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The Extended Kalman filter is more or less a mathematical "hack" that allows you to apply these techniques to mildly nonlinear systems.

The problem with Extended Kalman Filter is if I initialize the filter with poor conditions (i.e., the initial state), it will quickly diverge. If propagation and/or measurement updates happen at too great a timestep, it will quickly diverge.

I my view, EKF is not good for control engineering, due to the risk of diverging.

So my question is if Unscented Kalman Filter(UKF) is a better choise for me if I want to be sure that my controller is stable?

Or should i use the static original Kalman-Bucy Filter? I'm working with feedback systems.

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  • $\begingroup$ How are you discretizing the system? $\endgroup$
    – Chuck ♦
    Commented Oct 9, 2017 at 18:57
  • $\begingroup$ I don't know. @chuck $\endgroup$
    – euraad
    Commented Oct 9, 2017 at 20:32
  • $\begingroup$ Kalman filters are not controls, they are observer estimations, i.e. they improve the accuracy of your model state estimate. They are only suited for certain system types, particularly linear systems with Gaussian noise in the sensors. You may need to adjust your control strategy instead of your observer strategy to achieve stability. $\endgroup$
    – daaxix
    Commented Oct 19, 2017 at 11:30
  • $\begingroup$ So EKF is not stable? $\endgroup$
    – euraad
    Commented Oct 19, 2017 at 17:56
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    $\begingroup$ If one was clearly always better than another, there would only be that one kind, and the rest would only be found in footnotes and unread papers. Which one is better depends on your problem at hand. So your question should be "How do I decide whether to use a linear Kalman, EKF, or UKF?" (Or a particle filter or other general Baysian state estimator). $\endgroup$
    – TimWescott
    Commented Nov 18 at 16:02

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You mentioned that EKF wasn't very robust for your application. This means that the continuous time model is considerably non-linear. In this setting, the UKF is better than the EKF and handles the non-linearity better.

The original static Kalman-Bucy filter does not seem like a promising choice since it targets continuous time linear systems. So, between them, I would still lean towards UKF.

You might want to look at indirect feedback Kalman filters. Section 2 of the following reference describes a non-linear continuous time application similar to what you would encounter in robotic arm movement problems.

https://pdfs.semanticscholar.org/7d78/9dd851ccf6100a3045ab9347b35eb86a9106.pdf

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