Simplification / optimization of GPS track

Question

I\'ve got a GPS track produced by gpxlogger(1) (supplied as a client for gpsd). GPS receiver updates its coordinates every 1 second, gpxlogger\'s logic is very

Answer 1

You want to throw away uninteresting points. So you need a function that computes how interesting a point is, then you can compute how interesting all the points are and throw away the N least interesting points, where you choose N to slim the data set sufficiently. It sounds like your definition of interesting corresponds to high acceleration (deviation from straight-line motion), which is easy to compute.

Answer 2

I guess you need to keep points where you change direction. If you split your track into the set of intervals of constant direction, you can leave only boundary points of these intervals.
And, as Raedwald pointed out, you'll want to leave points where your acceleration is not zero.

Answer 3

Yes, as mentioned before, the Douglas-Peucker algorithm is a straightforward way to simplify 2D connected paths. But as you have pointed out, you will need to extend it to the 3D case to properly simplify a GPS track with an inherent time dimension associated with every point. I have done so for a web application of my own using a PHP implementation of Douglas-Peucker.

It's easy to extend the algorithm to the 3D case with a little understanding of how the algorithm works. Say you have input path consisting of 26 points labeled A to Z. The simplest version of this path has two points, A and Z, so we start there. Imagine a line segment between A and Z. Now scan through all remaining points B through Y to find the point furthest away from the line segment AZ. Say that point furthest away is J. Then, you scan the points between B and I to find the furthest point from line segment AJ and scan points K through Y to find the point furthest from segment JZ, and so on, until the remaining points all lie within some desired distance threshold.

This will require some simple vector operations. Logically, it's the same process in 3D as in 2D. If you find a Douglas-Peucker algorithm implemented in your language, it might have some 2D vector math implemented, and you'll need to extend those to use 3 dimensions.

You can find a 3D C++ implementation here: 3D Douglas-Peucker in C++

Your x and y coordinates will probably be in degrees of latitude/longitude, and the z (time) coordinate might be in seconds since the unix epoch. You can resolve this discrepancy by deciding on an appropriate spatial-temporal relationship; let's say you want to view one day of activity over a map area of 1 square mile. Imagining this relationship as a cube of 1 mile by 1 mile by 1 day, you must prescale the time variable. Conversion from degrees to surface distance is non-trivial, but for this case we simplify and say one degree is 60 miles; then one mile is .0167 degrees. One day is 86400 seconds; then to make the units equivalent, our prescale factor for your timestamp is .0167/86400, or about 1/5,000,000.

If, say, you want to view the GPS activity within the same 1 square mile map area over 2 days instead, time resolution becomes half as important, so scale it down twice further, to 1/10,000,000. Have fun.

Answer 4

I ran in to a similar issue. The rate at which the gps unit takes points is much larger that needed. Many of the points are not geographically far away from each other. The approach that I took is to calculate the distance between the points using the haversine formula. If the distance was not larger than my threshold (0.1 miles in my case) I threw away the point. This quickly gets the number of points down to a manageable size.

I don't know what language you are looking for. Here is a C# project that I was working on. At the bottom you will find the haversine code.

http://blog.bobcravens.com/2010/09/gps-using-the-netduino/

Hope this gets you going.

Bob