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It is known that the Kalman filter can filter the data with noise. I also find it works well after using it compared with FIR, low pass filter,etc. Now, I have a couple of questions about the advantages and disadvantages of the Kalman filter compared with FIR, low pass filter,etc. (In accordance with the conditions of using Kalman filter)

  1. Can we deem that traditional filters such as FIR and low-pass filter are designed to be used at specific frequencies, while kalman filter can filter signals with noises at any frequency as long as the computing speed is large enough and the system model does not change?
  2. The kalman filter can adjust the Kalman gain according to the actual measurement accuracy, so as to obtain the optimal solution. Is it right to think that Kalman filter is more intelligent than FIR? When the measuring instrument itself has errors, is it right to think the data obtained by using kalman filter is more accurate for the Kalman filter can adjust the weights of system model and measure respectively?
  3. When the noise of measurement is large (the instrument is not accurate), can the adoption of Kalman filter (the model is well established) obtain more accurate data than FIR, etc. That is, can the kalman filter be used to make up for the error caused by the low precision of the measuring instrument by establishing an accurate model?
  4. The core of kalman filter is a set of iterative equations. Can we think the kalman filter has the advantages of simple design and strong universality compared with FIR? Of course, it is based on the establishment of a good system model and measurement model.

What I understand is not necessarily right or sufficient. Please help me to answer my questions or give me any suggestions. Thanks!

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Kalman filters really aren't that special, and you seem to be missing the point of a Kalman filter. A Kalman filter is really just a generally time-varying, generally IIR, generally multi-input multi-output filter that's been designed using a specific procedure.

Can we deem that traditional filters such as FIR and low-pass filter are designed to be used at specific frequencies, while kalman filter can filter signals with noises at any frequency as long as the computing speed is large enough and the system model does not change?

Yes and no. Yes, typically time-invariant IIR and FIR filters are designed starting with a specification in the frequency domain -- but they don't have to be.

A Kalman filter is simply a filter that's designed based on a model of a process, to be optimal under a certain set of rules. But you can give me a filter specification for an IIR or FIR filter, and I can define a system model that will cause you to design a "Kalman filter" that asymptotically settles out to being exactly an IIR or FIR filter with that specification. Then if you make your "Kalman filter" into a steady-state Kalman, it will be that original IIR or FIR filter -- just with more (and more obscure) work behind it.

The kalman filter can adjust the Kalman gain according to the actual measurement accuracy, so as to obtain the optimal solution.

Well, no. The Kalman filter can adjust the gains according to the estimated or understood measurement accuracy. Depending on your religion, either no one, or God only, knows the actual measurement accuracy.

Is it right to think that Kalman filter is more intelligent than FIR?

I have never had an intelligent conversation with either. Zero equals zero, so no. A Kalman filter may be more applicable than a FIR filter in certain circumstances -- but often it is not.

When the measuring instrument itself has errors, is it right to think the data obtained by using kalman filter is more accurate for the Kalman filter can adjust the weights of system model and measure respectively?

Not necessarily. Particularly since Kalman filters have a well-known tendency to lack robustness in the face of inaccuracies of the system model -- get the system model wrong (and you will, because you're not God), and the filter won't be robust.

Sometimes it's far better to use a simple filter that's good enough, than a super-duper-fancy filter that would be really good if only you'd designed it right, based on information you don't have.

When the noise of measurement is large (the instrument is not accurate), can the adoption of Kalman filter (the model is well established) obtain more accurate data than FIR, etc. That is, can the kalman filter be used to make up for the error caused by the low precision of the measuring instrument by establishing an accurate model?

"Kalman" is a Hungarian surname that people whose ancestors come from a certain area of Germany tend to have. It does not mean "magic". A Kalman filter is just one way of making an optimal filter -- but it cannot do better than optimal.

Particularly for single-input, single-output systems, a plain old IIR or FIR filter, specified in the frequency domain, can do a better job (because of robustness issues) than some laboriously designed Kalman.

The core of kalman filter is a set of iterative equations. Can we think the kalman filter has the advantages of simple design and strong universality compared with FIR? Of course, it is based on the establishment of a good system model and measurement model.

We can think of the Kalman filter as being a right pain in the behind to design correctly, and one that forever more demands that you have staff on hand that understands it before your product can be adequately maintained. If simple will work, simple should be adopted -- and based on the number of people who can understand IIR & FIR filters vs. the number of people who truly understand how a Kalman filter works, I'd say that a Kalman filter is not "simple".

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