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I'm using an EKF and some gains are bigger than 1, is that possible? In the KF I understand that the typical values are [0-1], but in EKF??


I really appreciate your response. I was studying the equations for a simple system of position of a particle at constant velocity that I show in the figure, discretized with euler. In the Figure I show the equations to make the estimation for the three possible cases for this system, where we only measure x1, only x2 or both.

In the equations of the KF I see that for example I have expressions like xk1 + = (1-W11) * (xk1 -) + W11 * (z1), ie if W11 changes from zero (the filter uses only the prediction in this case to perform the estimation) to one (the system uses only the measurement in this case to make the estimation) and in the middle we have a mixture. That's why I thought that concept was unique. I do not understand when W should be greater than one. ("Mido" means meassure).

enter image description here

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Ok, so the question is not "Can the Kalman gain be bigger than 1?" but "Can the Kalman gain for this system be bigger than 1?"

In that case, I suggest you look at the evolution of the Kalman gain given your system and see if there are any conditions where it does. Perhaps for this particular system it can't be. You'll need to specify all the parameters of your signal model to do that.


Of course it's possible!

Why do you think the KF gain is less than 1? What the Kalman gain is depends on the system model and the data being processed.

There are plenty of examples showing gains greater than 1. See, for example, the image below taken from here.

enter image description here

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  • $\begingroup$ Hello, I see now that in my attempt to work with kalman filter in general, I choose a system that simplifies several things, that made the analysis lead to the conclusion that W should be between 0 and 1. That is the error which I committed. $\endgroup$ – rgpserverfault Sep 14 '17 at 21:21

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