I recently had a course in Applied signal processing where one of our tasks was to estimate the postion of an object from noisy measurements. A Kalman filter was used.
Figure 1: Original data and measurement with noise plotted together with the measured signal. The noise level is Gaussian with mean 0 and standard distribution 0.1.
Figure 2: Kalman filter with different R applied to observed data (blue line) and the signal without noise (green line).
The Kalman filter is quite impressive!