# Kalman Filter

• posted

I want to use Alpha-Beta-Gamma Filter (or Kalman Filter) for the following problem:

I have the position and velocity of products on the conveyor in time t=3Dt1. How can I estimate the position in time t=3Dt1+T (T is scan time) if I know acceleration a and max. velocity for this product? The product is on the conveyor.

Conveyor can change the speed every scan.

With acceleration a. It means, if conveyor has velocity at the time t=3Dt1 v=3DV1, then at the time t=3Dt1+T velocity can be

V1 or V1-a*T or V1+a*T.. I need probably Kalman filter and I am not sure if for my problem the Alpha-Beta-Gamma Filter would be good enough.

In literature there is formel for Alpha Beta-Gamma Tracking index: there is a formula for the calculation of the following coefficients :

=A5=E1 (k + 1) =3D =A5=E1 (k) + G =A5=E1 (=A5=E1 * - =A5=E1 (k)) =A5=E2 (k + 1) =3D =A5=E2 (k) + G =A5=E2 (=A5=E2 * - =A5=E2 (k)) G =A5=E1 =3D1-exp(-1/K =A5=E1) G =A5=E2 =3D1-exp(-1/K =A5=E2)

Kalpha and Kbeta are the first-order time constants dependent on the tracking index parameter .

How can I calculate these time constants?

I found for Alpha Beta filter the constants are calculated:

K=A5=E1=3D4.20-4.20*=A5=E1* for 0.506