Least Squares - Modifying an Existing Network

Some Least Squares programs refer to modifying an existing network as ‘Re-Processing’. You can modify an existing network at any time, adding more points or observations as needed. However, you must decide whether or not to allow the new data to affect the existing adjusted positions. TPC can not make this decision for you, but does provide the tools for you to implement whichever option you choose.

TPC supports three general methods of modifying a network 1) re-computing the entire network, 2) fixing adjusted points or 3) weighting adjusted points.

Re-Compute Entire Network

You can throw out any previous network adjustments and start over with the new data and old data combined. This is the default mode. Since TPC stores the raw coordinates at the time a survey point is added to the network, it can simply start with the raw coordinates each time you re-compute the network.

If you have the luxury of building the network prior to publishing it, this is an excellent method to use.

Fix Adjusted Points

Using this method, you fix any points that are adjusted, forcing their positions to remain unchanged in any subsequent adjustments. You accomplish this by turning on the ‘Fix’ Adjusted Coordinates option in the Update Survey page before you update the survey with the adjusted coordinates. TPC updates the survey points and sets the estimated standard error of each adjusted coordinate to FIXED.

If you have published and used the positions computed by a previous network adjustment, it may be inappropriate to allow their positions to change in subsequent adjustments. This option allows you to both expand and densify an existing network with new data without changing the positions of the fixed points.

The drawback to this method is that points that are adjusted first automatically have higher precision than points that are adjusted subsequently. In the case of going from high-order control to low-order control, this may be appropriate, but in the case of similar order control work, it creates a biased network.

Weight Adjusted Points

If you are considering the ‘Fix Adjusted Points’ method, you may have reason to use the third method of weighting the adjusted points.

Remember, a Least Squares solution uses estimated standard errors called A Priori values. In the case of coordinate positions, the estimated standard errors indicate how much the X, Y and Z coordinates are allowed to move. By replacing the estimated standard error with the standard deviations computed from the previous analysis, you can in effect, limit the amount that an adjusted point can move to a range that is consistent with new data being added to the network.

Let’s assume for instance that point 100 was previously adjusted with computed X and Y standard deviations of 0.05 and 0.08 respectively. Updating the estimated standard errors of point 100 to 0.05 and 0.08 respectively and re-solving the network will produce adjusted positions for point 100 that are within the originally accepted range of error. So although the position of point 100 may change, the amount of change will be limited to the standard deviation of the original solution.

You accomplish this weighting by turning on ‘Update Std Error of Coordinates’ in the Update page of the Least Squares Network Adjustment dialog.

Related Topics

Least Squares
Least Squares Overview
Least Squares Network Adjustment
Least Squares Blunder Detection
Least Squares Positional Tolerance
Least Squares Files
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