# Least Squares - Relative Positional Precision (RPP)

The 2011 standard defines RPP in section 3E as  follows: "Relative Positional Precision" means the length of the semi-major axis, expressed in feet or meters, of the error ellipse representing the uncertainty due to random errors in surveyed property relative to the monument, or witness, marking any other corner of the surveyed property at the 95 percent confident level.

Section 3Ev further states that "The maximum allowable Relative Positional Precision for an ALTA/ACSM Land Title Survey is 2 cm (0.07 feet) plus 50 parts per million (based on the direct distance between the two corners being tested)."

## Least Squares Error Ellipse

Based on this definition, you will want to evaluate the semi-major ellipse values (Su) for the corners of the surveyed property.  In a typical property survey where the PPM errors are very small, you will want to ensure that the Su values are less than 2 cm or 0.07 feet.

## The Relative Position Precision (RPP) Report

In addition to checking the Su values, you can also ask TPC to include the Relative Position Precision report.

This report accounts for the line of sight distance between each corner be adjusted and the fixed control points in the survey.  Although this does not allow the flexibility to compute RPP between any 2 corners, it does provide maximum allowable errors (consider this to be the maximum Su allowed).  You will want to check the Su values of survey corners with the maximum values computed in this report.  See the example below.

[ Error Ellipse ] and [ Adjusted Coordinates ] both provide Su

Station        Su (semi-major axis)

1            0.023

2            0.024

3            0.026

4            0.021

5            0.024

[ Relative Positional Precision (RPP)]

Maximum allowable RPP based on 0.07 Feet and 50 ppm

Station         From

1 from  A1=0.0712'  A2=0.0723'

2 from  A1=0.0719'  A2=0.0727'

3 from  A1=0.0717'  A2=0.0721'

4 from  A1=0.0728'  A2=0.0729'

5 from  A1=0.0726'  A2=0.0725'

Looking at the above data, we are 95% confident that our computed position for Station 1 would not change more than 0.023 feet in any direction (semi-major axis) 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 RPP given in the [ Relative Positional Precision ] section of the report, we see that we are allowed 0.0712' from A1 and 0.0723' from A2.  So our solution for Station 1 is within the Maximum allowable RPP.