Particularity Kalman Filter Computer Vision

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?

Answer 1

[Dima Lisin]

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.

Answer 2

[Federico Monti]

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