Biomedical Engineering Reference
In-Depth Information
l
y
ðÞ
[ l
y
b
y
ðÞ
[ b
y
k
1
ð
Þ
if
ð
k
1
Þ
l
y
ðÞ¼
l
y
b
y
ðÞ¼
b
y
k
1
ð
Þ
if
ð
k
1
Þ
:
ð
3
:
12
Þ
l
y
ðÞ
\l
y
b
y
ðÞ
\b
y
k
1
ð
Þ
if
ð
k
1
Þ
If there is no change of the switching probability, b
y
(k) is the same as b
y
(k - 1).
If the current switching probability is greater than the previous one, b
y
(k) could be
increased; otherwise, b
y
(k) could be decreased as shown in (
3.12
). Therefore, we
can calculate the difference (Dl
y
) between the current switching probability and
the previous one as follows:
Dl
y
¼
l
y
ðÞ
l
y
ð
k
1
Þ
ð
3
:
13
Þ
That means the adaptive hyper-parameter b
y
(k) can be increased or decreased
based on the current switching probability compared to the previous one. In
Fig.
3.6
, we have added the red line indicating how the difference of the switching
probability in Stage 2 would be used for Stage 1.
3.4.5 Combination of MC Conditioned Estimates
and Covariance
Combination of the MC conditioned estimates and covariance is done according to
the mixture equations
;
P
b
ðÞþ
DP
b
ðÞ
:
x
a
ðÞ¼
P
P
a
ðÞ¼
P
r
r
x
b
ðÞ
l
ab
ðÞ
l
ab
ðÞ
ð
3
:
14
Þ
b
¼
1
b
¼
1
where l
ab
is a switching probability presenting the relationship between channel
a and channel b within the same group y, and DP
y
(k) as an increment to the
covariance matrix to account for the difference between the intermediate state and
the state estimates from model b, expressed by x
b
ðÞ
x
b
ðÞ
x
b
ðÞð
x
b
ð
Þ
T
Note that the combination of the model-conditioned estimates and covariance
matrices in Fig.
3.2
is extended into Eq. (
3.14
) incorporating with the switching
probability and D(k). As can be seen in Chapter
3.4.1
, we also have adopted the results
of Chapter
3.3
on grouping criteria D(k) of Eq. (
3.9
). In Fig.
3.6
, the entire flow chart
illustrates the idea of MC-IMME proposed in this study. We have added the blue line
indicating how the difference (D(k)) in Stage 1 would be used for the IMME outcomes
of Stage 2, corresponding to (
3.14
). This combination is only for output purposes.
3.4.6 Computational Time
We have evaluated how much additional computational time is required when we
implement the proposed method by comparing it to KF and the IMME method in
Table
3.1
.
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