Hello,

I am working on an iPhone app where we are trying to calculate the acceleration of a moving car. Similar apps have accomplished this (Dynolicious), but the difference is that this app is designed to be used during general city driving, not on a drag strip.

This leads us to one big concern that Dynolicious was luckily able to avoid: hills. Yes, hills.

There are two important stages to this: calibration, and actual driving.

Our initial run was simple and suffered the consequences. During the calibration stage, I took the average force on the phone, and during running, I just subtracted the average force from the current force to get the current acceleration this frame. The problem with this is that the typical car receives much more force than just the forward force - everything from turning to potholes was causing the values to go out of sync with what was really happening.

The next run was to add the condition that the iPhone must be oriented in such a way that the screen was facing toward the back of the car. Using this method, I attempted to follow only force on the z-axis, but this obviously lead to problems unless the iPhone was oriented directly upright, because of gravity.

Some trigonometry later, and I had managed to work gravity out of the equation, so that the car was actually being read very, very well by the iPhone.

Until I hit a slope. As soon as the angle of the car changed, suddenly I was receiving accelerations and decelerations that didn't make sense, and we were once again going out of sync.

Talking with someone a lot smarter than me at math lead to a solution that I have been trying to implement for longer than I would like to admit. It's steps are as follows:

1) During calibration, measure gravity as a vector instead of a size. Store that vector. 2) When the car initially moves forward, take the vector of motion and subtract gravity. Use this as the forward momentum. (Ignore, for now, the user cases where this will be difficult and let's concentrate on the math :) 3) From the forward vector and the gravity vector, construct a plane. 4) Whenever a force is received, project it onto said plane to get rid of sideways force/etc. 5) Then, use that force, the known magnitude of gravity, and the known direction of forward motion to essentially solve a triangle to get the forward vector.

The problem that is causing the most difficulty in this new system is not step 5, which I have gotten to the point where all the numbers look as they should. The difficult part is actually the detection of the forward vector. I am selecting vectors whose magnitude exceeds gravity, and from there, averaging them and subtracting gravity. (I am doing some error checking to make sure that I am not using a force just because the iPhone accelerometer was off by a bit, which happens more frequently than I would like). But if I plot these vectors that I am using, they actually vary by an angle of about 20-30 degrees, which can lead to some strong inaccuracies. The end result is that the app is even more inaccurate now than before.

So basically - all you math and iPhone brains out there - any glaring errors? Any potentially better solutions? Any experience that could be useful at all?

Award: offering a bounty of $250 to the first answer that leads to a solution.