Figure 1. Illustration of how serial dependencies, modelled by the Kalman filter, can reduce noise and improve accuracy [6].
(A) Black lines show the changes in the physical dimension, grey the signal with added gaussian noise of space constant 0.3 in the high section, 0.2 in the low section. The red trace in the upper plot shows the output of the Kalman, clearly closer to the veridical stimulus than the raw noisy signal. The blue, lower trace shows a simple low-pass unadaptive filter, performing poorly, particularly near the edge. (B) Root mean squared (RMS) error from the real signal for the raw trace, Kalman filter and low-pass smoothing.