To do this, we have to discuss some statistical analysis theory. All GNSS manufacturers calculate accuracy the same way, but will often display different versions. The first thing to realize when discussing GPS is that "accuracy" technically refers to "precision." Think of a dart game; if you throw 5 darts and they all miss the dartboard, but all 5 darts are clustered within an inch of each other, your precision is great, but your accuracy needs improvement. That's how GPS/GNSS works. Accuracy is a statistically calculated value of how well the positions fall in with each other within a certain observation period. That usually begs the question.....
There are a number of factors that influence this. First, we are not on a stable platform. Our world is constantly moving and changing. Take a look at the graphic below to see how much our world has likely changed. Even though these changes took place over hundreds of millions of years, you get the idea.
The National Earthquake Information Center says the world has over 20,000 recorded earthquakes per year, or 55 earth quakes per day. Even if it is only by tiny fractions of a meter, our earth is changing 55 times per day. How do you determine how "accurate" a point is on an ever-changing surface? The answer is by setting a moving reference point.
For instance, in the United States, most of our RTK networks use a reference datum called the North American Datum of 1983(NAD 83). NAD 83 was created by reviewing over 250,000 different reference stations across the U.S. and freezing that information in time as of April of 2011.
In the US, the National Geodetic Society will publish an algorithm every few years to adjust between ITRF and our local datum. This is why GNSS is referencing “precision” rather than “accuracy,” because accuracy becomes more of an observation against an unknown reference point.
The bell curve provides us with a tool to utilize standardized measurements and better inform us of the distance (or “deviation”) between the average (mean)and the data point. Because the normal curve always has a mean of zero and a so-called standard deviation of one, we can begin to understand accuracy in these terms or positions.
To illustrate, suppose we take an even distribution of grades between 0 and 100.We have an average of 40 (high point of the curve), with a standard deviation of 21.6 points. This means that 68% of the values on the bell curve fall between 18.4 on the low side of the average, and 61.6 on the high side of the average.
Now, let’s take that and apply it to GNSS accuracy. Below are some real world results of the Asteri X3i Mod3, collecting around 1 minute’s worth of data on a second by second basis from our HPRTK correction service, plotted in a Georgia StatePlane NAD 83.
It is pretty impressive that all positions are in a tight little ½ inch diameter, but let’s look at how it relates to standard deviation and GNSS accuracy.
First, let’s take a manufacturer’s specification on the Asteri X3i Mod3. It states “accuracy” of 8 millimeter + 1ppmRTK. We are going to assume that our HPRTK network has a 50km baseline, so that adds about 5 millimeter to the 8 millimeter ,so we will assume our RTK precision is stated at 1.3 centimeter.
Next we will look at the “accuracy” the device reported. Our device, like most, reports 1sigma error in meters in latitude, longitude ,and altitude. We try to simplify this data for our users by just displaying a “horizontal” value.
This value is actually a calculation of the combination of both latitude and longitude by using the Pythagorean theorem. On the next page is what the above data looked like graphically, and then on a standard deviation graph. So, essentially we had a 1.6centimeter average reported (pretty close to the 1.3 centimeter) and a 1.6 millimeter standard deviation. That’s pretty precise!
Finally, let’s add that final level of detail to determine how it falls in with a reference. We collected this data over a local NGS monument. This monument was last adjusted to the NAD 83 reference datum in June of 2012, almost a decade ago. So, as we discussed earlier, our data has moved in relation to that point over the last decade. How much so depends on where we are and when we collected. Fortunately our monument in North East Georgia is in an area of fairly low tectonic movement. Below is what the collected data looks like in comparison to the monument. We have inserted a standard US quarter to give a better idea of scale than just a simple scalebar.
As you can see, the precision will remain the same, but our actual “accuracy” in comparison to a “known” reference point will shift a little bit. In our case, our absolute accuracy in comparison to our monument hovered around 2 centimeters (remember1.6 reported), with an absolute standard deviation of 1.9 millimeters; a precision that actually far exceeds the specification.
So, you can hopefully now see that while a GNSS receiver specification will usually mention “accuracy,” they are really talking about precision. The reported value gives a level of precision that each of the points will fall in with other points collected in the same session and in relation to a constantly changing framework. The accuracy that those positions fall in with your location on the earth will be very dependent upon what you are using as a reference, how well and how recently it was established, and most importantly, how you might be translating that to a different reference frame.
