Biomedical Engineering Reference
In-Depth Information
code vectors resulting in undesired information loss. This has been addressed
using continuous observation densities in HMM models (Liporace, 1982; Juang
et al., 1986; Qiang and Chin-Hui, 1997) to be a mixture of densities having
the general form
M
b
i
(
O
)=
c
jm
[
O
,
µ
jm
,
U
jm
]
(3.59)
m
=1
where 1
N
. Here
O
is the vector of observations to be modeled and
c
jm
is the mixture coecient for the
m
th mixture in state
j
.
≤
j
≤
is some log-concave
or symmetric density such as the Gaussian density with mean vector
µ
jm
and
covariance matrix
U
jm
for the
m
th mixture in state
j
. The coecients satisfy
the stochastic properties
M
c
jm
=1
m
=1
c
jm
≥
0
and the probability density function (pdf) is normalized as follows:
∞
b
j
(
x
)d
x
=1
−∞
where 1
N
. The estimation of the model parameters is given by the
following formulas:
≤
j
≤
t
=1
p
t
(
j, k
)
T
c
jk
=
t
=1
k
=1
p
t
(
j, k
)
T
M
t
=1
p
t
(
j, k
)
T
·
O
t
µ
jk
=
t
=1
p
t
(
j, k
)
T
t
=1
T
µ
jk
)
T
p
t
(
j, k
)
·
(
O
t
−
µ
jk
)(
O
t
−
U
jk
=
t
=1
p
t
(
j, k
)
T
where
p
t
(
j, k
) is the probability of being in state
j
at time
t
with the
k
th
mixture component for
O
t
.
There are other variants of HMM models such as the autoregressive HMM
models (Poritz, 1982; Juang and Rabiner, 1985) having observation vectors
Search WWH ::
Custom Search