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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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b
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Sy
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I
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N:
2089
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4864
On
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meth
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fo
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tifyin
g
Th
ev
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in
mo
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p
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[
1
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[
2
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Am
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4
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Hen
ce
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C
C
M)
is
w
i
d
ely
u
s
ed
d
u
e
to
its
s
i
m
p
lic
it
y
a
n
d
ea
s
e
o
f
i
m
p
le
m
en
tatio
n
.
Ho
w
e
v
er
,
it
i
s
an
o
p
en
-
lo
o
p
alg
o
r
i
th
m
t
h
at
r
elie
s
o
n
ac
c
u
r
ate
i
n
itial
SOC
an
d
p
r
ec
is
e
in
te
g
r
atio
n
o
f
cu
r
r
en
t
o
v
er
ti
m
e
[
5
]
,
[
6
]
.
I
n
p
r
ac
tice,
s
en
s
o
r
in
ac
cu
r
ac
i
es,
cu
r
r
en
t
d
r
if
t,
an
d
in
te
g
r
atio
n
er
r
o
r
s
ac
cu
m
u
late,
lead
in
g
to
s
i
g
n
i
f
ica
n
t
d
ev
iat
io
n
s
i
n
SOC
est
i
m
a
tio
n
u
n
le
s
s
p
er
io
d
ically
co
r
r
e
cted
w
it
h
o
th
er
m
et
h
o
d
s
.
T
h
e
o
p
en
-
cir
cu
it
v
o
lta
g
e
(
O
C
V)
m
et
h
o
d
ex
p
lo
its
t
h
e
d
ir
ec
t
co
r
r
elatio
n
b
et
w
ee
n
th
e
b
atte
r
y
’
s
O
C
V
an
d
its
S
OC
.
W
h
i
le
h
i
g
h
l
y
ac
cu
r
ate
u
n
d
er
r
esti
n
g
co
n
d
itio
n
s
,
th
i
s
m
e
th
o
d
r
eq
u
ir
es
p
r
o
lo
n
g
ed
id
le
p
er
io
d
s
to
r
ea
ch
elec
tr
o
ch
e
m
ical
eq
u
il
ib
r
i
u
m
—
m
ak
i
n
g
it
u
n
s
u
i
tab
le
f
o
r
r
ea
l
-
ti
m
e
ap
p
licatio
n
s
w
h
er
e
co
n
ti
n
u
o
u
s
o
p
er
atio
n
is
d
e
m
a
n
d
ed
[
7
]
,
[
8
]
.
T
o
o
v
er
co
m
e
t
h
e
li
m
itatio
n
s
o
f
m
o
d
el
-
i
n
d
ep
en
d
en
t
ap
p
r
o
ac
h
es,
d
ata
-
d
r
iv
e
n
tech
n
iq
u
e
s
s
u
c
h
as
n
eu
r
al
n
et
w
o
r
k
s
(
NN)
a
n
d
f
u
zz
y
lo
g
ic
(
FL
)
h
a
v
e
b
ee
n
ex
p
lo
r
ed
.
T
h
ese
in
tel
lig
e
n
t
alg
o
r
it
h
m
s
c
an
m
o
d
el
co
m
p
le
x
n
o
n
li
n
ea
r
b
eh
av
io
r
s
w
it
h
o
u
t
r
eq
u
ir
in
g
d
etailed
k
n
o
w
led
g
e
o
f
th
e
in
ter
n
al
b
atter
y
d
y
n
a
m
ics
[
9
]
–
[
1
2
]
.
Ho
w
e
v
er
,
th
e
y
d
ep
en
d
h
ea
v
il
y
o
n
lar
g
e,
h
ig
h
-
q
u
alit
y
tr
ai
n
in
g
d
ataset
s
a
n
d
s
u
b
s
ta
n
tial
co
m
p
u
tat
io
n
al
r
es
o
u
r
ce
s
.
Mo
r
eo
v
er
,
th
eir
g
e
n
er
aliza
tio
n
ca
p
ab
ilit
y
is
li
m
ited
w
h
e
n
o
p
er
atin
g
co
n
d
itio
n
s
d
i
f
f
er
f
r
o
m
t
h
o
s
e
i
n
t
h
e
tr
ain
i
n
g
d
ata,
r
aisi
n
g
co
n
ce
r
n
s
ab
o
u
t r
o
b
u
s
t
n
es
s
an
d
r
eliab
ilit
y
.
An
o
th
er
p
r
o
m
is
i
n
g
ap
p
r
o
ac
h
is
th
e
p
ar
ticle
f
ilter
(
P
F),
w
h
i
ch
h
a
n
d
les
n
o
n
lin
ea
r
a
n
d
n
o
n
-
Ga
u
s
s
ia
n
s
y
s
te
m
s
e
f
f
ec
tiv
e
l
y
b
y
r
ep
r
esen
ti
n
g
t
h
e
s
tate
d
is
tr
ib
u
tio
n
t
h
r
o
u
g
h
s
to
c
h
asti
c
p
ar
ticle
s
[
13
]
,
[
1
4
]
.
W
h
ile
f
le
x
ib
le
an
d
p
o
w
er
f
u
l,
th
e
P
F
s
u
f
f
e
r
s
f
r
o
m
h
ig
h
co
m
p
u
tatio
n
al
co
m
p
le
x
it
y
,
p
ar
ticle
d
eg
en
er
ac
y
,
a
n
d
s
a
m
p
l
e
i
m
p
o
v
er
is
h
m
en
t
—
i
s
s
u
es t
h
at
m
ak
e
i
t le
s
s
s
u
itab
le
f
o
r
e
m
b
e
d
d
ed
s
y
s
te
m
s
w
it
h
li
m
ited
p
r
o
ce
s
s
i
n
g
p
o
w
er
.
I
n
co
n
tr
ast,
t
h
e
Kal
m
a
n
f
i
lter
(
KF)
an
d
its
v
ar
ian
t
s
o
f
f
er
a
b
alan
ce
d
s
o
lu
t
io
n
b
y
co
m
b
in
i
n
g
p
h
y
s
ica
l
b
atter
y
m
o
d
el
s
w
i
th
s
tat
is
tical
esti
m
atio
n
th
eo
r
y
.
T
h
e
s
tan
d
ar
d
KF
is
o
p
tim
a
l
f
o
r
lin
ea
r
s
y
s
te
m
s
b
u
t
ca
n
n
o
t
b
e
d
ir
ec
tl
y
ap
p
lied
to
th
e
in
h
er
en
t
l
y
n
o
n
l
in
ea
r
d
y
n
a
m
ics
o
f
L
i
-
io
n
b
atter
ies.
T
o
ad
d
r
ess
th
is
,
th
e
ex
ten
d
ed
Kal
m
a
n
f
ilter
(
E
KF)
lin
ea
r
izes
th
e
s
y
s
t
e
m
ar
o
u
n
d
th
e
cu
r
r
en
t
o
p
er
atin
g
p
o
in
t
u
s
i
n
g
f
ir
s
t
-
o
r
d
er
T
ay
lo
r
s
er
ies
ex
p
an
s
io
n
s
,
en
ab
lin
g
r
ea
l
-
ti
m
e
s
tate
es
ti
m
a
tio
n
w
it
h
r
elativ
el
y
lo
w
co
m
p
u
tatio
n
a
l c
o
s
t [
1
5
]
–
[
1
8
]
.
T
h
e
E
KF
h
as
g
ain
ed
w
id
esp
r
ea
d
atten
tio
n
in
SO
C
esti
m
atio
n
,
p
ar
ticu
lar
l
y
w
h
en
co
u
p
led
w
i
th
eq
u
iv
ale
n
t
cir
cu
it
m
o
d
els
(
E
C
Ms)
s
u
c
h
as
t
h
e
T
h
ev
en
i
n
m
o
d
el
(
T
M
)
[
1
9
]
–
[
2
6
]
.
T
h
is
m
o
d
el
ef
f
ec
tiv
e
l
y
ca
p
tu
r
e
s
th
e
d
y
n
a
m
ic
v
o
lta
g
e
r
esp
o
n
s
e
o
f
th
e
b
atter
y
u
s
i
n
g
a
co
m
b
i
n
atio
n
o
f
r
esis
to
r
s
a
n
d
ca
p
ac
ito
r
s
,
alo
n
g
w
it
h
an
SOC
-
d
ep
en
d
en
t
O
C
V
s
o
u
r
ce
.
Ho
w
e
v
er
,
th
e
ac
cu
r
ac
y
o
f
E
KF
-
b
ased
esti
m
atio
n
cr
itica
ll
y
d
e
p
en
d
s
o
n
th
e
f
id
elit
y
o
f
t
h
e
u
n
d
er
l
y
in
g
m
o
d
el
p
ar
am
eter
s
—
s
u
ch
as
i
n
ter
n
al
r
esi
s
t
an
ce
,
p
o
lar
izatio
n
r
esi
s
ta
n
ce
,
a
n
d
ca
p
ac
itan
ce
—
all
o
f
w
h
ic
h
v
ar
y
w
it
h
SOC
,
te
m
p
er
at
u
r
e,
an
d
ag
in
g
.
P
o
o
r
p
ar
a
m
eter
id
en
tific
atio
n
lead
s
to
m
o
d
el
m
is
m
atc
h
,
r
esu
lti
n
g
in
e
s
ti
m
atio
n
b
ias a
n
d
in
s
tab
ilit
y
.
Desp
ite
ex
te
n
s
i
v
e
r
esear
ch
,
th
er
e
r
em
a
in
s
a
n
ee
d
f
o
r
a
s
y
s
te
m
a
tic
an
d
ac
cu
r
ate
m
et
h
o
d
o
lo
g
y
to
id
en
ti
f
y
t
h
e
SO
C
-
d
ep
en
d
en
t
p
ar
a
m
eter
s
o
f
t
h
e
T
M
an
d
in
te
g
r
ate
th
e
m
i
n
to
an
ad
ap
tiv
e
E
KF
f
r
a
m
e
w
o
r
k
f
o
r
h
ig
h
-
p
r
ec
is
io
n
S
OC
esti
m
at
i
o
n
u
n
d
er
d
y
n
a
m
ic
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
is
p
ap
er
aim
s
to
ad
d
r
ess
th
ese
ch
alle
n
g
e
s
b
y
p
r
o
p
o
s
in
g
an
o
n
li
n
e
-
ca
p
ab
le
m
et
h
o
d
f
o
r
s
i
m
u
lta
n
eo
u
s
T
M
p
ar
am
eter
id
en
tif
icat
io
n
an
d
SOC
esti
m
atio
n
.
T
h
e
m
ai
n
co
n
tr
ib
u
tio
n
s
o
f
t
h
i
s
w
o
r
k
ar
e
th
r
ee
f
o
l
d
:
−
P
r
ec
is
e
p
ar
am
eter
id
en
tif
ica
ti
o
n
:
u
s
i
n
g
ex
p
er
i
m
e
n
tal
d
is
ch
a
r
g
e
test
d
ata
an
d
least
s
q
u
ar
es
r
eg
r
ess
io
n
,
w
e
estab
lis
h
ac
cu
r
ate
f
u
n
ctio
n
al
r
elatio
n
s
h
ip
s
b
et
w
ee
n
th
e
T
M
p
ar
am
eter
s
(
,
R
₁,
R
₂,
C
₂)
an
d
S
OC
.
−
Mo
d
el
v
alid
atio
n
:
th
e
id
en
ti
f
ie
d
m
o
d
el
is
r
ig
o
r
o
u
s
l
y
v
a
lid
ate
d
ag
ain
s
t
ex
p
er
i
m
en
ta
l
p
u
ls
ed
d
is
ch
ar
g
e
d
ata,
d
em
o
n
s
tr
ati
n
g
h
i
g
h
v
o
lta
g
e
p
r
ed
ictio
n
ac
cu
r
ac
y
w
ith
a
m
ea
n
ab
s
o
lu
te
er
r
o
r
(
MA
E
)
o
f
0
.
0
0
5
9
V
an
d
r
o
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
o
f
0
.
0
0
7
4
V.
−
R
o
b
u
s
t SO
C
esti
m
atio
n
: a
n
E
KF a
lg
o
r
ith
m
is
d
esi
g
n
ed
b
ase
d
o
n
th
e
id
en
tif
ied
T
M
to
esti
m
ate
SO
C
in
r
ea
l
ti
m
e.
E
x
p
er
i
m
e
n
tal
r
es
u
lts
u
n
d
er
co
n
s
tan
t
-
cu
r
r
en
t
p
u
ls
ed
d
is
ch
ar
g
e
co
n
d
itio
n
s
s
h
o
w
ex
ce
lle
n
t
p
er
f
o
r
m
an
ce
,
w
it
h
an
SO
C
esti
m
atio
n
M
A
E
o
f
0
.
0
5
9
%
an
d
R
MSE
o
f
0
.
0
7
9
8
%,
c
o
n
f
ir
m
in
g
th
e
m
et
h
o
d
's
ac
cu
r
ac
y
,
f
a
s
t
co
n
v
er
g
e
n
ce
,
an
d
s
tab
il
it
y
.
B
y
i
n
te
g
r
atin
g
ac
cu
r
ate
p
ar
a
m
eter
id
en
tif
icat
io
n
w
it
h
an
E
K
F
-
b
ased
esti
m
atio
n
f
r
a
m
e
w
o
r
k
,
th
is
s
t
u
d
y
p
r
o
v
id
e
s
a
p
r
ac
tical
an
d
ef
f
ec
ti
v
e
s
o
lu
tio
n
f
o
r
h
i
g
h
-
f
id
elit
y
SO
C
esti
m
atio
n
i
n
L
i
-
io
n
b
att
er
ies,
s
u
i
tab
le
f
o
r
i
m
p
le
m
en
ta
tio
n
i
n
r
ea
l
-
w
o
r
ld
B
MS
ap
p
licatio
n
s
.
2.
L
I
-
I
O
N
B
AT
T
E
RY
M
O
DE
L
2
.
1
.
T
he
T
hev
enin
m
o
del o
f
a
L
i
-
io
n ba
t
t
er
y
A
p
r
ec
is
e
b
atter
y
m
o
d
elin
g
f
o
r
m
s
th
e
b
a
s
is
f
o
r
esti
m
at
in
g
t
h
e
SOC
o
f
t
h
e
b
atter
y
.
B
atter
y
m
o
d
els
ca
n
b
e
ca
teg
o
r
ized
in
to
th
r
ee
t
y
p
es
:
elec
tr
o
ch
e
m
ical
m
o
d
els
(
E
M)
[
2
7
]
,
[
2
8
]
,
m
at
h
e
m
atica
l
m
o
d
els
(
MM
)
[
2
9
]
,
an
d
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I
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ates t
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
R
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o
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f
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I
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N:
2089
-
4864
On
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ip
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3
.
Fit
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n
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ip
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
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t
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Vo
l.
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1
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Ma
r
c
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202
6
:
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-
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58
2
.
2
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2
.
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dentif
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s
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r
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atter
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h
e
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ar
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b
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h
e
b
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ter
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s
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th
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et
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2
∗
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latio
n
as
in
(
4
)
f
o
r
ea
ch
SO
C
v
al
u
e
b
ased
o
n
t
h
e
d
is
ch
ar
g
e
v
o
ltag
e
c
u
r
v
e,
t
h
e
eq
u
atio
n
1
(
S
)
is
p
r
esen
ted
in
(
4
)
.
Fig
u
r
e
5
d
ep
icts
th
e
cu
r
v
e
o
f
t
h
e
f
itte
d
r
elatio
n
s
h
ip
b
et
w
ee
n
R
1
a
n
d
SOC
u
s
i
n
g
th
e
n
o
n
li
n
ea
r
least
s
q
u
ar
es
m
eth
o
d
e
m
p
lo
y
i
n
g
M
A
T
L
A
B
:
1
(
S
)
=
1
+
2
×
+
3
×
2
+
4
×
3
+
5
×
4
+
6
×
5
(
5
)
W
ith
1
=
0
.
4139
,
2
=
−
1
.
689
,
3
=
6
.
352
,
4
=
−
11
.
92
,
5
=
10
.
56
6
=
−
3
.
528
T
h
e
p
o
ten
tial
r
an
g
e
f
r
o
m
V
d
to
V
e
allo
w
s
d
eter
m
i
n
i
n
g
t
h
e
v
alu
es
o
f
R
2
a
n
d
C
2
.
T
h
e
d
if
f
u
s
io
n
r
esis
ta
n
ce
R
1
is
d
eter
m
i
n
ed
f
r
o
m
(
6
)
:
2
=
−
=
3
.
873
−
3
.
767
1
.
7
99
=
0
.
059
(
6
)
T
h
e
r
elatio
n
s
h
ip
b
et
w
ee
n
r
esis
tan
ce
R
2
a
n
d
SO
C
w
a
s
o
b
tai
n
ed
b
y
p
er
f
o
r
m
i
n
g
t
h
e
s
a
m
e
ca
lc
u
latio
n
a
s
in
(
6
)
f
o
r
ea
ch
SOC
v
alu
e.
T
h
e
eq
u
atio
n
R
2
=f
(
SO
C
)
is
p
r
esen
ted
in
(
7
)
.
Fig
u
r
e
6
d
ep
icts
th
e
cu
r
v
e
o
f
th
e
f
itted
r
elatio
n
s
h
ip
b
et
w
ee
n
R
2
a
n
d
S
OC
u
s
i
n
g
t
h
e
n
o
n
li
n
ea
r
least s
q
u
ar
es
m
et
h
o
d
w
i
th
M
A
T
L
AB
.
2
(
S
)
=
1
+
2
×
+
3
×
2
+
4
×
3
+
5
×
4
+
6
×
5
(
7
)
W
ith
1
=
0
.
5238
,
2
=
−
3
.
814
,
3
=
12
.
08
,
4
=
−
18
.
09
,
5
=
12
.
94
6
=
−
3
.
594
T
o
d
eter
m
i
n
e
th
e
ti
m
e
co
n
s
ta
n
t
2
f
o
r
th
e
p
ar
t
f
r
o
m
V
d
to
V
e
p
r
esen
ted
in
th
e
b
atter
y
v
o
lta
g
e
d
is
ch
ar
g
e
cu
r
v
e,
w
e
ca
lcu
lated
th
e
p
o
ten
t
ial
V
f
,
w
h
ic
h
r
ep
r
esen
t
s
t
h
e
p
o
ten
tial
a
t
ti
m
e
2
,
u
s
in
g
th
e
f
o
llo
w
i
n
g
r
elatio
n
s
h
ip
:
f
=
V
+
0
.
63
×
(
−
)
=
3
.
833
+
0
.
63
×
(
3
.
873
−
3
.
833
)
=
3
.
858
V
(
8
)
B
ased
o
n
th
e
p
o
ten
tial V
f
,
w
e
d
ed
u
ce
2
:
2
=
2
5430
−
25380
=
5
0
s
(
9
)
T
h
er
ef
o
r
e,
th
e
d
if
f
u
s
io
n
ca
p
ac
it
y
C
2
i
s
ca
lc
u
lated
as
(
1
0
)
:
2
=
2
2
=
50
0
.
05
9
=
8
47
.
46
(
1
0
)
B
y
u
s
i
n
g
th
e
s
a
m
e
ca
lc
u
latio
n
p
r
o
ce
d
u
r
e
f
o
r
ea
ch
SOC
v
alu
e,
th
e
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
ca
p
ac
ity
C
2
an
d
SOC
w
as
estab
li
s
h
ed
.
T
h
e
eq
u
atio
n
C
2
=f
(
SO
C
)
is
p
r
esen
ted
in
(
1
1
)
.
Fig
u
r
e
7
s
h
o
w
s
t
h
e
cu
r
v
e
o
f
th
e
f
itted
r
elatio
n
s
h
ip
b
et
w
ee
n
C
2
an
d
SOC
u
s
i
n
g
th
e
n
o
n
l
in
ea
r
l
ea
s
t sq
u
ar
es
m
et
h
o
d
w
it
h
M
AT
L
A
B
.
2
(
S
)
=
1
+
2
×
+
3
×
2
+
4
×
3
+
5
×
4
+
6
×
5
+
7
×
6
+
+
8
×
7
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
On
lin
e
meth
o
d
fo
r
id
e
n
tifyin
g
Th
ev
en
in
mo
d
el
p
a
r
a
mete
r
s
o
f Li
-
io
n
b
a
tter
ies a
n
d
…
(
Mo
u
h
s
s
in
e
La
g
r
a
o
u
i
)
59
W
ith
1
=
202
.
7
,
2
=
9245
,
3
=
−
9
.
637
×
10
4
,
4
=
5
.
04
×
10
5
,
5
=
−
1
.
262
×
10
6
,
6
=
1
.
598
×
10
6
,
7
=
−
9
.
972
×
10
5
8
=
2
.
446
×
10
5
Fig
u
r
e
4
.
An
en
lar
g
ed
s
ec
tio
n
o
f
th
e
d
is
c
h
ar
g
e
v
o
ltag
e
c
u
r
v
e
co
r
r
esp
o
n
d
in
g
to
a
SOC
o
f
0
.
6
5
5
Fig
u
r
e
5
.
Fit
tin
g
c
u
r
v
e
o
f
t
h
e
R
1
-
SO
C
r
elatio
n
s
h
ip
Fig
u
r
e
6
.
Fit
tin
g
c
u
r
v
e
o
f
t
h
e
R
2
-
SO
C
r
elatio
n
s
h
ip
Fig
u
r
e
7
.
Fit
tin
g
c
u
r
v
e
o
f
t
h
e
C
2
-
SO
C
r
elatio
n
s
h
ip
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
15
,
No
.
1
,
Ma
r
c
h
202
6
:
54
-
67
60
3.
S
OC
E
S
T
I
M
AT
I
O
N
F
O
R
B
AT
T
E
R
I
E
S USI
N
G
E
KF
As
a
n
o
n
li
n
ea
r
s
y
s
te
m
,
th
e
b
atter
y
'
s
b
eh
a
v
io
r
is
d
escr
ib
ed
b
y
s
tate
a
n
d
o
b
s
er
v
atio
n
eq
u
atio
n
s
t
h
at
ac
co
u
n
t
f
o
r
b
o
th
p
r
o
ce
s
s
n
o
is
e
an
d
m
ea
s
u
r
e
m
e
n
t
n
o
i
s
e.
T
h
ese
g
o
v
er
n
i
n
g
eq
u
at
io
n
s
a
r
e
m
at
h
e
m
atica
ll
y
ex
p
r
ess
ed
in
(
1
2
)
an
d
(
1
3
)
:
+
1
=
(
,
)
+
(
1
2
)
=
ℎ
(
,
)
+
(
1
3
)
I
n
th
e
s
e
e
x
p
r
ess
io
n
s
,
t
h
e
d
is
c
r
ete
ti
m
e
in
d
e
x
k
in
d
icate
s
t
h
e
p
r
esen
t
ti
m
e
s
tep
.
T
h
e
n
o
n
l
i
n
ea
r
s
tate
tr
an
s
itio
n
f
u
n
ctio
n
(
,
)
d
escr
ib
e
s
th
e
s
y
s
te
m
d
y
n
a
m
ics,
w
h
i
le
ℎ
(
,
)
m
o
d
els
t
h
e
m
ea
s
u
r
e
m
e
n
t
r
elatio
n
s
h
ip
s
.
Her
e,
co
r
r
esp
o
n
d
s
to
th
e
s
y
s
t
e
m
s
tate
v
ec
to
r
,
t
o
th
e
co
n
tr
o
l
in
p
u
t,
an
d
to
th
e
m
ea
s
u
r
ab
le
o
u
tp
u
t.
T
h
e
ter
m
s
an
d
r
esp
ec
tiv
el
y
ch
ar
ac
ter
ize
t
h
e
p
r
o
ce
s
s
d
is
t
u
r
b
an
ce
an
d
m
ea
s
u
r
em
en
t
u
n
ce
r
tai
n
t
y
in
h
er
e
n
t i
n
th
e
s
y
s
te
m
.
As
d
ep
icted
in
(
12
)
an
d
(
13
)
,
w
e
ar
e
ass
u
m
i
n
g
th
at
b
o
th
f
u
n
ctio
n
s
ar
e
d
if
f
er
e
n
tiab
le
at
ev
er
y
o
p
er
atin
g
p
o
in
t.
(
,
)
≈
(
̂
−
1
,
)
+
(
,
)
|
=
̂
−
1
(
−
̂
−
1
)
(
1
4
)
ℎ
(
,
)
≈
ℎ
(
̂
−
,
)
+
ℎ
(
,
)
|
=
̂
−
(
−
̂
−
)
(
1
5
)
B
y
s
u
b
s
ti
tu
t
in
g
in
(1
4
)
an
d
(
1
5
)
in
to
in
(1
2
)
an
d
(1
3
)
,
th
e
lin
ea
r
ized
p
r
o
ce
s
s
an
d
m
ea
s
u
r
e
m
e
n
t m
o
d
el
s
tr
an
s
f
o
r
m
i
n
to
:
+
1
≈
̂
+
(
̂
−
1
,
)
−
̂
̂
−
1
+
(
1
6
)
ℎ
(
,
)
≈
̂
+
ℎ
(
̂
−
,
)
−
̂
̂
−
+
(
1
7
)
W
e
d
ef
in
e
̂
an
d
̂
in
th
e
f
o
llo
w
in
g
m
a
n
n
er
:
̂
=
(
,
)
|
=
̂
−
1
(
1
8
)
̂
=
ℎ
(
,
)
|
=
̂
−
(
1
9
)
=
[
2
]
=
[
1
2
]
(
2
0
)
=
(
2
1
)
=
(
2
2
)
W
h
er
e
is
th
e
s
y
s
te
m
s
tate
v
ec
to
r
at
th
e
s
am
p
li
n
g
ti
m
e
k
,
is
th
e
b
atter
y
c
u
r
r
en
t,
an
d
is
th
e
b
atter
y
v
o
ltag
e.
T
h
e
s
tate
tr
an
s
itio
n
eq
u
atio
n
s
ar
e
estab
lis
h
ed
th
r
o
u
g
h
d
is
cr
et
izatio
n
a
n
d
lin
ea
r
iza
tio
n
o
f
b
o
th
t
h
e
T
M
's
m
at
h
e
m
a
tical
r
elatio
n
s
h
ip
s
an
d
th
e
cu
r
r
en
t i
n
te
g
r
atio
n
m
eth
o
d
f
o
r
m
u
latio
n
,
as p
r
esen
ted
:
(
,
)
=
[
1
2
]
(
2
3
)
1
=
(
−
1
)
−
∆
3600
.
×
(
)
(
2
4
)
1
=
1
−
∆
3600
.
×
(
2
5
)
2
=
2
(
−
1
)
×
−
∆
2
(
)
.
2
(
)
−
2
(
)
(
1
−
−
∆
2
(
)
.
2
(
)
)
×
(
)
(
2
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
On
lin
e
meth
o
d
fo
r
id
e
n
tifyin
g
Th
ev
en
in
mo
d
el
p
a
r
a
mete
r
s
o
f Li
-
io
n
b
a
tter
ies a
n
d
…
(
Mo
u
h
s
s
in
e
La
g
r
a
o
u
i
)
61
2
=
2
×
−
∆
2
(
1
)
2
(
1
)
−
2
(
1
)
(
1
−
−
∆
2
(
1
)
2
(
1
)
)
×
(
)
(
2
7
)
ℎ
(
,
)
=
(
)
−
1
−
1
(
)
×
(
)
(
2
8
)
ℎ
(
,
)
=
(
1
)
−
2
−
1
(
1
)
×
(
)
(
2
9
)
W
e
n
ee
d
to
co
m
p
u
te
t
h
e
t
w
o
J
ac
o
b
ian
s
,
A
a
n
d
H,
in
o
r
d
er
to
u
s
e
t
h
is
m
o
d
el
i
n
t
h
e
E
KF
alg
o
r
ith
m
.
C
o
n
s
eq
u
e
n
tl
y
,
th
e
d
er
iv
ativ
e
o
f
t
h
e
f
u
n
ctio
n
an
d
f
u
n
ctio
n
ℎ
w
ith
r
esp
ec
t
to
th
e
s
tate
v
ar
iab
les
i
s
as
(
3
0
)
an
d
(
3
1
)
:
̂
=
(
,
)
|
=
̂
−
1
=
(
11
12
21
22
)
(
3
0
)
̂
=
ℎ
(
,
)
|
=
̂
−
=
(
1
2
)
(
3
1
)
Af
ter
ca
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iv
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h
e
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llo
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g
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:
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12
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21
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[
(
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2
3
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4
1
2
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4
5
1
3
+
5
6
1
4
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×
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)
×
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−
∆
2
2
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[
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(
)
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×
∆
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(
2
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2
3
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+
3
4
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4
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3
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5
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ter
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Fig
u
r
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8
illu
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tr
ates t
h
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ial
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at
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4.
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at
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ts
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o
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if
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ed
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atter
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ter
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i
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d
ii
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e
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er
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m
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ce
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KF in
es
ti
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tin
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u
n
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er
d
y
n
a
m
ic
d
is
c
h
ar
g
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co
n
d
iti
o
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.
4
.
1
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o
del v
a
lid
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t
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n r
esu
lt
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h
e
TM
p
ar
am
eter
s
—
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en
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ci
r
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it
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e
(
,
in
ter
n
al
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esis
t
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ce
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,
p
o
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izatio
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r
esis
tan
ce
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n
d
ca
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ac
itan
ce
2
—
w
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n
ti
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atter
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ter
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ch
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it
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Fig
u
r
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9
s
h
o
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et
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ee
n
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atter
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atter
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atter
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r
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d
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
R
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o
n
f
i
g
u
r
ab
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&
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SS
N:
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4864
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t
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a
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ith
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m
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n
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ate
t
h
e
SO
C
in
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ea
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ti
m
e.
T
h
e
in
itial
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C
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as
s
et
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f
u
ll
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th
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ilter
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ated
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itio
n
s
.
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h
e
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e
f
er
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w
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m
p
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ted
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s
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M
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ar
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tialized
.
0
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[
1
0
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1
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,
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=
[
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0
10
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8
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,
=
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−
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]
=
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Fig
u
r
e
11
s
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o
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e
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atter
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h
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atic
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atter
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1
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ated
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ati
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i
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iatio
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h
e
m
a
x
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e
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ti
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er
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d
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0
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1
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%,
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n
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Fi
g
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r
e
1
2
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b
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4
.
3
)
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er
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3
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1
6
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ac
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n
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s
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r
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ac
h
.
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h
e
s
u
p
er
io
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ac
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r
ac
y
o
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r
m
et
h
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is
p
r
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ar
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y
d
u
e
to
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e
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i
g
h
-
f
id
elit
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ar
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m
eter
id
en
ti
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ica
tio
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p
r
o
ce
s
s
,
w
h
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h
m
i
n
i
m
izes m
o
d
el
-
p
la
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t m
i
s
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a
tch
—
a
k
n
o
w
n
s
o
u
r
ce
o
f
e
s
ti
m
atio
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b
ias
in
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-
b
ased
m
et
h
o
d
s
.
T
o
ev
alu
ate
th
e
r
o
b
u
s
tn
es
s
o
f
o
u
r
ap
p
r
o
ac
h
,
F
ig
u
r
e
1
3
(
s
ee
s
u
b
s
ec
tio
n
4
.
3
)
s
h
o
w
s
th
a
t
t
h
e
SO
C
e
s
ti
m
atio
n
co
n
v
er
g
e
s
ac
r
o
s
s
v
ar
y
i
n
g
in
i
tial SO
C
v
al
u
e
s
(
SOC
₀
=
0
.
1
,
0
.
3
,
0
.
5
,
0
.
7
,
an
d
0
.
9
)
.
4.
3
.
I
nte
rpre
t
a
t
io
n
a
nd
co
m
pa
riso
n w
it
h e
x
is
t
ing
w
o
rk
T
h
e
s
tr
o
n
g
a
g
r
ee
m
e
n
t
b
et
w
e
en
est
i
m
a
ted
an
d
r
ef
er
e
n
ce
S
OC
v
alu
e
s
co
n
f
ir
m
s
th
at
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
s
u
cc
e
s
s
f
u
ll
y
ac
h
iev
e
s
its
p
r
i
m
ar
y
o
b
j
ec
tiv
e:
ac
cu
r
ate,
r
ea
l
-
ti
m
e
S
OC
e
s
ti
m
ati
o
n
th
r
o
u
g
h
p
r
ec
is
e
m
o
d
eli
n
g
an
d
ef
f
ec
ti
v
e
f
ilter
i
n
g
.
B
y
r
ig
o
r
o
u
s
l
y
id
en
ti
f
y
i
n
g
t
h
e
SOC
-
d
ep
en
d
en
c
y
o
f
all
k
e
y
m
o
d
el
p
ar
a
m
eter
s
,
th
e
m
et
h
o
d
r
ed
u
ce
s
r
elian
ce
o
n
h
eu
r
i
s
tic
as
s
u
m
p
tio
n
s
a
n
d
e
n
h
a
n
ce
s
th
e
E
KF
’
s
ab
ili
t
y
to
tr
ac
k
tr
u
e
SO
C
u
n
d
er
d
y
n
a
m
ic
co
n
d
itio
n
s
.
C
o
m
p
ar
ed
to
d
ata
-
d
r
iv
e
n
ap
p
r
o
ac
h
es
s
u
ch
a
s
NN
s
[
9
]
–
[
1
2
]
,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
r
eq
u
ir
es
le
s
s
co
m
p
u
tatio
n
al
p
o
w
er
a
n
d
av
o
i
d
s
th
e
n
ee
d
f
o
r
lar
g
e
tr
ai
n
i
n
g
d
atasets
.
U
n
lik
e
th
e
PF
[
1
3
]
,
[
1
4
]
it m
ai
n
tai
n
s
lo
w
co
m
p
u
tatio
n
al
co
m
p
lex
it
y
,
m
ak
in
g
it
s
u
itab
le
f
o
r
e
m
b
ed
d
ed
B
MS
ap
p
licatio
n
s
.
Fu
r
t
h
er
m
o
r
e,
t
h
e
u
s
e
o
f
a
p
h
y
s
icall
y
i
n
ter
p
r
etab
le
E
C
M
en
h
a
n
ce
s
tr
a
n
s
p
ar
en
c
y
a
n
d
f
ac
ilit
ates
i
n
teg
r
atio
n
w
it
h
o
th
er
B
MS
f
u
n
ctio
n
s
s
u
c
h
as h
ea
lt
h
m
o
n
ito
r
in
g
a
n
d
f
a
u
lt
d
etec
tio
n
.
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