# The GPS Paradox

### Or, how GPS is so wrong for measuring distance, yet perfectly "good enough."

by Dave Peckham, Owner, ICO Racing™

ICO Racing primarily specializes in making rally racing instruments. Let me explain rally racing a bit. A rally racer follows a "road book" which tells them what to expect on the trail at certain cumulative odometer distances. At each note in the road book, the rider should adjust their odometer to match the road book. The adjustment "resets" any accumulated difference between the roadbook and the odometer to zero.

Notice that I chose the word "difference" and not "error". Error is the difference between "truth" and some measured value. In rally racing, we expect both the road book and the odometer will have error, so truth is largely irrelevant.

Also notice that I haven't mentioned "accuracy". The primary goal with our instruments is to be consistent and to offer the rider mechanisms to "match" the unpredicatable error embedded in the road book. That is to say, we actually *want* the instrument to become just as *wrong* as the road book.

Sometimes "matching" is confused with "accuracy". For example, if a tape measure from brand X and a tape measure from brand Y produce matching measurements, but brand Z differs, we still can't say anything about their accuracy. For that, we need to compare them to "the truth". The truth might be from ISO, or NIST, or some other standard. Wherever the truth is, it's certainly not on the race course for us to check.

#### Wheel Sensors - the Gold Standard

In practical terms, nothing is better for measuring the distance of a path traveled on earth than a properly calibrated rolling measurement system. You'll notice that road crews and other surveyors still use a wheel. Yes, they use electronics to accurately measure distance between two points, but they still use a wheel to measure a path on the ground.

A wheel sensor takes all the twists and turns and rises and falls into account. Even still, it has its own sources of error, like skidding when braking, like wheelies, like the bit of flex in your knobbies, etc. But when it is in contact with the ground, it is measuring exactly the path that the bottom of your wheel traveled on the earth. It's literally measuring the "tracks" you left in the dirt.

#### GPS - new age tech vs. the ancient wheel

GPS is a system which measures position at a given moment. It tells you where you are. So, it does not measure distance at all. It provides latitude and longitude of your position with some measurable level of accuracy and precision. So, already the wrong tool for the job?

How do we determine a distance traveled using a GPS then? We can only approximate by calculating the distance between positions along our path, and summing those distances. We essentially have a series of line segments that approximate our traveled path.

What if you don't ride in a bunch of line segments? What if you are driving in a circle?

Consider this example... you are traveling along a circle which takes you exactly 1 second to circumnavigate. You have a GPS which measures your position every second (1Hz). So, as you ride round and round, the GPS takes a position every time you are at, say, 12 o'clock on the circle. No matter how long you ride, your cumulative distance will be zero because the distance between 12 o'clock and 12 o'clock is zero. In cartesian terms, the distance between (0,0) and (0,0) is zero. If you had a freeze-frame camera that also took your photo from above at the same time, it would look like you never moved from 12 o'clock.

If you drive very slowly or have a fast GPS, we have more positions, so we approximate a distance closer to the actual circumference of the circle. But if you drive really fast or have a slow GPS, we have fewer. Totally inaccurate!

OK, back to measuring between points on earth. You may have heard that the earth is not flat. It's not fake news--it's true. The earth approximates a sphere. So, if we draw a line between two points on earth, the line will go through the earth, not follow the surface. The shortest path which follows the surface of a sphere between two points on it is called the "Great Circle". Mariners and aviators have used the Great Circle for ages. There is a formula called Haversine which is used to calculate the Great Circle distance between points on a sphere.

Don't mountains and canyons mess up this spherical model? We like to ride in the mountains and on other uneven terrain--it's fun!!! Yup, another problem with this GPS based approach. Haversine doesn't account for this. So, we need some other approximation. Are you beginning to see the problems stacking up here, with all these approximations?

What about environmental issues? Yes, again the GPS is not perfect. Rain, tree cover, urban canyons, radio interference, and even relativity all conspire to make GPS less accurate.

#### OK, if GPS is so bad, then why do we make GPS instruments?

Well, because they are very much "good enough" for our application. In most cases, either wheel sensor or GPS instruments are perfectly useful* in rally racing*.

And in fact, GPS instruments offer some advantages to wheel sensor devices.

- They can tell us our compass heading
- They can be more robust, without a vulnerable, exposed sensor cable
- They can be easier to install
- They measure distance in a more "matching" way...
*sometimes*.

That last point deserves some explanation. Remember I talked about "matching" early on. This is what's important in rally racing--for your odometer to match the road book. Well, if your buddies made the road book with their wheel sensor bikes, then you're gonna have some differences to contend with if you use a GPS to follow their path. But if they made the road book using something like RallyNavigator.com, then you'll be in a better starting point with our GPS device. You see, your buddies' wheel sensors tracked all the ups and downs in the track as well as the twists and turns. But our GPS ignores elevation data. Why? Two reasons: 1) GPS vertical data is much less accurate than horizontal data, and 2) because most rally road books are being created today by using GPS mapping data in a 2D way, *also ignoring elevation data.*

Take for example, this view on Google Earth. It's a straight trail. Most people would draw the track exactly as I have. Let's say the Haversine distance is 1km.

But what if the end point is 1km higher than the start point? Wouldn't the actual distance traveled be more like 1.41421km (hypotenuse of a right triangle and all that jazz)?

OK, we could incorporate the elevation of the start and end points (from the map source) into our calculation. But then what if there were a lot of ups and downs between the points?

To approximate for all of those rises and falls, we'd have to add a track point at each of the local peaks and valleys in order to calculate the road book distance. Our bird's eye view would need to look like the pic below. The question is, how can you know where the peaks and valleys are when looking at the sat view, so that you can drop the right track points? You can't--not easily.

So, now we see a practical problem of making road books on a computer using GPS-based maps. It takes too damn long. Nobody wants to drop a track point every meter of a 300km stage so that they nail all the twist, turns, ups and downs. We are more efficient at resorting to the 2D view and using track points only where needed to approximate the curves, not the ups and downs.

So, now we're starting to see where the Rallye MAX-G shines "in real life". If the goal is for the road book and odometer to "match", then a RallyNavigator.com road book and a Rallye MAX-G are a match made in heaven.

Conversely, that "accurate" wheel sensor device would appear to be all wrong for following a GPS-based road book. And most likely, an uninformed rider would complain about the accuracy of one or the other, when in reality both are probably "wrong".

#### Enter AutoCal™...

So, what's a customer to do? How does one know or predict if all their buddies (or race organizers) are going to use a wheel sensor to lay out the course, or a GPS with or without elevation? They don't. And this is why ICO Racing invented AutoCal. It's a software feature found in all our Rallye MAX wheel sensor and Rallye MAX-G GPS instruments. Its sole purpose is to quickly make your well-calibrated device become *exactly as wrong* as the road book.

In closing, I hope that this article helps you navigate to a better understanding of the intricacies of rally navigation using either GPS or wheel sensor instruments.

Rally on!!!

--

Dave Peckham is owner of ICO Racing™, Rally Moto Shop™, and a contributing software engineer for RallyNavigator.com. He is the designer and lead engineer of the Rallye MAX and Rallye MAX-G.