Using GPS Networks

Ellis R. Veatch II, PS

Why a network?

The buzzword of GPS these days is RTK. RTK is inherently a method that produces side shots. Checks are not built into the method. When doing RTK, we must develop and utilize procedures to provide checks, such as re-occupying our RTK points using a different base station at a different time. The resulting averaged points will have improved accuracy. However there will be no direct measurements between the points. This is fine for photo control, topo, alignment stakeout and slope staking, etc., but may not meet the needs of tasks such as section break-down, or other boundary surveys where direct measurements between points may be required. These tasks may be better done using rapid static post-processed techniques, which have built in redundancy and point-to-point measurements. The network approach provides us with pretty reliable indications as to the accuracy of the points in relation to each other, not just to a base station.

This article is going to present a simplified method of designing a network for GPS surveys. It is not a scientific treatise on networks or least squares adjustments. It is intended to be a basic guide for the average surveyor that has projects that would be better done with a network approach rather than with RTK.

The basic rules

The basic rules of simple network design are:

• Connect the dots
• Measure the short lines

We want to be able to arrive at accurate points. Therefore we want to make sure that we control the distribution of errors as best we can. Following these two simple rules will provide a good distribution of errors.

To do this reasonably efficiently, we need to use at least 3, and preferably 4, receivers. In all projects I bid when I was really a surveyor, it was always more cost efficient to use 4 receivers than 3 receivers. Using only two receivers to attempt a network would be very inefficient.

The following is a possible set of 8 sessions, using 4 receivers, for thenetwork of points shown. It follows both rule number one and rule number two. Generally, rule number one will provide also for rule number two. Note that not every pair of points is directly connected, e.g. between URBAN and LOCKMAN, but the point spacing in that area is fairly homogeneous and this structure should provide for a good distribution of the residual errors.

The design session occupations are as follows:

THAPA

BENSON 54102 URBAN TTMPS

BENSON ADVANTAGE BARTLETT JERSEY

KIEFT ADVANTAGE NCS HOLLAND

JERSEY GIFFLES HOLLAND

SPENCER GIFFLES LEICA CARL

BULLDOG TTMPS BURTCH CARL

JERSEY TTMPS METCO LEICA

Note: One station isalways used as a hinge between each set of occupations. Sometimes two stations may hinge, but in general it is most efficient to try to hinge on only one point and notto double measure lines. This of course does not apply to high accuracy network procedure requirements. Follow the procedures specified by your contract.

Use all vectors or only the “independent” ones?

Much has been writtenabout the use of “trivial” or dependent vectors in a network. If you are doing session processing (where all the data between all the points in a session is considered at the same time), you will only use the resulting independent vectors in the adjustment. However most, if not all, of the manufacturer’s software today does not use session processing. Generally, the manufacturer’s software processes vector by vector independently. When processing this way, you can use all the vector solutions in your adjustment. Some surveyors will use only the “independent” vectors from a session even though it was processed vectorby vector.

Should you use only the“independent” vectors, or all the vectors available? In reality, it doesn’t really matter. However, choose your method and stick to it. Don’t mix and match

Below is the same set of points as shown above, measured in 10 sessions (an increase of 20%), where only three of the six possible vectors per session were used. That is, only the “independent” vectors (3 out of 6) of each session were used. The processing time was about 20 minutes because ofhaving to select individual vectors for processing. The resulting adjusted positions (minimally constrained with Bulldog held as control) are listed below the network plan.

The observed sessions areas follows:

LOCKMAN 54102 BURTCH THAPA

LOCKMAN URBAN BENSON METCO

ADVANTAGE BARTLETT KIEFT METCO

JERSEY NCS KIEFT METCO

JERSEY HOLLAND NORM LEICA

NCS HOLLAND NORM GIFFLES

SPENCER BULLDOG CARL GIFFLES

TTMPS LEICA CARL SPENCER

TTMPS URBAN BURTCH BULLDOG

THAPA 54102 BENSON ADVANTAGE

Station             Northing           Easting            Ht.       3D Q

Below, I show the same network using all the vectors contained in the 10 sessions. The processing took 3 minutes instead of 20. The resulting adjusted positions (minimally constrained with Bulldog held as control) are listed below the network plan.

<!--[if!vml]--> <!--[endif]-->

Station             Northing           Easting           Ht.       3D Q

Notice that there is very little difference in the adjusted positions of our points (4 mm N, 3 mm E, and 9 mm H at most). However, the 3D position quality figures in the all-vector adjustment are about twice as small as those in the adjustment of only the “independent” vectors. The all-vector adjustment is more optimistic because of the increased number of vectors. This is something to keep in mind. Are the statistics overly optimistic or more realistic?

This is an example where the network was designed to use only the “independent”vectors, therefore the vector between LOCKMAN and METCO doesn’t follow rule number one. If you design your sessions to use only the “independent” vectors, process it accordingly. If you are going to process all vectors, design it with the two basic rules in mind, and hinge your sessions accordingly. I would have designed the sessions as shown in the first section following my basic rules. Using all vectors is simpler to design and faster to process. Time saved is money earned.

Note: If you’d like to investigate this topic in more depth, you might start with “Session Versus Baseline GPS Processing” by Michael R.Craymer and Norman Beck, which appears in Proceedingsof ION GPS-92, 5^th International TechnicalMeeting of the Satellite Division of the Institute of Navigation, Albuquerque, NM, 16-18 September 1992, pp.995-1004.

Statisticalindicators simplified

The final accuracy of our network positions is determined in the least squares adjustment. We do not need to be statisticians to perform such adjustments, but we do need to know what those statistics are telling us, and how to use them to help usweed out any blunders. Leica’s SKI-Pro adjustment module,MOVE3 (licensed from Grontmij Geo Imformatie bv,Roosendaal, The Netherlands) uses terminology that is a little different than some other common adjustment packages. Let’s look at these terms and try to figure out what they are telling us.

F-test

This value is referred toas the Standard Error of Unit Weight, or the Variance Factor in other software. All it indicates is how well are estimates of error, and our actual errors, agree. A value of 1 would indicate that the actual errors in the data are exactly what we expected. A value less than one indicates that the actual data is better than we expected. A value greater than one indicates that the actual data is worse than we expected. The value does not indicate anything else. Ideally this value should be close to one. We can control this value by scaling our estimates of error.

W-test andT-test

The W-test and the T-testwould be referred to as the Normalized Residuals orStandardized Residuals in other software packages. The W-test is the equivalent of the normalized residuals ofthe vector components, while the T-test is the equivalent of the normalized 3D residual of the vector. These values essentially tell us which vectors are the outliers. The vector with the highest T-test value will be shown as an outlier (in my screen shots they appear as red vectors). Avalue of 5 would indicate residuals that are 5 times higher than expected based on our estimates of error. Use these values as a guide to weeding out and removing blunders. Utilize the actual residuals in ADJUSTED OBSERVATIONS section to determine when to stop. Remember that there will probably always be an outlier. An outlier is not necessarily a bad vector.

The W-test and the T-test values are dependent on the estimates of error. Make sure you use valid estimates of error in your adjustments.

Summary

For some surveys, RTK is not the best method to use. RTK is suitable for topo and stakeout type projects, but for control or “traverse” type projects, a network approach is much more suitable. The network provides advantages not available with RTK. However, we want to be as efficient as possible in obtaining these advantages. As we have seen above, the difference between using all vectors in a session or using only the “independent” vectors is very slight. The planning and processing is much simpler and faster using all vectors. For general surveys this would be the approach I would take. Keep it as simple as possible. If your clients, particularly government entities, have other requirements, follow them. And remember that the most important task in any network is to know how to weed out the blunders using the statistical indicators in thea djustment.

Keep it simple

• Connect the dots
• Measure the short lines
• Process everything
• Weed out the blunders

And enjoy your networking.

Network versus RTK