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Kalman Filters

Keywords: filter, inference, kalman

Categories: Inference and Reasoning

Author(s): Sam Corbett

Consider tracking a man in a crowd, who, now and then, disappears behind other people, behind features of the landscape, behind traffic and so forth. Or consider the task of following a submarine by radar, using sonar echoes. Kalman filters can be used to accurately estimate the position of the man and the submarine using only the noisy observations available.

Named after its inventor, Robert Kalman, a Kalman filter is an ‘optimal recursive data processing algorithm’*, providing a means for extracting information from and estimating, so that error is minimized statistically, the state of a physical system, from observations corrupted by noise, biases, device inaccuracies and other such false signals, over time.

The filter is optimal in that it combines all possible measurement data and previous knowledge of the system to produce its estimate and recursive in that it does not need to reprocess all previous data to produce a new estimate. Since the filter is an algorithm it works with discrete samples rather than continuous inputs. It performs conditional probability density propagation for problems in which the system can be described through a linear model and in which measurement noises are white, (implying that noise value is not correlated in time) and Gaussian.

If the system being modelled does not readily fit the linear Gaussian model the extended Kalman filter can be applied instead.

A particularly useful, in depth introduction can be found at

* Stochastic Models, Estimation and Control, Peter S. Maybeck, 1979, pg. 4



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