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 $High < Law$ then I would just flip them.

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.