Definition of Root Mean Square (RMS) Error and RMSE Formula (Especially for GATE-Geospatial 2022)

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Root Mean Square Error (RMSE) also known as Root Mean Square Deviation is one of the most widely used statistics in GIS.

We use RMSE in a variety of applications when compare two data sets. RMSE measures how much error there is between two datasets.

Deriving the RMS Error

After six coefficients (A-F) are estimated, the digitized coordinates of the first control point can be used as the inputs (the x and y values) to compute the X and Y values, respectively.

If the digitized control points were perfectly located, the computed X and Y values would be identical to the control pointีšs real-world values.

The deviations between the computed (estimated) X and Y values and the actual coordinates then become errors associated with the first control point on the output.

Root Mean Square Error Example

For example, we can compare a predicted LiDAR elevation point with a surveyed group measurement.

  • Predicted value is LiDAR elevation value
  • Observed value is surveyed elevation value
This Diagram Shows Predicted Value and Observed Value

RMSE Formula

Root mean square error takes the difference for each LiDAR value and survey value.

You can swap the order of subtraction because the next step is to take the square of the difference. This is because the square of a negative value will always be a positive value.

After that, divide the sum of all values by the number of observations. Finally, we get a RMSE value.

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