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# Particularity Kalman Filter Computer Vision

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Federico Monti on 3 Sep 2015
Closed: MATLAB Answer Bot on 20 Aug 2021
Hi everybody! I have a theoretical question about an implementation that MATLAB gives about the Kalman Filter obtainable with the function configureKalmanFilter.
In particular, whenever there has been the need to write a Kalman Filter aimed to track position, velocity and acceleration I've also written a state transition matrix that contemplates also the acceleration into the estimation of the variable associated to the position, basically writing the formula:
x(t+1) = x(t) + v(t) + 0.5*a(t)
(where the time does not compare near the acceleration term since it's unitary)
Analyzing instead the solution it is proposed into the function I observed that only the velocity term is considered in the computation of the state, ignoring any acceleration.
My question is so: Why did you choose to apply such structure instead of entirely rewriting the typical equation of uniformly accelerated motions?

Dima Lisin on 3 Sep 2015
Hi Federico,
The configureKalmanFilter function lets you specify the motion model, which can be 'ConstantVelocity' or 'ConstantAcceleration'. If you choose 'ConstantAcceleration' then the state transition matrix A will be set to account for the acceleration. If you have a motion model, in which acceleration is not constant, then you would have to construct the vision.KalmanFilter object "manually" using the constructor, and specify the appropriate state transition matrix.

Federico Monti on 3 Sep 2015
Ok but it is considered only in the computation of the velocity not in the one of the position, i.e. we have:
x(t+1) = x(t) + v(t) + wn1(t) v(t+1) = v(t) + a(t) + wn2(t) a(t+1) = a(t) + wn3(t)
where we don't take into account the acceleration in the computation in the space. My question is why we do this and we don't consider also the acceleration.
Thank you