Least Squares - Relative Positional Accuracy (RPA)

the 2005 Accuracy Standards for ALTA/ASCM Land Title Surveys define Relative Positional Accuracy as "the value expressed in feet or meters that represents the uncertainty due to random errors in measurements in the location point on a survey relative to any other point on the same survey at the 95 percent confidence level." The maximum allowable accuracy per the standard is 0.07 feet and 50 ppm. The standard requires that an ALTA/ASCM Land Title Survey contain a certificate to this extent. TPC provides two such certificates in the \Blocks\ALTA\ folder. See ALTA/ASCM Land Title Surveys.

Confusion Over RPA in the Press

Two articles by Gary Kent (The American Surveyor, June 2007 and The American Surveyor, July/August 2006) both state that "There continues to be a great deal of misunderstanding and confusion over the definition and application of Relative Positional Accurcay in the ALTA/ASCM standards."

What the ALTA/ACSM Standard Does Not Specify

Perhaps the confusion over RPA comes from unspecified assumptions the standard makes. Because RPA involves a PPM component, the network path between any two survey points in part determines the RPA of the two points, but the standard does not specify a minimum (shortest path) or maximum (longest path). Certainly, a 'best case' RPA and 'worst case' RPA could be computed in almost any network, but the standard makes no specifications to this point.

Also, at the time TPC introduced RPA into it's Least Squares Analysis report there were no examples of RPA readily available from ASCM.

Traverse PC's Least Squares Analaysis

The Standard states that Relative Positional Accuracy may be tested by (1) comparing the relative location of points in a survey as measured by an independent survey of higher accuracy, or (2) the results of a minimally constrained, correctly weighted least square adjustement of the survey.

TPC provides the second option (2) via it's least squares traverse or network adjusment as stated by the standard. TPC provides pre-defined A Priori values clearly labeled ALTA/ACSM 2005 Standard and solves the traverse or network at the 95 percent confidence level.

Traverse PC's RPA Assumptions

In order to provide additional RPA reporting, TPC has to make assumptions not otherwise stated in the Standard. To that end, TPC computes the maximum allowable 'line of sight' RPA of every adjusted point from every fixed point in the traverse or network analysis. The least squares adjustment, by definition, guarantees that the actual RPA between the adjusted point and the fixed points is within the reported maximum.

In the absence of clearer specifications from ACSM this provides a smorgasboard of RPA data.

Reading the Report

[ Positional Tolerance ]

Station Radius

1 0.023137

2 0.024657

3 0.026170

4 0.021125

5 0.024583

[ Relative Positional Accuracy (RPA)]

Maximum allowable RPA based on 0.07 Feet and 50 ppm

Station From

1 from A1=0.1277' A2=0.2314'

2 from A1=0.1920' A2=0.2715'

3 from A1=0.1780' A2=0.2185'

4 from A1=0.2801' A2=0.2991'

5 from A1=0.2652' A2=0.2521'

Looking at the above [ Positional Tolerance ] data, we are 95% confident that our computed position for Station 1 would not change more than 0.02317 feet in any direction if we were to recompute it with a higher order survey using the same fixed control points A1 and A2 used in the Least Squares analysis. If we then look at the Maximum allowable RPA given in the [ Relative Positional Accuracy ] section of the report, we see that we are allowed 0.1277' from A1 and 0.2314' from A2. So our solution for Station 1 is within the Maximum allowable RPA.

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