Biomedical Engineering Reference
In-Depth Information
Figure
4.11
depicts the overall architecture of the proposed online input channel selection
approach. The embedded input vector
x
j
(
n
) at the
j
th channel is filtered by an FIR filter with a
coefficient vector of
w
j
(
n
), yielding the filter output vector
z
(
n
) = [
z
1
(
n
), … ,
z
M
(
n
)]
T
. The autoco-
variance matrix
R
(
n
) of
z
(
n
), and the cross-correlation vector
p
(
n
) between
z
(
n
) and desired output
y
(
n
), are recursively estimated by (
4.37
) and (
4.38
), respectively. Then, the online variable selection
algorithm receives
R
(
n
) and
p
(
n
) to yield an LAR coefficient vector
g
(
n
) = [
g
1
(
n
), … ,
g
M
(
n
)]
T
. Note
that some of elements in
g
(
n
) can be equal to zero because of the
L
1
-norm constraint in the LAR
procedure (Figure
4.12
). Because the estimate of desired output is here the weighted sum of the
channel filter outputs, an instantaneous error becomes
(4.45)
ˆ
( )
T
e n
( )
=
y n
( )
−
y n
=
y n
( )
−
g
( )
n
z
( )
n
The update of
w
j
(
n
) can then be accomplished by
w
(
n
+ =
1
)
w
( )
n
+
h
e n g
( )
( )
n
x
( )
n
(4.46)
j
j
j
j
Note the difference between this update rule and the one in (
4.43
) by additional weights on
the filter outputs.
x
1
(
n
)
w
10
z
-1
ζ
1
(
ν
)
Σ
g
1
(
n
)
w
1
L
-1
z
-1
y
ˆ
n
)
Σ
x
M
(
n
)
w
M
0
z
-1
z
M
(
n
)
Σ
w
ML
-1
z
-1
Adapted by LMS
Adapted by on-line variable selection
FIgURE 4.11:
A diagram of the architecture of online channel selection method.
