Tech Chat | Evaluating RTK Accuracy in Different Dimensions

In the realm of surveying, ensuring the accuracy of your measurements is paramount. Whether you're working on large-scale mapping projects or precise property boundary determinations, understanding and evaluating the accuracy of your RTK surveying can significantly impact your results. This blog introduces essential formulas and concepts to help you assess uncertainty in various dimensions of RTK surveys, making your work more reliable and efficient.

One-dimensional Accuracy

One-dimensional accuracy measures the true error in individual measurements. To assess this, we use the following formula, which considers the diagonal elements Pxx, Pyy, Pzz of the covariance matrix PΔX:

In Earth-Centered Earth-Fixed (ECEF) XYZ coordinates, the standard deviations (formal errors) of the estimated vector components are given by:

To achieve more accurate results in surveying, transforming coordinates is often necessary. Using the transformation matrix R from ENU (East-North-Up) coordinates to XYZ coordinates:

The standard deviations in ENU coordinates are defined as:

Bidimensional Accuracy

Bidimensional accuracy typically refers to horizontal errors. The horizontal error is defined by the following formula:

Three or Multiple Dimensional Accuracy

Three-dimensional accuracy includes all three spatial dimensions. It is closely related to the concept of Dilution of Precision (DOP), which includes PDOP, VDOP, HDOP and etc. that are commonly usered in RTK surveying. Please refer to our previous blog for more details about these indicators.

Tech Chat | How accurate is your GNSS device? – DOP Indicators

Root Mean Square (RMS) Errors

RMS errors are commonly used in RTK survey software to specify accuracy.

Let's consider ΔEi, ΔNi, ΔUi as the errors in the East, North, and Vertical components of the i-th position estimate sample. The RMS errors for vertical, horizontal (bi-dimensional), and three-dimensional accuracy are defined as follows:

Vertical RMS:

Horizontal RMS:

3D RMS:

These formulas provide a comprehensive way to evaluate the accuracy of your RTK system, ensuring that you can rely on your measurements for precise and reliable surveying results.

Learn more about SingularXYZ RTK products,

X1 GNSS Receiver
Sfaira ONE Plus GNSS Receiver
P2 Plus GNSS Receiver