Is the Kalman filter just a low-pass filter?

Re:Is the Kalman filter just a low-pass filter? by jbay808 on Thursday July 28, 2022 @08:27PM (#32271698)

Author here. Yes, if the system has a high-pass behaviour, then the corresponding Kalman filter will converge to a high-pass filter, and so on. Non-low-pass-like behaviour can emerge from the prediction step, if the model is not unitary. If there's interest, I might write a followup article where a Kalman filter takes on a bandpass nature.

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Re:Is the Kalman filter just a low-pass filter? by motohagiography on Thursday July 28, 2022 @11:51PM (#32272963)

I read Gaussian and Cauchy distributions as inputs, but can you add arbitrary distributions other than those two examples, and expect the filter to yield artifacts from those distributions? Naively, I'm thinking of different coloured noise as inputs, and what kind of artifacts a Kalman filter would produce over them.

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Re:Is the Kalman filter just a low-pass filter? by freemint on Friday July 29, 2022 @07:05AM (#32275451)

With multi modal distribution you can end up stuck in any of the modes or even stuck in a low likelihood region in between the modes.

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Re:Is the Kalman filter just a low-pass filter? by galangalalgol on Thursday July 28, 2022 @09:08PM (#32271969)

I have seen it derived that it is equivalent to a matched filter, but I could not repeat said derivation.

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Re:Is the Kalman filter just a low-pass filter? by roger_ on Friday July 29, 2022 @06:39AM (#32275291)

I'd expect BPF behavior when estimating the rate of a noisy input (e.g. state: speed, observation: position), but I can't think of a process model that would be truly high-pass.

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Re:Is the Kalman filter just a low-pass filter? by buescher on Friday July 29, 2022 @09:55AM (#32276917)

Ambient temperature effects on a photodiode.

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