Least Squares – Analyze

Analyzing a Survey

TPC analyzes the selected traverses in your survey to create a Least Squares network with the appropriate point and observation records. You can analyze all the traverses in the survey, creating a network for the whole survey or you can analyze selected traverses, creating a partial network.

Each survey can have only one Least Squares network associated with it. This Least Squares data is stored in a separate ASCII text file with the extension .LSA. So the survey JOB1.TRV would have a JOB1.LSA network file.

Analyzing a Traverse

When you adjust a traverse using Least Squares, TPC analyzes just that traverse. TPC considers the closing points and angles you entered in the Closure View along with all the control points in the traverse. If you included the closing point and closing angle as the last two points in the Traverse View, TPC will use this data instead of the closing angle you enter in the Closure View.

Each traverse can have only one Least Squares adjustment associated with it. The Least Squares data is stored in a separate ASCII text file using the traverse name as the filename and the extension .LSA.

Standard Error Estimates (default)

When generating observations from survey data, TPC uses the A Priori values established for this analysis in the Miscellaneous tab. You will want to select estimates of standard error that are appropriate for the equipment and methods used in your survey.

Standard Error Estimates by Traverse

You can also assign A Priori values to a traverse. When TPC generates observations from that traverse, it will use the A Priori values of the traverse instead.

  1. To generate A Priori values for a traverse, go to the Traverse View for a traverse and choose Tools | Least Squares Standard Errors...
  2. To generate A Priori values for multiple traverses, go to the Traverse Manager, select the traverse you want to set and choose Tools | Least Squares Standard Errors...
In steps 1 and 2, you can also remove the A Priori values for a traverse(s), in which case TPC will revert back to the A Priori values for the least squares analysis for these traverse observations.

Including Survey Points

When TPC searches a selected traverse, it looks for control points that are being computed. These are automatically included in the analysis. TPC also looks for control points that are needed to compute points that have been included. If an observation that includes a horizontal angle references a backsight point that has not yet been included, TPC adds that backsight point. The Least Squares solution requires that observed data be compared to inversed data, so the reference points must be present in the analysis.

Including Protected Points

If a protected survey point is included, TPC must determine whether or not this point should be ‘fixed'. Remember, a fixed point is not allowed to move in the Least Squares solution. TPC relies on the ‘Fix Protected Points' option in the Analyze dialog. to determine whether or not to fix protected points.

Side Shot Points are Not Included

Side shot points are not included. Instead, TPC provides an option to re-compute them when you update the survey or traverse with the adjusted (computed) coordinates. This option is available in the Update page.

Including Observations

TPC adds observations based on the raw data stored in the selected traverses. A foresight observation in a traverse, will create a horizontal angle record and a horizontal distance record. If the 3D option is selected, a vertical angle or vertical distance record will also be added.

If you traversed to the same point more than once (it is included as a foresight in more than one selected traverse), TPC will create additional observation records each time it is encountered. The point itself is only included once, so the extra observations create what is called ‘Redundancy'.

Including Redundant Observations

TPC allows you to recall an existing point into a traverse then enter observed data like a distance or angle to that point. In this special situation, the observed data does not recompute the observed point. It simply creates what is called ‘Redundancy'. Your traverse or survey can include any number of redundant observations. As a rule, the more redundant observations you include, the stronger (more accurate) the solution.

Related Topics

Least Squares
Least Squares Network Adjustment
Redundant Data


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