Sunday, April 4, 2021

GPS Noise and Data Rates

I'm noise sensitive, so perhaps it is quite fitting that I spent some time looking at "noise" in GPS units, and the relation between noise and data rates. Between the relatively cold water around Cape Cod and Cape Cod's dubious distinction to be the hot spot for the Brazilian P.1 variant of the COVID virus, on-the-water testing will have to wait a while. So the tests I report here are all stationary tests.

One big advantage about stationary tests is that we know exactly what speed the GPS should report: 0.00. Everything else is an error. As Tom Chalko did with Locosys GPS units many years ago, we can use this to learn about the error characteristics of GPS chips. There's one little caveat about the directionality of speed in speedsurfing, and the non-directionality of measured speed when the actual speed is 0, but we can ignore this for now.

For this series of tests, I am using a Sparkfun Neo M9N GPS chip with an active ceramic antenna (25 x 25 x 2 mm from Geekstory on Amazon). I'm logging either via USB to the a Surface computer, or with the Openlog Artemis I described in my last post. Compared to the M9 chip with the onboard chip antenna I used before, the current combo gets a lot better reception.

Let's start with an utterly boring test, where the GPS had a perfect, unobstructed view of the sky on a sunny day (the GPS was on top of the roof rack on our high roof Nissan NV van):

At the beginning, there's a little bit of speed when I switched the GPS on, and moved it to the top of the van. I had used the GPS just a few minutes earlier, so this was a "hot start" where the GPS very quickly found more than 20 satellites. After that, it recorded a speed close to zero (the graph on top), with an error estimate around 0.3 knots (the lower graph).

Let's switch to a more interesting example. The next test was done inside, over a period of almost 2 hours. The GPS was positioned right next to a wide glass door, so it had a clear view in one direction. Here's the graph:

At three different times, the GPS recorded speeds of more than 1 knot, even though it was not moving at all. With a typical estimated accuracy of about +/- 0.5 knots for each point, that number is actually a bit lower than expected. But what raises some red flags is that each point with a speed above one knot is closely surrounded by several other points that are also much higher than average. This is reflected in the top speeds averaged over 2 and 10 seconds: 0.479 knots and 0.289 knots. In fact, all top 5 speeds over 10 seconds are near or above 0.2 knots.

Let's look at one more test run - this one done at 8 Hz overnight, for about 10 hours:
The GPS was at exactly the same spot for this test. The overall results is similar, with a bunch of spikes between 0.5 and 0.9 knots. The top results for 2 second and 10 second averages are a bit lower, but we still see a couple of 10 second "speeds" of 0.2 knots.

Now wait a minute - I just said that the recording at the 3-fold lower data rate that covered a 5-fold longer observation period had lower observed errors. That is exactly the opposite of what we would expect! At first glance, the errors appear random, or at least mostly random. For random errors, statistic tells us that if we measure more often, the measured error will go down. Going from 25 samples per second down to 8 samples per second should reduce the observed error by about 77% - but that's not what we see!

The explanation for what we see is that the error is not entirely random - in fact, it has a substantial non-random element. That's quite obvious in the 25 Hz graph, where we can see a wave pattern in the error estimates, and clusterings of high speed points when the "error wave" is higher.

To have a closer look at the (non-)randomness of the observed errors, I copied the data from GPS Speedreader into a spreadsheet program, and then shuffled the observed speeds randomly. Next, I looked at all 2 second periods in the shuffled data, and compared the results to the results from the original data set. With completely random data, shuffling should not have an effect - we'd see the same top speeds. But if the original reported speeds (= errors) were not randomly distributed, we should see a difference. Here's a screen shot that shows the results for a test recorded at 18 Hz:

The average 2 second speed is 0.062 knots for the original and the 4 different shuffle tests, as expected. But in the shuffled sets, the maximum observed 2-second speed was between 0.093 and 0.097 knots - more than 3-times lower than in the original data set. Essentially, this proves that the error in the data set was not randomly distributed.

For comparison, here is the same analysis for a test recorded at 5 Hz:

For the 5 Hz data, we also observe a difference, but it is much smaller: the original data had a 2-second maximum that was about 50% higher than the shuffled data sets.

In my next post, I'll look into what's behind the non-randomness of the error. However, I'll leave you with a little puzzle and show the results of one of the tests I did:

Can you figure out what I did here? Here are a few hints: it involved a gallon plastic jug filled with water, and the numbers 2, 3, 5, and 30. Good luck, Sherlock!

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