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The Kalman-filter model


Often times we would like to estimate the state of a system given a set of measurements taken over an interval of time. The state of the system refers to a set of variables that describe the inherent properties of the system at a specific instant of time. Kalman filtering is a useful technique for estimating, or updating the previous estimate of, a system's state by (1) using indirect measurements of the state variables and (2) using the covariance information of both the state variables and the indirect measurements. Intuitively, the idea is to use information about how measurements of a particular aspect of a system are correlated to the actual state of the system.

To illustrate this concept, suppose we know that the average height and weight for males in the U.S. is 178 cm and 71 kg, respectively. That means, that in the absence of any other information, a randomly selected group of males will most likely have a mean height of 178 cm and a mean weight of 71 kg. But suppose we are told that the height of one of the males is 150 cm. How would the estimate of his weight change? Suppose we also know that the length of his forearm is 25 cm. Would that provide an even better estimate of his weight? The answer is ``yes'' if we know how the various measurements are correlated to one another. In human anatomy, we can exploit the correlations among various anthropometric quantities to make estimates using limited data. Kalman filtering is one such technique for using the correlation information to derive better estimates of unknown quantities.

Ramani Pichumani
Mon Jul 7 10:34:23 PDT 1997