As I have reported in previous GPS Observer columns (POB November 2004, December 2005), the National Geodetic Survey (NGS) is in the process of readjusting the National Spatial Reference System (NSRS). This will be the first-ever three-dimensional national adjustment. Detailed information about this readjustment is available on the NGS website at In addition to readjusted coordinates, the output of the readjustment will be an accuracy value at the two standard deviations (2σs) level for each component of the station's position. Since the detailed information on the format of the data sheet has not been published, this gives me leeway to speculate on what will happen.

Fig. 1

An Explanation

There are two features of this readjustment that need to be repeated:
  1. Only GPS will be adjusted. Classical geodetic observations will not be included.
  2. The CORS stations will serve as control, i.e., CORS positional coordinates will be held fixed.
All GPS data that was submitted to NGS by June 1, 2005 will be reviewed and, if appropriate, loaded into its database. NGS plans to use a Helmert Blocking strategy. Helmert Blocking, which breaks up a network into a hierarchy of small networks or blocks for a final and complete network adjustment, was used for the original NAD 83 adjustment (NAD 83 (1986)). This new adjustment will be designated NAD 83 (NSRS).

If you are a GPS surveyor familiar with least squares network adjustments, you know that a by-product of every adjustment is the a-postari variance-covariance matrix. The diagonal elements of this matrix are the variances of every component (X, Y, Z or w, l, h) of every station in the adjustment. The variance is the square of the standard deviation, σ2. As stated earlier, NGS will give the accuracy statement for each station's positional component as 2σ, which is 95% probability, in order to be consistent with the document on Standards and Specifications of GPS Relative Positioning.1

Fig. 2

An Example

This may sound complicated, but it's not. The data sheet for each GPS station will list the adjusted position and the accuracy values. As an example to show what may happen, I selected a GPS station in New Mexico to show what additional information will be available. Figure 1 shows the Federal Base Network (FBN) for the United States. With this map on my computer screen I clicked on New Mexico and got Figure 2. Notice on Figure 2 that I highlighted station "˜SRA A.'

Figure 3 on page 50 is a portion of the NGS data sheet for station "˜SRA A,' a station in the New Mexico High Accuracy Reference Network (HARN) with a B-Order horizontal component and a Third-Order Class II ellipsoid height component. The Point Identification, PID, is AC7062. Since this is not a CORS station, the readjustment will calculate a new position and accuracy values for each component; the components will be geodetic latitude, geodetic longitude and ellipsoid height, which are underlined in Figure 3. The new data sheet for this station may look something like the following:

What does the accuracy statement really mean? Perhaps the best way to explain this is to look again at Figure 2 on page 48. Stars denote the CORS stations, which will all be fixed. Every other station on the map will be adjusted to the CORS network. I think it's safe to say that the accuracy statements for each adjusted station can be called a "national accuracy," the accuracy of the station in the national network.

For many GPS surveyors, their comment about the accuracy statement will be, "So what?" Their previous work was adjusting their observations to either HARNs and/or CORS, and always holding those stations fixed. If they will be adjusting to the CORS network, no changes are necessary since all CORS stations will be fixed. The change comes when a local network is tied to a non-HARN station.

Let's say a surveying firm observed a local network in New Mexico, and the only national station in the network is station SRA A, the station shown in Figure 2. When the network is adjusted, and the adjustment is a minimally constrained adjustment, they can fix station SRA A to make sure the network is consistent with no blunders. However, for the final adjustment, they will have to constrain each component of SRA A to the accuracy value shown on the station data sheet. By doing that, the accuracy values, after adjustment, for all stations in the new network will be its accuracy in the national network.

Learning the New Adjustment

Can you and I apply these weighted constraints with the network adjustment packages in use today? I'm not up on every available adjustment package, but I'd be shocked if this feature were not available. The network adjustment software developers will have to make sure the users apply a weight w = 1/σ2, not 1/(2σ)2.

What about the GPS surveyor? Will she understand the weighting process? NGS has in place a four-hour educational seminar that explains how to use the accuracy data in an adjustment. GPS equipment manufacturers will have to instruct their training personnel on the adjustment so customers can be properly educated.

I hope we don't have too many situations like the one I experienced years ago. A GPS surveying firm was awarded a contract to establish control for a county government. The firm hired me to design the network and perform the network adjustment. I adjusted the network by tying it to the state HARN; the adjustment gave the adjusted position of each station plus the standard deviation of each component.

I was with the surveying firm when they delivered the final product to the county surveyor. An explanation was given for everything, including the accuracy statements. The county surveyor said, "I appreciate all you have done, but for the time being I'm going to use the data without the accuracies. We have no way of using the accuracies." With modern geographic information systems, this is not a problem. GIS specialists know how to include coordinate accuracies into their databases; we need surveyors to become just as knowledgeable.