How are the solutions obtained ?

OPUS-derived ITRF positional coordinates are the average of 3 distinct single-baseline solutions computed by double-differenced, carrier-phase measurements from 3 different National CORS sites using program PAGES. The reference ITRF coordinates for the CORS have been obtained from the NGS Integrated Data Base (IDB)and have been updated to the midpoint of the time interval when the submitted data were observed. Hence, OPUS-derived ITRF coordinates correspond to the position of the point at this instant in time. Points in the coterminous United States move between 9 and 22 mm/yr horizontally, relative to ITRF.

OPUS-derived NAD 83 positional coordinates are also the average of 3 distinct single-baseline solutions. The procedure followed to compute final NAD 83 coordinates at epoch 2002.0 is as follows:

First, the 3 derived ITRF intersite vector components, given at the midpoint of the data time interval, are individually transformed to the NAD 83 reference frame. Secondly, the NAD 83 coordinates of the three reference CORS stations, retrieved from the NGS IDB, are also updated to the midpoint of the interval, applying the NAD 83 velocities available from the data sheet. Vector components and CORS NAD 83 coordinates are added to determine 3 different values of the coordinates of the unknown point on the NAD 83 frame at the midpoint epoch. These 3 quantities are averaged to determine a unique value for the coordinates of the point at this epoch. Finally, these coordinates are then transformed in time to the epoch date of January 1, 2002 by using the NAD 83 velocity for the point as predicted by the HTDP (Horizontal Time-Dependent Positioning) software.

Because NAD 83 positional coordinates in the coterminous United States are referenced to the North American tectonic plate, NAD 83 velocities are typically very small. NAD 83 velocities in excess of 5 mm/yr, however, are prevalent in States along the Pacific Coast. Note that the OPUS-derived NAD 83 positional coordinates are not obtained by a direct transformation of their corresponding ITRF coordinates

While 3 single-baseline solutions are computed, the solutions can not be considered as completely independent.  Local biases at the user 's submitted station will not be averaged away by the combination.  For example, local multipath error, or error in the height of the Antenna Reference Point (ARP) will not be evident in looking at the solution variation.  On the other hand, use of 3 single-baselines does provide a gauge of error contributions from the various National CORS stations.

What is the accuracy of the result ?

Accuracy estimates for GPS reductions obtained by formal error propagation are notoriously optimistic.  For this reason, OPUS does not rely only on the formal errors.  Instead, the peak-to-peak error, or error range is provided for each coordinate component (XYZ and NEU).  The peak-to-peak error is the difference between the maximum and the minimum value of a coordinate obtained from the 3 baseline solutions.  A completely random population with a standard deviation of 1.0 cm, when sampled 3 times, will have a peak-to-peak error of 3.3 cm or less, 95% of the time.  In other words, if you see a peak-to-peak variation in the ellipsoidal height of 3.3 cm or higher, there is a 5% chance that such a variation came from data that had a 1.0 cm (one sigma) precision.  It is, of course, more likely that 3.3 cm or higher variation indicates a precision larger than 1.0 cm.

A key element, which bears repeating, is that accuracy estimates depend upon freedom from systematic error.  For example, if there is an error in identification of the antenna type, the wrong antenna phase center variation model and wrong phase center-ARP offsets will be applied to the data. This could lead to errors of 10 cm or more that will not be displayed in the peak-to-peak error value.

The advantage of providing a peak-to-peak error measure obtained from 3 baselines solved from different National CORS is that the error range also reflects the errors in the reference coordinates of the CORS stations.  The accuracies that can be obtained with modern GPS receivers and geodetic models are such that as your observational time spans get longer your results will improve so that the small errors in the reference coordinates can become a relatively more significant component of the total error.  In fact, on the average, one should obtain larger peak-to-peak errors in the NAD 83 coordinates, when compared to the ITRF coordinates, from the same observational data.  This is due to the procedures used to derive the CORS coordinates.  To serve our users, the NAD 83 coordinates of the National CORS are updated less frequently than ITRF coordinates.  However, this also results in the NAD 83 coordinates being somewhat less accurate.

Because of the automatic character of OPUS solutions, and the critical nature of elements such as antenna identification and ARP height measurement, NGS provides a disclaimer to all OPUS results, “This position was computed without any knowledge by the National Geodetic Survey regarding equipment characteristics or field operating procedures.”

How to get a more accurate result

The single best way to get a more accurate result is to submit a longer time span of data.  While we currently accept a minimum of 2 hours of data, we recommend at least 4 hours of data.  As an example, our height modernization surveys, which routinely achieve 1 cm, one sigma, ellipsoidal height accuracy, require three or more sessions, each at least 5.5 hours long, on two or more days, where two of the observation time spans are offset to sample different satellite geometries.  While good results can be obtained with 2 hour solutions, we have found that longer time spans are consistently more reliable.

In addition, using a longer time span of data allows greater averaging of multipath error.  Alternatively, if one is able to use a multipath-suppressing antenna and/or receiver, (e.g. choke-ring antennas, --- correlation receivers), then more accurate results should be obtained from a given amount of data.  However, even if a such improved antennas/receivers are used locally, longer data sets are still useful, since such antennas and receivers are not always used at the National CORS sites, themselves.

Little improvement will be obtained by submitting GPS data taken every 5 seconds or, even, every 1 second. This is because of the time correlation of multipath error is typically on the order of 10 to 20 minutes.  For example, the height modernization surveys, described above, are typically collected at a 30 second data rate.

If you submitted your solution very soon after taking your data, then it is possible that predicted orbits, rather than precise, post-fit orbits were used to obtain your solution.  The priority for orbit selection is:

IGS precise orbits (typical delay 10-14 days) highest accuracy

IGS rapid orbits (one day delay)

IGS predicted orbits (near real-time)

The orbit source will be indicated on your solution.  If a lower accuracy orbit was used, you may wish to resubmit your solution at a later time when a more accurate orbit is available.  In addition, not all CORS data are available at NGS within one hour, and sometimes, not available within one day.  This means that more distant CORS stations may have been used for the OPUS solution.  While baseline length is much less critical than measurement time span, this can sometimes also be a reason to resubmit your data .

It is possible that more accurate results can be obtained for a given set of data through manual processing through suitable software.  Such processing can include manual cycle slip editing, deletion of outliers, incorporation of local meteorological measurements, and experimentation with allocation of tropospheric parameters, variable cut-off angle, and different constraints of the carrier phase ambiguities to integer values.  However, manual processing alone is not a guarantee of accurate results.  Accurate results, particularly for long lines, depend on the fidelity of the geodetic models incorporated in the GPS reduction software.  OPUS has an extensive set of geodetic models in the PAGES software engine and the reliability of the automated processing (data editing, integer fixing, etc.) has been repeatedly demonstrated for NGS’s own processing.

At the highest level of accuracies, one is limited by the accuracy of the reference coordinates of the National CORS.  The NAD 83 datum is generally less accurate than that of the ITRF.  One could take the ITRF coordinate, and apply the Helmert transformation to generate an “NAD 83” coordinate (this can be done with HTDP).  If one does this, one will actually obtain a coordinate that has good consistency with the National CORS, but will have less consistency with the NAD 83 coordinates in the NGS Integrated Data Base.  NGS is currently engaged in a new GPS survey across the country to obtain 2 cm (2 sigma) ellipsoid heights for 2002.  When this effort is completed, the nation will have a uniformly high level of accuracy in both the NAD 83 and the ITRF reference systems.  More information is available at our web page on the New Reference System.

As a final note, please, triple check the antenna type and the height of the ARP submitted to each OPUS run.  A chain is only as strong as its weakest link.  Antenna type and the height of the ARP are critical links in the GPS data reduction chain.

What to look for in a quality solution

There are no absolute rules, but we can certainly provide some guidance on OPUS solutions.

First, make sure the antenna type and the ARP height are correct.

Next, review the solution statistics:

A good OPUS run should typically use 90% or more of your observations.

OPUS should have fixed at least 50% of the ambiguities

The overall RMS should seldom exceed 3 cm.

The peak to peak errors should seldom exceed 5 cm.  (This depends, of course, on the accuracy you are trying to achieve.)