larger standard deviations). OPUS-S uses only carrier phase data.
In summary, the suggested criteria for a good OPUS-RS solution are as follows:
• correct antenna type and antenna height used
• precise or rapid orbit from IGS used
• > 90% observations used
• both W-ratios exceed 3
• RMS of normalized residuals < 1
• RMS difference < 5 cm in latitude, longitude, and ellipsoid height (except for sessions shorter than 30 minutes in which case the RMS difference in ellipsoid height should be less than 10 cm).
Another criterion for a good OPUS solution, which NGS has yet to study, is the need for good satellite geometry as may be measured, for example, by the geometric dilution of precision (GDOP). For observing sessions exceeding two hours in duration, the value of GDOP probably does not matter much because of the volume of available GPS data. However, the value of GDOP during a 15-minute observing session probably does strongly influence the precision of the coordinates computed with OPUSRS. So research on this topic remains on NGS’ “to do” list.
Moreover, with either OPUS-S or OPUS-RS, it is a good idea to conduct multiple observing sessions at the same location and to compare OPUS-generated coordinates among the different sessions to see if separate values agree with each other within their specified error estimates.
More detailed information about OPUS and its precision may be found in OPUS-related articles available on the Web at www.geodesy.noaa.gov/CORS/Articles and in a collection of scientific papers written by several authors and published by the American Society of Civil Engineers under the title, CORS and OPUS for Engineers: Tools for Surveying and Mapping Applications.
Richard Snay served as an NGS scientist from 1974 to 2010. Rich managed the U.S. CORS program from 1998 to 2007, and he supervised the NGS Spatial Reference System Division from 2003 to 2010.
Kevin Choi has served as an NGS scientist since 2009. Kevin currently maintains the OPUS-RS utility, and he developed interactive web-based maps that allow users to view the precision of OPUS-RS as a function of geographic location.
Gerald Mader has served as an NGS scientist since 1983. Gerry has supervised the NGS Geosciences Research Division since 1996, and he has been the leading architect of all things OPUS.
Charles Schwarz served as an NGS scientist from 1974 to 1990. Charlie supervised the NGS Systems Development Division from 1990 to 2005. He was the lead systems analyst involved in developing and implementing OPUS-RS.
Tomás Soler has served as an NGS scientist since 1979. Tom supervised the NGS GPS Branch from 1990 to 2003. He currently serves as Chief Technical Officer in the NGS Spatial Reference System Division, and he conducted most of the experiments described in these three articles.
Neil Weston has served as an NGS scientist since 1994. Neil has supervised the NGS Spatial Reference System Division since 2010, and he has been the "go to" person for OPUS since its inception.
A 587Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE