Comparing sub-meter GPS accuracy

For the past year or so, I have been interested in sub-meter GPS receivers.  There are several on the market and they basically work in the same fashion.  I will write another blog later on how they work, but for now I want to focus on one particular aspect that is confusing to a lot of folks.  How good are the receivers?

To understand the answer, you need to know that all GPS work in the same way, using a satellite array to calculate the position of the receiver on Earth.  However, there are many factors that affect the location calculated by the receiver.  Some of these have to do with the satellites, some with the receiver, most with complexities in the Earth’s surface and atmosphere (and some errors are due to the mathematical representations of Earth positions).  The receiver is set to collect a number of positions and then present the average position.  The variables that are most important to the user are the accuracy of the average position and the precision, or ‘repeatability,’ of the collected positions.  These two factors are not the same!  A receiver might calculate the average position within 50 centimeters of the true position (good accuracy), but the spread of points might be quite dispersed (poor precision).  Alternatively, the average position might be many meters off of the true position (poorer accuracy), but each point might be within several centimeters of each other (great precision).  The accuracy can usually be shifted by choosing different models for the Earth’s surface in your software.  This is known as the ‘geoid’ and common ones in the United States are WGS84 and NAD27.  The bottom line?  The better the receiver, the better the precision.

So, how do the companies quantify the quality of the precision?  Here are some examples of similar real-time, sub-meter GPS receivers culled from data sheets available online.  The data are simplified and re-formatted for consistency.  I focused only on the differentially-corrected (using WAAS) accuracy of horizontal measurements.  All the data sheets have a footnote that these are ideal conditions with satellites near the horizon, clear of obstructions, etc.:

Geneq SX Blue II
DGPS Horizontal Accuracy:     < 60cm 2dRMS*

Topcon GMS2
DGPS Horizontal Accuracy:     < 50cm RMS

Magellan ProMark3
DGPS Horizontal Accuracy:     <100cm RMS

Trimble GeoXT
DGPS Horizontal Accuracy:     < 100cm RMS

 *Furthermore, the SX Blue II data sheet also lists < 30cm RMS and < 25cm CEP for DGPS horizontal accuracy.

 What does this mean?  Note there are three different benchmarks—RMS, 2dRMS, and CEP.  Each is a statistical measurement achieved by averaging the distances to each measured point from the average.  RMS is the most commonly used and means ‘root mean square.’  (HRMS means ‘horizontal RMS’ and is the value given above but I dropped the H as it is redundant.)  The RMS is calculated by taking the square root of the average of the squared errors along the X and Y axes.  The one-sigma level is 67% so that means that you can expect a 67% probability that your measurements will be within the distance stated.  2dRMS means “two times the RMS” or two-sigma.  Therefore, the distance stated will be achieved with a 95% probability.  That is significantly different!  Put in simplest terms, 2dRMS is likely 95% of the time and RMS is likely 67% of the time.  That is why the SX Blue claims <60cm 2dRMS and <30cm RMS.  Finally, CEP is the “circular error probable” and is a measure of the circle centered on the true location that collects 50% of the error distribution.  In practice, it is not as valuable or universally used as RMS or 2dRMS.

BOTTOM LINE:  Not all data sheets are the same so check if you are looking at RMS, 2dRMS, or CEP when comparing.  Based on the data sheets listed above, the SX Blue II is the best for single receiver, real-time differential correction.

What about post-processing or two-receiver systems?  Another day…

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