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kalman filter understanding - one measurement two variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129455] kalman filter understanding - one measurement two variables
  • From: eladsh× <elad.shpiner at gmail.com>
  • Date: Mon, 14 Jan 2013 23:32:05 -0500 (EST)
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Hi.
i am quite a beginner in kalman filters and cant understand one issue.
consider the most common example of location estimation with regular location/velocity/acceleration. i've seen many such examples.
the measurement is the current location.
the states are the location and the velocity.
acceleration is noise.
so we get 2*2 equations.
So my question is about the part where you use the Kgain.
x = x_up+ k*(z-H*x_up);

the measurement z is only one scalar (the location).
but the velocity variable uses that measurement as well, although it's not even it the right units.
since the velocity is not measured, would it make sense to always use the estimated value ?  
or create a new measurement as the intervals of the location measurement.
How come the unmeasured variable has a component of the measurement ?
How come it works ? 
what contribution does the unmeasured variable has to the system?
I appreciate your answers
elad



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