Applications of Kalman filter

Could someone explain where a Kalman filter could be applied? I read the wiki purdue sigbots thing about it and it talks abotu averaging data values… Is there anyway I could apply this to my odometry or PID? any advice on how?

A potential application of a Kalman filter would be to get a more accurate heading from both a tracking wheel based odometry and a inertial sensor. One could use a Kalman filter to combine the heading values of both sensors into one more accurate heading. However in my limited experience, heading is one of the things wheel based odometry tracks well, and the inertial sensor also has build up error, so the Kalman filter might be redundant in this application.

Otherwise it could also be used to combine distance sensor based odometry and tracking wheel based odometry. However, distance sensor based odometry simply has dead zones that a Kalman filter is simply is not built to compensate for. Still I could see some filter method being used to combine these two odometry methods.