SBAS (WAAS) and NDGPS Accuracy and Statistics

October 21, 2010  - By 0 Comments

There’s something I’ve been wanting to write about since the ION-GNSS conference a few weeks ago. However, a nasty cold, a 10-day trip to Europe (INTERGEO conference), and some jet lag have kept me from it until now.

Here goes.

First of all, most of the presentations from the CGSIC meeting are available on the USCG Navigation Center website. You can view them by clicking here. There’s some very good reading and most of it is pretty light-weight and in PDF format.

One of the presentations at the CGSIC (Civil GPS Service Interface Committee) meeting during the ION-GNSS conference was “Integrating NDGPS and SBAS —
An Optimal Real-time GPS Mapping Solution,” presented by Jean-Yves Lauture of Geneq, Inc.

I’m publishing two of the slides from his presentation in order to:

  1. Show the accuracy potential of WAAS and NDGPS given a high performance L1 receiver.
  2. Discuss the statistical names/values used to express GPS accuracy.

First of all, each of the slides below are at the same scale. Each ellipse is 20 cm with the outside limit (radius) being one meter.

I’ve known for quite sometime that SBAS (WAAS in this case) is capable of sub-meter precision with a single-frequency GPS receiver. These results are a bit better than what I’ve seen personally, and keep in mind it’s a limited data set of 1,800 continuous epochs, but impressive none the less. Also, keep in mind that the WAAS Performance Analysis Report published quarterly by the FAA’s National Satellite Test Bed shows the 95% horizontal accuracy value for Denver, Colorado, (near where this data was collected) being .547 meters for the quarter ending June 30, 2010 (7,856,354 samples collected over three months).


30 minutes of WAAS-corrected data (each ellipse represents 20cm)


The results I didn’t expect were the slide below, which shows NDGPS-corrected results using the same receiver/antenna. Keep in mind this is a GPS L1 receiver using phase-smoothed pseudorange measurements, not a GPS L1/L2 receiver using a carrier-phase float solution. If you look closely, you’ll see it states the baseline distance is 200 km. Granted, this is a limited data set, and I’ll be interested in seeing further results. If this was a dataset presented by a manufacturer or other party with some sort of interest, I wouldn’t publish it, but this is data collected by an objective entity (a credible U.S. government agency) so that earns, in my mind, a level of credibility.

The results are pretty impressive. All data points fall within ~20 cm.

30 minutes of NDGPS-corrected data (each ellipse represents 20cm)

Keep in mind that this data was collected recently, and we are currently in a period of low ionospheric activity. In other words, data was collected under near-ideal conditions. At the end of the day, my point is that GPS L1 accuracy using SBAS and NDGPS has gotten pretty darned good.

Accuracy Statistics

The second reason I’m publishing the slides is to discuss accuracy statistics.

Look at the small box inside each slide showing 99%, 95%, 68%, and 50% accuracies.

If you look at the data points, it might not be immediately apparent how those values were arrived at. For example, how could a group of data points all within ~20 cm have a 95% confidence of 37 cm?

To explain this, there was a good article published in GPS World in 2007 titled “GNSS Accuracy: Lies, Damn Lies, and Statistics” by Frank van Diggelen. It does a good job explaining statistical expressions (RMS, 2DRMS, etc.).

Keep in mind that most manufacturers express horizontal GPS accuracy specifications based on 68% confidence. When the specification sheet states “sub-meter” HRMS (horizontal RMS) precision, that means 68% of the time; the horizontal accuracy will be less than a meter. In reality, that “sub-meter” receiver won’t consistently deliver sub-meter precision. If you convert the 68% HRMS value and express it with 95% confidence (2D HRMS), the actual horizontal precision for that same receiver will be well over one meter. That’s the precision you can expect from the receiver, not the 68% confidence value.

Thanks, and see you next time.

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