I'm quite new to the world of Kalman filter, so I have some doubts about it.
I will use a simple case study:
if we have a 1 dimensional world where a body is moving with a changeable acceleration, could it be possible to estimate its current position and velocity with a Kalman Filter? (since accelerometer measurements could be noisy). I found a lot of examples, but they use other kinds of tracking techniques like GPS. I would like to understand if an accelerometer could be enough to estimate the state and how to set up the Kalman Filter.
Thank you in advance, Michele
Kalman filter is often used to combine measurements from different sources (e.g. accelerations from accelometer, angular velocity from gyro, and absolute position measurements from GPS).
Usually you define what is the state variable that describe the current status of your system (e.g. position, velocity, acceleration). And provides a process model (what you believe the state should behaved -- in your case, a constant acceleration model), and a measurement model (how the current state you be observed). In your case, the measurement model H can only observe acceleration, and never have any information about position. The essentially making this Kalman filter unobservable, you can think of it as a under-determined system.
With no measurements governing the position state, the covariance matrix P will just keep blowing up, and no way it can provide anything close to realistic value.
So the answer is No, you are not able to use Kalman filter with a constant acceleration model without any absolute measurements of position keeping it from blowing up.