Position estimate (kalman filtering question)?

Question

I have a machine pulling a weight, attached by a rubber band, up an incline that has a slowly varying slope. I know the position of the machine well (about 0.1%), but the rubber band introduces a great deal of positional uncertainty. I want to know the position of the weight at any time T. Fortunately, I have accelerometers attached to the weight.

Is a Kalman filter suitable for this task?
1) My accelerometer measurements are simply observations, not controller inputs
2) The mean of my position error is most likely _not_ zero (the weight will typically lag the machine position)
3) How can I eliminate the gravity component of the acceleration so that I can use it in the model (note that the slope of the incline varies, albeit slowly)?
4) I have no way to know or model the frictional forces. I can only sense the effect through the accelerations.
5) In some cases the weight comes to an abrupt halt with subsequent stretch in the rubber band followed by rapid acceleration

Mostly I need pointers to documentation or other sources of information that will help me formulate the problem properly.

Theory textbooks are useless. This is a real world problem. I need to implement it in an actual program.

Answer 1

Interesting problem, although it hardly sounds like "real world", and more like a lab experiment.

I) To use a Kalman filter you need a constant data stream. Pulling a weight up an incline, unless you can make it continuous, does not appear to be a Kalman filter app.

II) You stated the accuracy of the machine, but not the required accuracy for the weight.

III) The friction behaviour will depend on the velocity of the weight, which will turn into kinematic when weight and machine will not lag. Before that, you can emulate it into a bunch of starts and stops, each one with its own trigger, which you can measure with the accelerometer.

IV) You need to formulate a model. Formulate a model for the

a) start and stop phase.
b) kinematic phase

(b) is easy, so, lets concentrate on (a)

Question: Is the incline surface smooth?

i) If it is, the sticking force will always be the same, for a certain incline angle and we can model it.

ii) If it is not, then, we have a statistical problem and filtering will now be necessary. I would suggest a weighted least squares algorithm.

Eliminating the gravity component of your accelerometer is easy. Simply subtract the "weight at rest" signal.

Update your question, or mail me if you need further help.

Answer 2

I paintings on AHRU plane almost ordinary. Myself and different mechanics have in no way heard of an AHRU clear out. it could could do with something with course making plans in an FMS device.