We need to estimate the position and orientation of differential drive robot by using encoders and imu sensor. For this specific case, is there any advantage of using Kalman filter than taking the average of encoder data and imu data. What I mean by taking the average is finding position at each sampling step by using encoders and imu seperately and taking our estimate at that time instant as the weighted average of encoders and imu. For next time step use this estimate as previous position value for both encoders and imu and then again calculate the individual estimates and take again the weighted average as final estimate. And continue this way.
If Kalman filter would do a better job than this simple weighted averaging, could you please explain intuitively why.