Biomedical Engineering Reference
In-Depth Information
Sect. 3.3 on grouping criteria D(k) of Eq. ( 3.9 ). The difference (D(k)) can be
minimized with respect to time k, so we can adjust to estimate the filter state from
a coarse probability to a dense probability.
3.4.2 MC Likelihood Update
The above estimates and covariance are used as input to the filter matched to
M a ðÞ , which uses z a ðÞ to yield x a (k) and P a (k). The likelihood functions cor-
responding to each channel are computed using the mixed initial condition and the
associated covariance matrix ( 3.10 ) as follows: K y (k) = p[z(k)| M y (k), x 0 a (k-1),
P 0 a (k-1)], where y is a group number and r(y) is the number of sensors for each
group y. To reduce the notation complexity, r is simply used for r(y).
3.4.3 Switching Probability Update
corresponding
K a
Given
the
likelihood
function
ðÞ
to
each
channel,
the
switching probability update is done as follows:
K y ¼ r P
r
c y ¼ P
G
l y ðÞ¼ c y K y ðÞ c y ;
K a ;
K y c y ;
y ¼ 1 ; ... ; G ;
ð 3 : 11 Þ
a ¼ 1
y ¼ 1
where K y is the likelihood function for a group y, c y is the summarized normali-
zation constant, r is the channel number of a group y, and G is the number of
group. Equation ( 3.11 ) above provides the probability matrices used for combi-
nation of MC-conditioned estimates and covariance in the next step. It can also
show us how to use these parameter results for collaborative grouping criteria with
multiple sensors.
3.4.4 Feedback from Switching Probability Update to Stage 1
for Grouping Criteria with Distributed Sensors
For
the collaborative
grouping,
we introduced
the adaptive hyper-parameter
in Sect. 3.3.1 . The adaptive hyper-parameter b y ðÞ can be dynamically
increased or decreased depending on the weight of the channel. The weight of
channel can be represented as the switching probability. That means we can use
the switching probability
b y ðÞ
l y
ð
ðÞ
Þ as a reference to adjust the adaptive hyper-
parameter as follows:
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