# How are the GCP Errors defined in the Quality Report?

The Pix4 Quality Report contains the following errors for the GCPs:

• Mean: The mean/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).

Note: The errors are given in the same unit as the project (meter or international foot).

Mean

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

Mean = μ = Σ(ei)/N

Where eis the error of each point for the given direction.

N: The number of GCPs

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

Example: If all GCPs have a systematic error of 5 cm in the Z direction, the Mean Z error will be 5cm.

Sigma

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

Sigma = σ = sqrt(Σ(ei - μ)^2)/N)

Where ei si 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 Example: If all GCPs have a systematic error in Z of 5 cm, the Mean Z error will be 5cm. If the Sigma Z error is 1cm, the probability of a point to have an error in the interval [4,6] cm is 68.2%.

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.

Example: If all GCPs have a systematic error in Z of 5 cm, the Mean Z error will be 5cm. The Sigma Z error will show the probability of the points of the project to have an error of +-1cm, +-2 cm and +-3 cm, if σ = 1 cm (as if there was no systematic error). The RMS error will be bigger than 5 cm, as it does not remove the systematic error.