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An important general form for adaptive filters
is the Least Mean Squares (LMS) filter.
This type of adaptive filter is easy to implement and is widely
used because of this. The filter uses a gradient search technique
in order to determine how to improved the filter coefficients.
This gradient search is also reason for the basic weakness of the
filter: it has a relatively slow convergence rate.
Suppose we consider the Nth order FIR filter,

(6) 
the filter error is,

(7) 
With the LMS filter, we adjust the values of the coefficients, ,
proportional to the error, ,

(8) 
where is a ``learning factor'' which controls how strongly
the error is weighted. This equation is the consequence of the
requirement to minimize the mean square value of , hence the
name of the filter.
Next: The RLS filter
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Previous: The Kalman filter
Skip Carter
20080820