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I'm looking for the best coordinate system projection to use for cartesian calculations while a vehicle is running from its starting location to about 100 miles from that spot.

The offline format for coordinates will be WGS84 geodetic coordinates. For online operation I am looking for the best coordinate system projection to use. We have decided that the best way to go about this is to define a projection with the origin at the vehicle's starting location.

Currently the primary candidates are an orthographic aka standard cartesian coordinate system set tangent to the earth at the starting lat/lon of the robot, or a transverse mercator projection defined at the starting x/y coordinate of the robot. We are avoiding UTM coordinates because we are likely to be on or near UTM boundaries so distortions would be a problem.

I am leaning towards the transverse mercator coordinate system, though I am not 100% confident how to appropriately configure the datums, particularly the scale factor, at arbitrary lat/lon coordinates.

For orthographic it seems that distortion would become a problem as early as the 50 mile mark from the starting location.

Ultimately my question is which coordinate system would be the best choice, and how to I choose parameters such as the scale factor appropriately based on the starting location?

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Is this for an online system or print? Within a 100 mile radius, you don't exactly hit terrible distortion unless these cars are in the Arctic. Why not just use Spherical Mercator and standard web maps? If it's for print and you need rulers to work, disregard this comment. – tmcw Mar 8 '13 at 19:26
This is for on a computer. WGS84 is used in files that are loaded up, but we need to select a projection for the user since calculations entirely in WGS84 are too CPU intensive. Also we don't always have an internet connection :-) – Andrew Hundt Mar 8 '13 at 19:49
Andrew, the main point of @tmcw's comment is that the distortions in question are tiny when you use any reasonable projection. For instance, if you use a suitable version of TM (even at polar latitudes), the distortion will not exceed 0.02% over 100 miles. If you're on the boundary of UTM, the distortion will get just a little bit larger than 0.04%: that's only 200 feet in a 100 mile journey. Note, too, that this is distortion in measuring distances: there are essentially no positioning errors. Do you really need greater precision than this? If so, how much? – whuber Mar 8 '13 at 20:35
Perhaps this is because I am misinterpreting some of the effects of distortion. So, if I have a point indicating the location of a telephone pole stored in a file in WGS84, and a vehicle that has an origin point for the projection 100 miles away where it initially started and a current position from GPS in lat/lon, the distortion will be the same for both the vehicle and the pole so that even with this distortion the telephone pole will be placed on the side of the road rather than potentially in the middle of it? – Andrew Hundt Mar 8 '13 at 20:46
I'm not sure I completely understand that, Andrew, but when you have a (lat, lon) for the pole and a GPS (lat, lon) for the vehicle nearby, then you scarcely need a projection to determine their spatial relationship (bearing and distance): what you need to worry about are the accuracies of the two coordinates: they will surely be far worse than any inaccuracies of projection. (To determine distances and bearings, first multiply the two longitudes by the cosine of the average of the two latitudes, then use Euclidean calculations.) – whuber Mar 8 '13 at 22:08

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