The following errors for the Ground Control Points (GCPs) and Checkpoints (CPs) in photogrammetry project are calculated:

- Mean: The average error in each direction (X,Y,Z).
- Sigma: The standard deviation of the error in each direction (X,Y,Z).
- RMS: The Root Mean Square error in each direction (X,Y,Z).

In order to calculate the values, tie points (GCPs and CPs) need to have **measured coordinates**** that are compared with their calculated position**. To measure the coordinates of points, typically total stations and RTK GNSS receivers are used.

**Mean**

For a given direction (X,Y or Z) it is defined as: Mean = μ = Σ(ei)/N

Where ei is the error of each point for the given direction.

N: The number of tie points.

The *Mean Z error* helps to recognize systematic errors due to bad GCP acquisition.

**Sigma**

For a given direction (X,Y or Z) it is defined as:

Sigma = σ = sqrt(Σ(ei - μ)^2)/N)

Where ei is the error of each point for the given direction.

μ: The mean error for the given direction

N: The number of GCPs

Assuming the error is Gaussian, *the Sigma error* gives confidence intervals around the *Mean error*:

- 68.2% of the points of the project will have an error of +-σ
- 95.4% of the points of the project will have an error of +-2σ
- 99.6% of the points of the project will have an error of +-3σ

A graph showing the Gaussian distribution.

**RMS**

For a given direction (X,Y or Z) it is defined as:

RMS = sqrt(Σ(ei^2)/N)

Where ei is the error of each point for the given direction.

N: The number of GCPs

The *RMS error* will take into account the systematic error. If *Mean error*=0, the *RMS error* will be equal to the *Sigma Z error*. The comparison of the *RMS error* and *Sigma error* indicates a systematic error.

Of the 3 indicators, the RMS Error is the most representative of the error in the project since it takes into account both the mean error and the variance.

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