Kalman filter?

Question

I have an application involving integrating accelerometer readings to obtain position. The application is essentially a mass/spring/friction problem, but with places where the mass is halted _very suddenly_. The spring force must then build up enough for the mass to break free from where it is stuck. Movement is away from the center of the Earth, so when the mass breaks free it can move upward quickly, overshooting the endpoint of the spring, and then fall back (it doesn't just oscillate, it actually travels over the same interval more than once)

Also:
1) I can process the data at a later time instead of in real time, so I can "looking into the future" data-wise
2) I have an independent measure of average velocity
3) I know my end position as well as starting position
4) There are points where it is very clear that no motion is taking place (velocity = 0) .

For this problem is a Kalman filter the best choice?
Should I restart integration at the zero velocity points?

That should say
... so I can "look into the future" data-wise

Answer 1

you can use Kalman filter, actually, according to what i understand, you have three independent measurement for position:
accelerometer, average velocity, and start/end position knowledge.

You can use the average speed measurement to "predict" the position, the accelerometer reading to "update" the position and the knowledge of the start/end position to restart everything.

you have to take care that the measurements (speed, accelerometer) read position, so you have to integrate accelerometer reading twice and speed reading one time.

Answer 2

I can't say that I fully understand your problem statement, but I do have a fair amount of experience with Kalman filters.

If the only measurement you have is an accelerometer reading, than a Kalman filter probably won't assist you that greatly.

The Kalman Filter is ideal for providing an optimal estimate of a variable in the presence of multiple sources of information about that variable. In navigation, for example, there are inertial inputs, GPS inputs, stellar fixes, etc, each with their own a priori error factors. (E.g. we know that the inertial nav unit has a 5% error in acceleration measurement, and the stellar fix has a 2% angular error.) The Kalman filter can account for the knowledge of the disparate measurement accuracies to still provide the optimal estimate of the measured quantity.

In your case, you have only one measurement: acceleration. Each measurement has the same error profile. The Kalman filter won't help you.

However, since you are processing the data after the fact, you should be able to just integrate the acceleration readings at each interval to obtain the actual position vs time graph. If you need to smooth it, some first or second order (alpha or alpha-beta) filters should do the trick fine.