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Posted by leo on March 10, 2009, 3:49 am
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=t1. How can I estimate the position in time t=t1+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=t1 v=V1, then at the time t=t1+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 :
¥á (k + 1) = ¥á (k) + G ¥á (¥á * - ¥á (k))
¥â (k + 1) = ¥â (k) + G ¥â (¥â * - ¥â (k))
G ¥á =1-exp(-1/K ¥á)
G ¥â =1-exp(-1/K ¥â)
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¥á=4.20-4.20*¥á* for 0.506<¥á<1.0
K¥á=5.90-7.56*¥á* for 0.184<¥á<0.506
K¥á=7.14-14.29*¥á* for 0.<¥á<0.184
K ¥â =5.397-5.397*¥â* for 0.931< ¥â <1.0
K ¥â =2.047-1.797* ¥â * for 0.27< ¥â <0.931
K ¥â =1.672-0.407* ¥â * for 0.< ¥â <0.27
How can I calculate these constants for ¥á- ¥â-¥ã filter?
How can I determine tracking index for my problem (see above)?
I have scan time=2 msec and it is constant. But how can I determine:
¥ò©ú : The measurement noise standard deviation which is determined
from
the object detection
scheme, i.e. the measurement process.(in my case it is accuracy from
encoder value or¡¦?).
¥òa: The maneuvering accelerations standard deviation. This parameter
is related to the
object dynamics.
I would be very much grateful to you, if you could let me know your
opinion on this problem.
Thanks in advance
LEO
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