Problems with Unscented Kalman Filter

[Guillem]

Hi guys,

I have problems understanding UKF and its environment. I will ask a couple of questions and see if you can help me.
I have a nonlinear system (SYS) with one input called P (scalar) and one output called IP (also scalar). I would like to estimate the future output (the IP), so in my UKF I put as input u=P, and as a measurement z=IP.
To estimate, the UKF uses (among other things) the Unscented Transformation (UT), which transforms the sigma points calculated from the states. Here comes the first question:

· The states which UKF can estimate have to be the same as my SYS states? Or is just a name? Can I understand my IP estimation as the UKF states (in this case, state, because is scalar)?
[If you don't understand the question: The UKF estimates states. My system SYS have internal states (like all the systems). Is the UKF able to estimate the output of SYS? Or it just can estimate these internal states?]

Now, I saw that the measurement has to be also transformed by the Unscented Transformation (to correct the estimation error).

· Must the measurement transformation be equal to the Sigma points transformation?

Well, this would be the first part. I need this for a thesis and I haven't done anything about Control Theory in my degree.

Thank you for your time.

 

[Future Bruno]

Yes, the UKF estimates states. The UKF can estimate the output of your system SYS, by using the Unscented Transformation (UT). The UT transforms the sigma points calculated from the states, which gives an estimation of the output. The measurement transformation must be equal to the Sigma points transformation in order for the UKF to correctly estimate the output.