Biomedical Engineering Reference
In-Depth Information
converges to zero over a period of time. Therefore, we can find out the following
relationship: D k ð Þ D ðÞ . In the standard IMME, it is assumed that the mixing
probability density is a normal distribution all the time. Now we derive the
switching probability l a ðÞ for the estimated parameter from mixing probability
(l ij ). Since it is hard to get l ab k 1
ð
Þ directly, we used a tractable estimation
l ab k 1
ð
Þþ D k 1
ð
Þ , as follows:
l ab k 1
ð
Þ¼ l ij k 1
ð
Þþ D k 1
ð
Þ;
ð 3 : 9 Þ
where l ij is the mixing probability that represents the conditional transition
probability from state i to state j, and l ab is the switching probability that repre-
sents the conditional transition probability from channel a to channel b. Note that
we define mixing probability (l ij ) as switching probability (l ab ). That means our
assumption is still valid in the switching probability, i.e., switching probability
density follows a normal distribution (see appendix). The equality of Eq. ( 3.9 )is
true because the value of D(k-1) can be zero as k goes to the infinity. We can use
the right side of Eq. ( 3.9 ) to dynamically select the switching probability (l ab ) with
D(k). Equation. ( 3.9 ) above provides us with a method to design the filter for
distributed sensors at the second stage, because the switching probability can be
adjusted more dynamically based on D(k) in the second stage filter. We will
explain how to estimate the MC estimates and covariance using ( 3.9 ) in the next
Chapter.
3.4 Sensors Multi-Channel IMME: Proposed System
Design
The proposed method with collaborative grouping for distributed sensory data can
achieve the efficient target estimation by using geometric relationships of target
information emerging from distributed measurements. Figure 3.5 shows a general
block diagram to represent the relationship between the proposed method (MC-
IMME) and IMME.
In MC-IMME, grouping data can be used for target-tracking estimation with
IMME. Geometric information of distributed measurements is used for the
switching probability update in the target estimation. Even though the proposed
method needs the initialization process that is the same as in the IMME prediction,
the interactive relationship with distributed sensors can compensate for the pre-
diction estimate error. For the interactive tracking estimate, the proposed system
design herein can be extended from Figs. 3.2 , 3.3 , 3.4 , 3.5 , 3.6 .
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