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I have heard that Extended kalman filter is a nonlinear kalman filter. But the problem with Extended kalman filter is that it can linearize on very bad places, which make it very unstable, if your process is very nonlinear.

So then the Unscented kalman filter was invended to solve this problem.

But I need to know advantages and disadvantages of Extended kalman filter VS Unscented kalman filter to make the choose which one I'm going to learn. Please help me choose.

My goal is to: 1. Estimate a mathematical state space model by input and output mesurements. 2. Create a good filter. 3. Create a good optimal LQG regulator.

My main working area is in hydraulics system. So it's nonlinear systems, but not so extreamly nonlinear systems. The only nonlinear in hydraulics is the pressure fall formula:

$$ Q = C*A*\sqrt{p_2 - p_1}$$

Q = Flow. C = Parameter. A = Area, $\Delta = p_2 - p_1$ = pressure difference

So, Extended kalman filter might fits me? Right?

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In practise: I'd give Extended Kalman filter a try at first and validate if the filter works well enough for the given problem. If it doesn't, I'd try Unscented Kalman filter or particle filters.

Extended Kalman filter solves the nonlinear estimation problem by linearising state and/or measurement equations and applying the standard Kalman filter formulas to the resulting linear estimation problem. The linearisation yields to approximation errors which the filter doesn't take into account in the prediction/update steps. Therefore Extended Kalman filter's error estimates tend to underestimate state uncertainties.

In comparison, Unscented Kalman filter picks so called sigma point samples from the filtering distribution and propagates/updates them through the (nonlinear) state and measurement models. The resulting weighted set of sigma points represents now the updated filtering distribution, which, is then approximated as a moment matched Gaussian distribution. This results state estimates which represent the state uncertainty better than the estimates obtained from the EKF with an increased computational cost.

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  • $\begingroup$ Can you show me how to compute a estimation of a state by using UKF? I know how EFK works. Not UKF. $\endgroup$
    – euraad
    Dec 21, 2017 at 14:37
  • $\begingroup$ I'd encourage you to read the chapter 5 of Bayesian filtering and smoothing (freely available for personal use). A pseudocode of the traditional formulation of the unscented Kalman filter is listed in Algorithm 5.14. $\endgroup$
    – user515430
    Dec 21, 2017 at 16:00

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