geometry - How do I make a low pass filter (average of readings over time) for compass?

I'm making a prototype for android that pulls compass data from the phone. I want to stabilize it so it is less jerky, by taking the average of the last couple of readings.

I have done this for accelerometer readings with great success, but adding every measurement to a queue and then collapsing it and dividing it by the queue size (= calculating the average) but for angles this is different.

If my measurements are for example:

350, 359, 360

I could calculate the average as 356.3

But if my measurements are

350 359, 1

Then my average is 236 which is a radically different angle.

Is there any way you guys can think of I could deal with this?

Answer

You could convert each angle to a 2D vector and sum the vectors, then convert the result back to an angle.

In pseudocode:

totalVector = [0, 0]
for each angle:

    vector = [cos(angle), sin(angle)]
    totalVector += vector
if length(totalVector) < aSmallNumber:
    # error, angles are all over the place so there's no meaningful average
avgAngle = atan2(totalVector.y, totalVector.x)