# 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.

## Related Topics

Least Squares

Least Squares Blunder Detection

## Editions

Premium, Professional