TPC can reduce random error inherent in survey measurements through a Least Squares adjustment. A Least Squares adjustment can be applied to something as simple as a resection and as complicated as a 3-dimensional network. The result is adjusted coordinates that are statistically more accurate than those derived from simple intersection and traverse adjustments. Learn more about Least Squares in the Least Squares Overview.
You can find the Least Squares Network Adjustment tool in Tools | Least Squares Network Adjustment. A step-by-step guide on how to use the Least Squares Network Adjustment tool in TPC is included in the Advanced Learning Guide.
Additional help topics on the Least Squares Network Adjustment dialog box can be found here.
TPC can reduce random error inherent in survey measurements through a Least Squares adjustment. A Least Squares adjustment can be applied to something as simple as a resection and as complicated as a 3-dimensional network. The result is adjusted coordinates that are statistically more accurate than those derived from simple intersection and traverse adjustments.
Learn how to use TPC's Least Squares Network Adjustment toolTPC automatically uses Least Squares to solve resection points. This method allows the greatest flexibility in the data you collect to generate the resection position.
TPC can adjust traverses of Closed Loop or Close Point-To-Point types using Least Squares. These two closure types satisfy the condition of having a fixed point to begin from and a fixed point to end on.
A Least Squares network is not limited to the sequence of points defined by a traverse. Although Least Squares can use the points defined by a traverse, it can also combine traverses to form a network then solve the network simultaneously.
Solving a Least Squares Network allows you to reconcile all your data at once providing the strongest solution possible.
A blunder is an observation that is in error by more than the typical systematic or random error normally encountered. It's a BIG error that happened because two numbers were transposed or the wrong back sight point was sighted or there was a glitch in the data transfer or something. Blunders are generally 'one time' errors that don't appear elsewhere in the survey.
Positional tolerance is a standard of accuracy for survey points. A computed position either meets the standard or it does not. The standard defines the radius of a circle about a theoretical point based on its distance to the nearest controlling station. As long as a computed position lies within the positional tolerance of the theoretical point, it meets the standard. The higher the standard the smaller the radius about the theoretical point and thus the smaller the positional tolerance.
A Least Squares solution requires you to follow certain steps on your way to a solution. These steps insure that you give proper consideration to each phase of the Least Squares solution.
The resection and traverse solutions go through these same steps but do it behind the scenes without your intervention since the solution is based on such a well defined set of data.
TPC reports the Chi Squared value of a solution, using the computed standard error of the solution (reference variance) and the degrees of freedom. The test either passes or fails at the 99% significance level.
TPC can report observation and coordinate blunders it identifies during a Least Squares solution. Once identified, you can exclude the offending observations or coordinates and compute a new solution or you can take whatever steps are necessary to correct the observation or coordinate then compute a new solution.
Positional tolerances define the radius of a circle about a theoretical point based on its distance to the nearest controlling station. Positional tolerances are derived from a Least Squares solution that gives consideration to stations that control the positions of dependent stations. Generally, these controlling stations are monuments of fixed legal position and the dependent stations are new monuments that are being set.
When you ‘Pre-Analyze’ a Least Squares solution, you want to see what the adjusted coordinates and observations are without actually applying them to your survey. This step allows you to determine the strength of the Least Squares data and solution.
When TPC solves a Least Squares network or traverse, it is doing the pre-analysis. The survey is not actually updated until you choose to Adjust it with the Least Squares solution.
What do you do when you have more points to add to a survey that has been adjusted by Least Squares? Or what if you have an updated position for one of your fixed control points?
These situations and others require you to re-run or re-process the Least Squares solution.
When you do a network adjustment, the Least Squares analysis, including all data and adjustments is stored in a file with the same name as the survey but with a .LSA extension. If your survey is JOB1.TRV, the Least Squares analysis file will be JOB1.LSA. This file is stored in the same folder as the survey.
Additional resources and a step-by-step guide on using Least Squares Network Adjustment in TPC is available in the Advanced Learning Guide.
Least Squares
Least Squares Overview
Least Squares Resection
Least Squares Traverse Adjustment
Least Squares Network Adjustment
Least Squares Blunder Detection
Least Squares Positional Tolerance
Least Squares Files
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