# How can I find the average bearing using a set of zig-zaggy coordinates, knowing the user travelled in a straight line during that period?

Some background:

I'm developing an app which uses augmented reality and GPS data in order to improve the True North accuracy of the device.

Currently, iPhones have a True North accuracy of about 15º at best, which is fine for displaying a heading on maps, but not good enough when you want to overlay things onto the world using Augmented Reality. As the AR "scene" can be aligned to gravity and True North, I thought I could use the GPS updates as the user moves through the world in order to improve the True North accuracy, down to perhaps within 1º of accuracy.

Each time a new coordinate is received, about once per second, I store it along with the user's current position within the AR scene (measured on a x/y/z axis). After 10 seconds, if the user has moved in a straight line, I'm able to compare the user's position 10 seconds ago with their position now, in order to determine their bearing, and I can compare data points across that span of time to ensure they walked in a straight line.

Knowing that they did walk in a straight line for 10 seconds, and their bearing, I can theoretically take their GPS coordinates from the readings across the same period and take that bearing. Thus, I can then measure the angle of difference between the user's bearing and the GPS bearing, and know how inaccurate the user's bearing is.

The problem is that the GPS data is a lot more zig-zaggy. Here's a screenshot from a period when I was walking in a straight line, along a pavement.

The green circles on the map represent each recent location estimate and their range of accuracy (in this case about 25m). The yellow line is the route between each of those GPS points. The other data shown can be ignored - green icon is the most accurate GPS estimate, and the orange icon is where the user is presumed to be based on that estimate and their movement since then, with the blue line just being a line between those points.

I've used a few techniques to try and get the true bearing of the GPS path, but because of inaccurate data points, like the point where it suddenly jumps north incorrectly, that throws off the average bearing.

The question:

So, the data I have:

• I know the user has moved in a straight line for the past 10 seconds (and indeed in this example for more than 15 seconds before that)
• I have a coordinate for the user's location, taken every second

The 25 most recent coordinates:

``````lat: 51.481508456031484, long: -0.014432226002130824
lat: 51.481507477162651, long: -0.0144049132597354
lat: 51.481506884611207, long: -0.014389807458603288
lat: 51.481509960771142, long: -0.014373092399400777
lat: 51.481507855339153, long: -0.014348176495456588
lat: 51.481509945317967, long: -0.014317286536546627
lat: 51.481505189244366, long: -0.014294481275542248
lat: 51.481506703609959, long: -0.014272413434476617
lat: 51.481505235807262, long: -0.01425324957115618
lat: 51.481498779846952, long: -0.014239295878236219
lat: 51.481501712942894, long: -0.014214523322743366
lat: 51.481508305052301, long: -0.014194804404044298
lat: 51.481512575463469, long: -0.014166769148728857
lat: 51.481519965341164, long: -0.014157078200848361
lat: 51.481521638215781, long: -0.01413473757481863
lat: 51.481520698352988, long: -0.014114195453429512
lat: 51.481518763912348, long: -0.014092665529632791
lat: 51.481516373462448, long: -0.014073392691598534
lat: 51.481517130888442, long: -0.014052945595763552
lat: 51.481522471260533, long: -0.014031560984244714
lat: 51.481519806277156, long: -0.014018366235482322
lat: 51.481521076237108, long: -0.0140037919026139
lat: 51.481522270228304, long: -0.013984366007679964
lat: 51.48152335719741, long: -0.013964033303506903
lat: 51.481522384989098, long: -0.013942519179059738
``````

Goal: Use 10 of these points to find an average bearing of the route, which isn't made inaccurate by the outlying results.

• Welcome to GIS SE. As a new user, please take the Tour. This question is more statistics than geography, and is missing all of the math where you show your work. Ten points is such a small sample size, you might not ever develop a perfect heuristic, but if you're looking to eliminate outliers, you should be comparing the bearings generated between differing sets of points and looking for members which change the bearing the most. Aug 21, 2017 at 12:08
• I'd take an average of 2 regression lines xy and yx and remove 1,2,3 most distant points from 2 lines. Points to be projected first... Aug 22, 2017 at 2:57