Design of Multivariable Optimum Filters

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Abstract
The paper considers in detail a case of multivariable optimum filter design which is of engineering interest. This is the problem of extracting the best resemblance, in a minimum mean-square-error sense, of a message available in differently corrupted forms from a number of sources, given the statistical characteristics of message and disturbances. The solution is shown to involve an essential difference from the familiar case for a single source. Other multivariable optimum studies are not in principle different from the one considered here and consequently require the same type of analysis. A numerical example of the design of the optimum combination of filters for deriving a message from two noisy sources is given.

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