User`s guide

RLS Adaptive Filter
5-375
5RLS Adaptive Filter
Purpose Compute filter estimates for an input using the RLS adaptive filter algorithm.
Library Filtering / Adaptive Filters
Description The RLS Adaptive Filter block recursively computes the least squares estimate
(RLS) of the FIR filter coefficients.
The corresponding RLS filter is expressed in matrix form as
where λ
-1
denotes the reciprocal of the exponential weighting factor. The
variables are as follows.
Variable Description
n The current algorithm iteration
u(n) The buffered input samples at step n
P(n) The inverse correlation matrix at step n
k(n) The gain vector at step n
The vector of filter-tap estimates at step n
y(n) The filtered output at step n
e(n) The estimation error at step n
d(n) The desired response at step n
λ The exponential memory weighting factor
kn()
λ
1–
Pn 1–()un()
1 λ
1–
u+
H
n()Pn 1–()un()
-----------------------------------------------------------------------=
yn() w
ˆ
H
n 1–()un()=
en() dn() yn()–=
w
ˆ
n() w
ˆ
n 1–()kn()e
∗
n()+=
Pn() λ
1–
Pn 1–()λ
1–
kn()u
H
n()– Pn 1–()=
w
ˆ
n()