I recently implemented a Kalman filter on the simple example of measuring a particles position with a random velocity and acceleration. I found that Kalman filter worked well, but I then asked myself what's the difference between this and just doing a moving average? I found that if I used a window of about 10 samples that the moving average outperformed the Kalman filter and I'm trying to find an example of when using a Kalman filter has an advantage to just using the moving average.
I feel like a moving average is far more intuitive than the Kalman filter and you can apply it blindly to the signal without worrying about the state-space mechanism. I feel like I am missing something fundamental here, and would appreciate any help someone could offer.