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Assume we have minute-bars of OHLC stock prices. Then, applying Kalman filter to those prices separately, we can remove a measurement noise and obtain the estimates of the states of the price processes.

The observations is: after Kalman filtering, some high prices become smaller than low prices. Can it cause some problems?

In my opinion, it is not a problem. In a feature creation after filtering, it it happens that $High < Low$ then I would just flip them.

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    $\begingroup$ You haven't explained the purpose of the Kalman filter. $\endgroup$
    – Brian O'Donnell
    Commented Dec 20, 2019 at 14:49
  • $\begingroup$ It is more common to use the closing price. This will avoid the problem you are seeing. $\endgroup$
    – Brian O'Donnell
    Commented Dec 20, 2019 at 15:27
  • $\begingroup$ I would like to use all prices in the bar $\endgroup$
    – ABK
    Commented Dec 20, 2019 at 15:28

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how about preprocessing the data and create mid_price = (H+L)/2 and range = H-L. And your Kalman filter apply to mid_price and range. Then you will not have the problem as you described

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