I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
1
3
,
No
.
4
,
Dece
m
b
er
20
2
4
,
p
p
.
8
8
6
~
8
9
9
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
0
.
1
1
5
9
1
/ijap
e
.
v
1
3
.
i
4
.
pp
886
-
899
886
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
p
e
.
ia
esco
r
e.
co
m
Perf
o
rma
nce
ana
ly
sis
of CKF alg
o
rithm f
o
r
batte
ry
So
C
estima
tion wi
th
i
t
s a
g
ing
ef
fec
t
G
.
G
ee
t
ha
Ra
v
a
li
,
K
.
N
a
ra
s
im
ha
Ra
j
u
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
a
n
d
El
e
c
t
r
o
n
i
c
s
En
g
i
n
e
e
r
i
n
g
,
K
o
n
e
r
u
La
k
s
h
ma
i
a
h
Ed
u
c
a
t
i
o
n
F
o
u
n
d
a
t
i
o
n
,
V
a
d
d
e
sw
a
r
a
m,
I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
1
0
,
2
0
2
3
R
ev
is
ed
J
u
l 1
,
2
0
2
4
Acc
ep
ted
J
u
l 1
9
,
2
0
2
4
Th
e
p
e
n
e
tratio
n
o
f
e
lec
tri
c
v
e
h
icle
(EV)
in
a
u
t
o
m
o
b
il
e
m
a
rk
e
t
is
v
e
ry
m
u
c
h
d
e
p
e
n
d
e
n
t
o
n
t
h
e
b
a
tt
e
ry
tec
h
n
o
l
o
g
y
.
Its
siz
e
,
we
ig
h
t,
a
n
d
c
o
st
a
re
issu
e
s
o
f
c
o
n
c
e
rn
.
T
o
e
ffe
c
ti
v
e
ly
u
t
il
ize
th
e
b
a
tt
e
ry
e
x
p
e
rti
se
,
p
re
c
ise
e
stim
a
te
o
f
sta
te
o
f
c
h
a
r
g
e
(S
o
C)
is
v
it
a
l
w
h
ich
g
r
e
a
tl
y
d
e
p
e
n
d
s
o
n
th
e
b
a
tt
e
ry
m
o
d
e
l.
Cu
rre
n
t
m
o
d
e
ls
lac
k
c
o
n
si
d
e
ra
ti
o
n
f
o
r
v
a
ri
a
ti
o
n
s
in
b
a
tt
e
ry
c
a
p
a
c
it
y
o
v
e
r
t
h
e
i
r
li
fe
sp
a
n
.
Th
is
p
a
p
e
r
d
e
v
e
l
o
p
s
a
b
a
tt
e
ry
m
o
d
e
l
wh
ich
d
e
p
ic
ts
th
e
d
e
p
leti
o
n
o
f
b
a
tt
e
r
y
c
a
p
a
c
it
y
with
it
s
li
fe
.
S
u
b
se
q
u
e
n
tl
y
,
th
is
m
o
d
e
l
h
a
s
b
e
e
n
u
ti
li
z
e
d
fo
r
e
stim
a
ti
o
n
u
sin
g
a
d
v
a
n
c
e
d
Ka
lma
n
fil
terin
g
(KF)
a
lg
o
ri
th
m
s.
F
o
r
t
h
e
d
e
v
e
l
o
p
e
d
m
o
d
e
l
,
th
e
d
e
sig
n
a
n
d
e
ffe
c
ti
v
e
n
e
ss
o
f
t
h
e
c
u
b
a
tu
re
Ka
lma
n
f
il
ter
(CKF)
is
a
p
p
li
e
d
a
s
a
p
ro
p
o
se
d
r
o
b
u
st
sta
te
-
e
stim
a
to
r
fo
r
t
h
is
p
r
o
b
lem
.
M
o
re
o
v
e
r,
a
c
o
m
p
a
ra
ti
v
e
a
n
a
ly
sis
wa
s
u
n
d
e
rtak
e
n
wit
h
e
x
i
stin
g
n
o
n
-
li
n
e
a
r
KFs
b
a
se
d
o
n
p
e
rfo
rm
a
n
c
e
m
e
tri
c
s.
Th
e
o
p
ti
m
a
l
c
h
o
ice
o
f
e
stim
a
to
r
is
id
e
n
ti
fied
,
th
r
o
u
g
h
t
h
e
re
su
lt
s
o
b
ta
i
n
e
d
fr
o
m
t
h
e
Oc
tav
e
/M
AT
LAB
sim
u
latio
n
.
Th
e
o
u
tco
m
e
s
sh
o
w
CKF
a
lg
o
rit
h
m
b
a
se
d
S
o
C
e
stim
a
to
r
is
su
p
e
rio
r
to
o
t
h
e
rs
in
e
n
su
ri
n
g
h
ig
h
a
c
c
u
ra
c
y
,
stro
n
g
r
o
b
u
stn
e
ss
e
v
e
n
u
n
d
e
r
c
h
a
n
g
e
s
i
n
in
it
ial
c
o
n
d
it
io
n
s
(i.
e
.
,
i
n
it
ial
S
o
C,
p
ro
c
e
ss
a
n
d
se
n
s
o
r
n
o
ise
lev
e
ls),
sy
ste
m
'
s
a
b
il
it
y
t
o
c
o
n
v
e
r
g
e
q
u
i
c
k
ly
wh
il
e
e
n
su
rin
g
t
h
a
t
th
e
m
a
x
im
u
m
e
rro
r
in
sta
te
o
f
c
h
a
rg
e
(S
o
C)
e
stim
a
ti
o
n
re
m
a
in
s
with
in
1
%
a
fter co
n
v
e
rg
e
n
c
e
.
K
ey
w
o
r
d
s
:
B
atter
y
m
an
ag
em
en
t sy
s
tem
B
atter
y
m
o
d
el
C
ap
ac
ity
d
eg
r
ad
atio
n
E
lectr
ic
v
eh
icle
Kalm
an
f
ilter
L
ith
iu
m
-
io
n
b
atter
y
State
esti
m
atio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
K.
Nar
asimh
a
R
aju
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
Ko
n
er
u
L
ak
s
h
m
aiah
E
d
u
ca
tio
n
Fo
u
n
d
atio
n
Vad
d
eswar
am
,
An
d
h
r
a
Pra
d
es
h
,
I
n
d
ia
E
m
ail: n
ar
asimh
ar
aju
_
ee
e@
k
l
u
n
iv
er
s
ity
.
in
NO
M
E
N
CL
A
T
UR
E
z
:
S
tate
o
f
ch
ar
g
e
x
[
k
+1
]
:
State
p
r
ed
ictio
n
tim
e
u
p
d
ate
v
(
t)
:
T
er
m
in
al
v
o
ltag
e
t
:
Sam
p
lin
g
in
ter
v
al
i(
t)
:
B
atter
y
in
s
tan
t d
is
ch
ar
g
e
cu
r
r
en
t
1
:
C
u
r
r
en
t th
r
o
u
g
h
R
1
an
d
C
1
η
:
C
o
u
lo
m
b
ic
-
ef
f
icien
c
y
ℎ
[
]
:
Hy
s
ter
esis
Q
:
C
ap
ac
ity
:
R
ate
o
f
d
ec
ay
T
:
T
em
p
er
atu
r
e
M
:
M
ax
im
u
m
p
lu
s
/m
in
u
s
h
y
s
ter
esis
R
:
R
esi
s
tan
ce
Sg
n
(
z)
:
F
o
r
ce
s
s
tab
ilit
y
f
o
r
b
o
th
d
is
/ch
ar
g
e
C
:
C
ap
ac
itan
ce
,
,
:
A
r
b
itra
y
co
n
s
tan
ts
A[
k
]
:
State
tr
an
s
itio
n
m
atr
ix
R
:
G
as c
o
n
s
tan
t
B
[
k
]
:
C
o
n
tr
o
l
-
in
p
u
t
m
atr
ix
Z
:
A
d
ju
s
tab
le
f
ac
to
r
u
[
k
]
:
C
o
n
tr
o
l in
p
u
t
A
:
F
ac
to
r
o
f
p
r
e
-
ex
p
o
n
e
n
tial te
r
m
:
A
ctiv
atio
n
en
er
g
y
T
:
A
b
s
o
lu
te
tem
p
er
atu
r
e
:
C
y
cles u
n
d
er
d
is
ch
ar
g
e/c
h
ar
g
e
:
O
u
tp
u
t e
q
u
atio
n
:
S
en
s
o
r
n
o
is
e
:
Pro
ce
s
s
n
o
is
e
∑
̃
,
+
:
E
r
r
o
r
c
o
v
ar
ian
ce
esti
m
ate
μ
:
Mean
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f CK
F
a
lg
o
r
ith
m
fo
r
b
a
tter
y
S
o
C
esti
ma
tio
n
w
ith
its
a
g
in
g
effec
t
(
G
.
Gee
th
a
R
a
v
a
li
)
887
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
d
e
v
elo
p
m
e
n
t
o
f
elec
tr
ic
v
eh
icle
s
(
E
Vs)
will
m
itig
ate
co
n
tin
g
en
t
o
n
f
o
s
s
il
f
u
els
f
o
r
tr
a
n
s
p
o
r
tatio
n
.
B
y
u
s
in
g
elec
tr
icity
,
wh
ich
ca
n
b
e
g
en
er
ated
f
r
o
m
a
v
ar
iety
o
f
s
o
u
r
ce
s
,
co
u
n
tr
ies
ca
n
en
r
ich
t
h
eir
u
tili
ty
ch
o
ices
th
er
ef
o
r
e
m
itig
ate
its
r
elian
ce
o
n
o
il
im
p
o
r
ts
.
Ultim
ately
,
t
h
e
o
v
e
r
ar
ch
in
g
g
o
als
in
clu
d
e
m
itig
atin
g
clim
ate
ch
an
g
e,
l
o
wer
in
g
th
e
tr
an
s
p
o
r
tatio
n
s
ec
to
r
'
s
g
lo
b
al
em
is
s
io
n
s
wh
ile
p
r
o
g
r
ess
in
g
in
th
e
s
tr
id
e
to
a
clea
n
e
r
,
g
r
ee
n
er
f
u
tu
r
e
[
1
]
.
T
h
e
d
ev
e
lo
p
m
en
t
o
f
E
Vs
f
o
s
ter
s
tech
n
o
lo
g
ical
in
n
o
v
atio
n
in
v
ar
io
u
s
asp
ec
ts
,
d
r
iv
in
g
im
p
r
o
v
em
e
n
ts
in
p
er
f
o
r
m
an
c
e,
r
an
g
e,
ef
f
icien
cy
,
an
d
u
s
er
ex
p
er
ien
ce
.
So
m
e
n
o
tab
le
ar
ea
s
o
f
in
n
o
v
atio
n
in
clu
d
e
b
atter
y
tech
n
o
lo
g
y
,
en
er
g
y
s
to
r
a
g
e,
elec
tr
ic
m
o
to
r
s
an
d
d
r
iv
etr
ain
s
y
s
tem
s
,
r
an
g
e
ex
ten
s
io
n
,
v
eh
icle
-
to
-
g
r
id
tec
h
n
o
lo
g
y
,
au
to
n
o
m
o
u
s
d
r
iv
in
g
in
teg
r
atio
n
,
an
d
ch
ar
g
in
g
i
n
f
r
astru
ctu
r
e
[
2
]
,
[
3
]
.
T
h
e
ac
h
iev
em
e
n
t
o
f
f
u
r
th
er
a
d
v
an
ce
m
e
n
ts
an
d
wid
esp
r
ea
d
ad
o
p
ti
o
n
o
f
elec
tr
ic
v
e
h
icles
h
in
g
es
s
ig
n
if
ican
tly
o
n
t
h
e
ef
f
ec
tiv
en
ess
o
f
b
atter
y
p
ac
k
s
as
th
e
p
r
im
a
r
y
p
o
wer
s
o
u
r
ce
.
I
n
E
V
m
a
r
k
e
t,
l
ith
iu
m
-
io
n
b
atter
ies
ar
e
b
e
co
m
in
g
ev
e
r
m
o
r
e
p
r
ev
alen
t
co
m
p
ar
e
d
to
o
th
e
r
s
o
win
g
to
th
eir
s
u
p
er
io
r
en
er
g
y
/
p
o
wer
d
en
s
ity
,
ze
r
o
m
em
o
r
y
im
p
ac
t,
d
ee
p
er
life
ex
p
ec
tan
cy
,
an
d
ex
te
n
d
ed
c
y
clin
g
[
4
]
,
[
5
]
.
C
o
n
s
eq
u
e
n
tly
,
a
c
r
itical
asp
ec
t
o
f
en
h
a
n
cin
g
m
o
d
er
n
EV
p
er
f
o
r
m
an
ce
is
th
e
cr
u
cial
s
o
f
twar
e
co
m
p
o
n
e
n
t
o
f
b
atter
y
m
an
ag
em
en
t
s
y
s
tem
s
in
v
o
lv
es
p
ar
am
eter
s
(
v
o
ltag
e,
cu
r
r
en
t
an
d
tem
p
e
r
atu
r
e)
an
d
s
tates
(
s
tate
o
f
ch
ar
g
e
(
So
C
)
,
s
tate
o
f
h
ea
lth
(
So
H
)
,
an
d
s
tat
e
o
f
p
o
wer
(
So
P
)
)
m
o
n
ito
r
in
g
[
6
]
.
So
C
ac
ts
as
a
k
ey
elem
en
t
a
n
d
h
o
s
t
f
o
r
o
th
er
o
p
er
atio
n
s
an
d
ca
lcu
latio
n
s
,
th
u
s
,
p
r
ec
is
e
So
C
es
tim
ate
m
ax
im
iz
es
b
atter
y
co
n
s
u
m
p
tio
n
b
y
p
r
o
v
id
in
g
ac
c
u
r
ate
tr
av
el
d
is
tan
ce
an
d
en
s
u
r
es
s
af
e
o
p
er
atin
g
lim
its
f
o
r
th
e
b
atter
y
.
So
C
g
iv
es
d
ef
in
ite
esti
m
ates
in
d
r
iv
in
g
r
an
g
e
an
d
th
e
lef
to
v
er
ca
p
a
city
with
in
th
e
p
ac
k
th
at
p
lay
s
an
en
er
g
etic
p
o
s
itio
n
in
o
p
tim
izin
g
th
e
c
h
ar
g
i
n
g
an
d
d
is
ch
ar
g
i
n
g
p
r
o
ce
s
s
es
co
n
tr
o
l
[
7
]
.
Dir
ec
t
m
ea
s
u
r
em
en
t
o
f
So
C
is
n
o
t
f
ea
s
ib
le
s
in
ce
it
i
s
n
o
t
a
p
h
y
s
ical
q
u
an
tity
.
Th
er
e
f
o
r
e
,
So
C
ca
n
o
n
ly
b
e
r
eliab
ly
esti
m
ated
.
E
v
en
s
o
,
d
r
iv
en
b
y
t
h
e
in
ten
s
e
n
o
n
lin
ea
r
p
r
o
p
e
r
ties
an
d
tim
e
-
v
a
r
ian
ce
s
y
s
tem
o
f
b
atter
ies,
ch
allen
g
es
p
er
s
is
t
to
ac
h
iev
e
p
r
ec
is
e
ass
ess
m
en
ts
o
n
S
o
C
u
pon
in
tr
icate
r
ea
l
-
wo
r
ld
cir
cu
m
s
tan
ce
s
,
co
m
p
o
u
n
d
ed
b
y
o
th
er
d
iv
er
s
e
in
f
lu
en
ci
n
g
f
ac
t
o
r
s
lik
e
fl
u
ctu
atin
g
tem
p
er
atu
r
e
r
an
g
e,
an
d
a
g
in
g
s
tatu
s
[
8
]
.
Ov
er
th
e
p
ast
d
ec
ad
e
,
m
o
s
t
r
es
ea
r
ch
in
th
e
is
s
u
e
h
as
em
p
h
asized
th
e
u
s
e
o
f
en
h
a
n
cin
g
th
e
a
cc
u
r
ac
y
o
f
So
C
est
im
atio
n
to
o
f
f
er
a
clea
r
co
n
ce
p
t
to
th
e
r
esear
ch
er
s
an
d
m
an
u
f
ac
tu
r
er
s
f
o
r
th
e
im
m
in
e
n
t
E
V
p
r
o
g
r
ess
io
n
.
Var
io
u
s
So
C
esti
m
atio
n
tech
n
iq
u
es
th
at
a
r
e
wid
ely
em
p
lo
y
ed
ar
e
v
o
ltag
e
-
b
ased
/lo
o
k
-
u
p
,
cu
r
r
en
t
-
b
ased
/co
u
lo
m
b
-
co
u
n
tin
g
/
a
m
p
er
e
-
h
o
u
r
i
n
teg
r
atio
n
,
m
o
d
el
-
b
a
s
ed
,
an
d
d
ata
-
d
r
iv
e
n
tech
n
iq
u
e
s
.
I
n
m
ajo
r
ity
o
f
th
e
ca
s
es,
r
esear
ch
er
s
p
r
ed
o
m
in
an
tly
f
o
cu
s
ed
o
n
m
o
d
el
-
b
ased
an
d
d
ata
ap
p
r
o
ac
h
es [
9
]
,
[
1
0
]
.
T
h
e
tr
ad
itio
n
al
lo
o
k
-
u
p
tab
le
u
s
ed
th
e
d
ir
ec
t
-
m
ap
p
i
n
g
c
o
r
r
elatio
n
b
etwe
en
So
C
a
n
d
p
ar
am
eter
s
d
escr
ib
in
g
ex
te
r
io
r
c
h
ar
ac
ter
is
tics
,
s
u
ch
as
im
p
ed
an
ce
a
n
d
o
p
en
-
cir
cu
it
v
o
ltag
e.
T
h
e
r
elatio
n
was
tab
u
lated
th
r
o
u
g
h
th
o
r
o
u
g
h
lab
test
s
.
I
n
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
,
esp
ec
ially
b
ey
o
n
d
c
o
n
tr
o
lled
lab
o
r
ato
r
y
s
ettin
g
s
,
lith
iu
m
io
n
b
atter
ies
(
LIB
)
was
ty
p
ically
o
p
er
ated
c
o
n
tin
u
o
u
s
ly
,
h
en
ce
n
o
t
p
r
ac
tical.
I
n
c
o
n
tr
ast,
th
e
co
lo
u
m
b
co
u
n
tin
g
(
CC
)
was
f
air
ly
ac
cu
r
ate
u
n
d
e
r
k
n
o
wn
in
itial
co
n
d
itio
n
s
,
p
r
ec
is
e
s
en
s
o
r
ca
lib
r
atio
n
,
a
n
d
a
g
i
n
g
le
v
els.
I
n
ac
cu
r
ac
ies
c
o
u
ld
n
'
t
b
e
av
o
id
ed
i
n
th
is
ca
s
e
b
ec
au
s
e
o
f
its
o
p
en
-
l
o
o
p
m
ec
h
an
is
m
.
Desp
ite
th
e
s
im
p
licity
o
f
tr
ad
itio
n
al
m
et
h
o
d
s
(
v
o
ltag
e,
an
d
c
u
r
r
e
n
t
-
b
ased
)
,
th
e
r
esu
lts
r
ea
lize
th
e
f
laws
o
f
lo
n
g
r
esti
n
g
tim
e,
u
n
k
n
o
wn
in
itial
So
C
,
h
ig
h
ac
cu
r
a
cy
m
ea
s
u
r
em
en
t
in
v
o
ltag
e,
an
d
s
en
s
o
r
er
r
o
r
.
T
h
i
s
u
n
ce
r
tain
in
itial
v
alu
e
cr
ea
tes
an
er
r
o
r
o
f
2
0
%
m
o
r
e
wh
ich
ca
n
b
e
r
ed
u
ce
d
by
ef
f
ec
tiv
e
er
r
o
r
r
ec
alib
r
atio
n
f
r
o
m
th
e
m
ap
p
in
g
r
elatio
n
s
h
ip
o
f
So
C
v
er
s
u
s
o
p
en
cir
cu
it
v
o
ltag
e
(
OC
V
)
tab
le
as
p
r
esen
ted
in
[
11
]
,
[
1
2
]
.
W
ith
k
n
o
wn
i
n
itial
So
C
,
s
en
s
o
r
ca
lib
r
atio
n
,
an
d
u
p
d
ate
d
ca
p
ac
ity
,
am
p
er
e
-
h
o
u
r
in
teg
r
atio
n
(
AHI
)
attain
s
ac
cu
r
ate
ac
cu
r
ac
y
as
s
tated
in
[
1
3
]
.
Fro
m
th
e
au
th
o
r
’
s
f
in
d
i
n
g
s
,
it
is
o
b
s
er
v
ed
th
at
th
e
co
m
b
in
atio
n
o
f
th
ese
m
eth
o
d
s
m
ay
p
o
s
s
ib
ly
g
iv
e
b
etter
ac
cu
r
ac
y
b
u
t
r
em
ain
s
u
b
i
q
u
ito
u
s
a
n
d
in
ap
p
licab
le
f
o
r
o
n
lin
e
ass
ess
m
en
t
.
T
h
e
id
ea
o
f
a
co
m
b
in
ed
ap
p
r
o
ac
h
is
s
u
p
p
o
r
ted
b
y
s
tu
d
ies
[
1
4
]
,
[
1
5
]
,
wh
ich
d
eliv
er
ef
f
icien
t
o
p
er
atio
n
.
Desp
ite
th
e
f
ac
t
,
m
e
asu
r
in
g
th
e
OC
V
in
r
ea
l
-
tim
e
p
r
o
v
es
ch
allen
g
in
g
d
u
e
to
u
n
ce
r
tain
d
r
iv
in
g
cy
cles,
co
m
p
lex
a
p
p
licatio
n
cir
c
u
m
s
tan
ce
s
,
an
d
o
t
h
er
v
a
r
iab
les.
B
ased
o
n
th
ese
f
in
d
in
g
s
,
id
e
n
tify
in
g
a
p
r
ec
is
e
an
d
s
tr
aig
h
tf
o
r
war
d
m
o
d
el
is
a
c
r
u
cial
co
n
ce
r
n
,
n
e
ce
s
s
itatin
g
th
e
wid
esp
r
ea
d
u
tili
za
tio
n
o
f
m
o
d
el
-
b
ased
m
et
h
o
d
s
(
an
aly
tic
an
d
s
tatis
tical/em
p
ir
ical
lin
ea
r
izatio
n
)
lik
e
o
b
s
er
v
er
s
,
an
d
f
ilter
in
g
tech
n
iq
u
es
f
o
r
ac
cu
r
ate
So
C
esti
m
atio
n
[
1
6
]
-
[
1
8
]
.
An
o
th
er
p
o
s
s
ib
ilit
y
wo
u
ld
b
e
d
ata
-
d
r
iv
en
ap
p
r
o
ac
h
es
,
t
h
at
r
ely
o
n
th
e
an
al
y
s
is
an
d
u
tili
za
tio
n
o
f
d
ata
f
o
r
esti
m
ati
o
n
p
r
o
ce
s
s
.
I
n
s
tead
o
f
r
ely
in
g
s
o
lely
o
n
p
r
ed
ef
in
e
d
m
o
d
els,
th
ese
ap
p
r
o
ac
h
es
u
s
e
r
ea
l
-
wo
r
ld
d
ata
to
m
ak
e
p
r
e
d
ictio
n
s
an
d
ass
ess
th
e
s
tatu
s
o
f
a
b
atter
y
.
Fro
m
th
e
ex
p
er
im
en
tal
d
atasets
,
r
esear
ch
er
s
em
p
lo
y
m
eta
-
h
e
u
r
is
tic
tech
n
iq
u
es,
an
d
m
a
ch
in
e
lear
n
in
g
o
r
s
tatis
tical
m
eth
o
d
s
to
p
r
o
ce
s
s
an
d
in
ter
p
r
et
th
e
in
f
o
r
m
atio
n
o
b
tai
n
ed
f
r
o
m
th
e
b
atter
y
[
1
9
]
,
[
2
0
]
.
T
h
e
y
d
o
n
'
t
r
ely
o
n
a
p
r
ed
e
f
in
ed
m
o
d
el
s
tr
u
ctu
r
e
an
d
ca
n
ad
ju
s
t
to
d
iv
er
s
e
a
n
d
d
y
n
am
ic
s
ce
n
a
r
io
s
.
Als
o
,
ca
n
lear
n
d
ir
ec
tly
f
r
o
m
o
p
er
atio
n
a
l
d
ata,
r
e
d
u
cin
g
th
e
im
p
ac
t
o
f
m
o
d
elin
g
e
r
r
o
r
s
.
B
u
t
t
h
e
n
,
t
h
e
y
c
o
m
e
w
i
t
h
i
n
h
e
r
e
n
t
d
r
a
w
b
a
c
k
s
l
i
k
e
l
i
m
it
e
d
g
e
n
e
r
a
l
i
z
at
i
o
n
,
d
a
t
a
d
e
p
e
n
d
e
n
c
y
,
a
b
s
e
n
c
e
o
f
p
h
y
s
i
c
a
l
i
n
t
e
r
p
r
e
t
a
b
il
i
t
y
,
o
v
e
r
f
i
tt
i
n
g
,
c
o
m
p
u
t
a
t
i
o
n
a
l
c
o
m
p
l
e
x
i
t
y
,
a
n
d
r
o
b
u
s
t
n
e
s
s
c
o
n
c
e
r
n
s
.
To
an
ticip
ate
th
e
i
n
ter
n
al
d
y
n
am
ic
b
eh
av
io
r
s
o
f
a
b
atter
y
,
i
t
is
ess
en
tial
to
cr
ea
te
a
m
o
d
el
f
o
r
th
e
b
atter
y
.
E
q
u
iv
alen
t
cir
cu
it
m
o
d
els
[
2
1
]
,
c
h
ar
ac
ter
ized
b
y
t
h
eir
s
im
p
le
s
tr
u
ctu
r
es,
o
f
f
er
a
p
r
ac
tical
ap
p
r
o
ac
h
with
o
u
t
r
eq
u
ir
in
g
p
r
io
r
k
n
o
w
led
g
e
o
f
elec
tr
o
ch
em
is
tr
y
as
m
en
tio
n
ed
in
[
22
]
.
Ho
wev
er
,
th
ese
co
n
v
en
tio
n
al
m
o
d
els
lack
p
h
y
s
ical
in
s
ig
h
ts
,
an
d
u
n
ce
r
tain
ties
lik
e
h
y
s
ter
esis
an
d
ag
in
g
ef
f
ec
t
an
d
,
co
n
s
eq
u
en
tly
,
ar
e
n
o
t
s
u
itab
le
f
o
r
esti
m
atin
g
th
e
h
e
alth
-
r
elate
d
s
tates
an
d
p
o
wer
m
an
ag
em
en
t
.
I
n
c
o
m
p
ar
is
o
n
,
m
o
d
els
r
o
o
ted
i
n
f
u
n
d
am
e
n
tal
elec
tr
o
ch
em
ical
an
d
th
er
m
o
d
y
n
a
m
ic
p
r
in
cip
le
s
,
co
m
m
o
n
ly
r
ef
e
r
r
ed
to
as
p
h
y
s
ics
-
b
ased
m
o
d
els
lik
e
p
s
eu
d
o
-
two
-
d
im
en
s
io
n
al
as
p
r
esen
ted
in
[
23
]
,
ex
ce
l
in
p
r
o
v
id
in
g
m
o
r
e
v
alu
ab
le
an
d
ess
en
tial
in
f
o
r
m
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dece
m
b
er
20
2
4
:
8
8
6
-
899
888
T
h
ey
p
r
o
v
e
a
d
ep
t
at
p
r
ed
ictin
g
b
atter
y
h
ea
lth
an
d
p
lay
a
cr
u
cial
r
o
le
in
th
e
d
ev
elo
p
m
en
t
o
f
o
p
tim
al
co
n
tr
o
l
s
tr
ateg
ies
[
24
]
.
B
u
t
th
en
im
p
lem
en
tin
g
h
ig
h
ly
n
o
n
lin
ea
r
p
ar
tial
d
if
f
er
en
tial
-
alg
e
b
r
aic
eq
u
atio
n
s
o
n
b
atter
y
m
an
ag
em
en
t
s
y
s
tem
(
B
MS
)
f
o
r
o
n
lin
e
ap
p
licatio
n
is
im
p
r
ac
tical
d
u
e
to
co
m
p
u
tatio
n
al
co
m
p
lex
ity
as
m
en
tio
n
ed
in
[
25
]
.
I
n
lig
h
t
o
f
th
ese
c
o
n
cl
u
s
io
n
s
,
th
er
e
is
a
n
ee
d
f
o
r
a
n
e
n
h
an
ce
d
cir
cu
it
m
o
d
el
o
f
a
lith
iu
m
-
io
n
b
atter
y
th
at
ca
n
ad
d
r
ess
u
n
ce
r
tain
ties
,
th
er
eb
y
m
a
k
in
g
ac
cu
r
ate
esti
m
atio
n
p
o
s
s
ib
le.
A
m
o
n
g
t
h
e
e
x
is
tin
g
m
o
d
els,
th
e
ab
s
en
ce
o
f
d
eg
r
ad
atio
n
d
y
n
a
m
ics
,
ca
p
ac
ity
esti
m
atio
n
a
n
d
ad
ap
tiv
e
esti
m
atio
n
o
f
u
n
k
n
o
wn
er
r
o
r
c
o
v
ar
ian
ce
r
esu
lt
s
in
in
ac
cu
r
ac
y
o
f
th
e
p
er
f
o
r
m
an
ce
as
m
en
tio
n
e
d
in
[
26
]
,
[
2
7
]
.
Fo
r
m
an
y
y
ea
r
s
,
th
is
ca
p
ac
ity
d
eg
r
ad
atio
n
/
ag
in
g
ef
f
ec
t
p
h
e
n
o
m
e
n
o
n
was
s
u
r
p
r
is
in
g
ly
n
e
g
lecte
d
in
t
h
e
m
o
d
ellin
g
an
d
esti
m
atio
n
p
r
o
ce
s
s
.
T
h
e
ab
o
v
e
f
in
d
in
g
is
r
elate
d
to
th
e
s
tu
d
y
o
f
[
2
8
]
th
at
th
e
th
eo
r
y
o
f
L
i
-
io
n
b
atter
y
ag
ein
g
r
esu
lts
in
ca
p
ac
ity
f
ad
e,
a
n
d
n
o
n
lin
ea
r
ag
ein
g
.
T
h
ese
s
tu
d
ies
f
o
cu
s
o
n
d
ev
elo
p
in
g
a
m
o
d
el
th
at
ca
n
p
r
e
d
ict
life
tim
e
p
r
ed
ictio
n
o
f
ce
ll
ca
p
ac
ity
.
Fo
llo
win
g
th
is
,
f
o
r
ec
asts
b
o
th
lin
ea
r
/
n
o
n
lin
ea
r
d
eg
r
ad
atio
n
b
ased
o
n
v
a
r
ied
co
n
s
tan
t
cu
r
r
e
n
t
cy
clin
g
d
ata
(
C
/3
ch
ar
g
in
g
-
4
C
d
is
ch
ar
g
in
g
)
(
h
er
e
C
-
C
r
ate;
a
r
elativ
e
m
ea
s
u
r
e
o
f
cu
r
r
en
t
)
,
d
e
m
o
n
s
tr
atin
g
a
9
8
%
g
o
o
d
n
ess
-
of
-
f
it
-
er
r
o
r
with
s
u
r
p
ass
in
g
th
e
p
er
f
o
r
m
a
n
ce
o
f
e
s
tab
lis
h
ed
ag
in
g
m
o
d
els.
T
h
e
r
esu
lt
in
[
2
9
]
-
[
3
2
]
ad
d
r
ess
ed
ce
r
tain
ch
allen
g
es m
en
tio
n
ed
ea
r
lier
,
s
u
g
g
esti
n
g
an
en
h
an
ce
d
b
atter
y
m
o
d
el
f
o
r
So
C
esti
m
atio
n
an
d
d
eg
r
ad
e
d
-
ca
p
ac
ity
th
r
o
u
g
h
an
im
p
r
o
v
e
d
ex
ten
d
e
d
K
alm
an
f
ilter
(
KF
)
.
A
s
im
ilar
m
o
d
el
is
u
s
ed
b
y
[
3
3
]
with
p
ar
ticle
s
war
m
o
p
tim
izatio
n
te
ch
n
iq
u
e
to
m
itig
ate
th
e
p
o
te
n
tial
f
o
r
p
r
ed
ictio
n
d
ev
iatio
n
,
alo
n
g
s
id
e
f
o
s
ter
in
g
th
e
p
r
o
ce
s
s
-
n
o
is
e
co
v
ar
ia
n
ce
v
ec
t
o
r
r
esu
ltin
g
f
r
o
m
ac
c
u
m
u
lated
er
r
o
r
s
d
u
r
in
g
p
r
o
l
o
n
g
e
d
o
p
e
r
a
tio
n
.
In
co
n
tr
ast,
th
e
s
tu
d
y
b
y
[
34
]
in
d
icate
d
th
at
an
im
p
r
o
v
e
d
ad
ap
tiv
e
ex
ten
d
e
d
Kalm
an
f
ilter
can
ac
co
m
p
lis
h
co
-
esti
m
atio
n
f
o
r
b
atter
y
ca
p
ac
ity
a
n
d
So
C
an
d
is
p
r
o
v
en
,
en
s
u
r
in
g
th
at
th
e
So
C
er
r
o
r
r
em
ain
s
with
in
±
1
.
2
%
d
u
r
i
n
g
th
e
in
iti
al
5
0
s
ec
o
n
d
s
,
an
d
th
e
r
elativ
e
ca
p
ac
ity
er
r
o
r
is
r
estricte
d
to
with
in
2
%
af
ter
co
n
v
er
g
en
ce
.
Ho
we
v
er
,
th
e
s
tu
d
y
s
o
lely
c
o
n
s
id
er
ed
t
h
e
h
y
s
t
er
esis
ef
f
ec
t,
an
d
co
m
p
lex
ity
o
f
d
r
iv
in
g
co
n
d
itio
n
s
an
d
o
v
e
r
lo
o
k
ed
th
e
p
o
ten
tial c
h
allen
g
es th
at
th
e
b
at
ter
y
en
co
u
n
ter
s
d
u
r
i
n
g
p
r
o
lo
n
g
ed
e
x
p
o
s
u
r
e
to
h
ig
h
C
-
r
ates
an
d
ag
in
g
as
s
h
o
wn
b
y
th
e
s
tu
d
ies
in
[
35
]
,
[
36
]
.
On
th
e
o
t
h
er
h
an
d
,
a
s
ea
r
ch
o
f
th
e
liter
atu
r
e
r
ev
ea
led
th
at
lim
ited
s
tu
d
ies
h
av
e
f
o
cu
s
ed
o
n
m
ac
h
in
e
lear
n
in
g
(
ML
)
tech
n
iq
u
es
d
u
e
to
th
e
co
m
p
lex
ity
i
n
m
o
d
el
-
b
ased
[
37
]
,
[
38
]
.
Hav
in
g
s
aid
th
at
in
f
u
tu
r
e,
in
teg
r
atio
n
o
f
m
o
d
el
an
d
d
a
ta
-
d
r
iv
en
m
eth
o
d
s
ca
n
b
e
an
e
f
f
ec
tiv
e
p
r
o
g
r
ess
io
n
f
o
r
f
u
r
th
e
r
ac
c
u
r
ac
y
[
39
].
Au
t
h
o
r
s
in
[
4
0
]
,
[
4
1
]
ad
d
e
d
th
at
m
u
lti
-
s
tate
esti
m
atio
n
p
lay
s
a
cr
itical
r
o
le
in
th
e
en
h
an
ce
m
e
n
t
o
f
b
atter
y
p
er
f
o
r
m
an
ce
.
T
h
e
ir
m
eth
o
d
o
lo
g
y
in
co
r
p
o
r
ates
th
e
ap
p
licatio
n
o
f
an
en
s
em
b
le
-
em
p
ir
ical
m
o
d
e
d
ec
o
m
p
o
s
iti
o
n
with
a
d
ap
tiv
e
n
o
is
e,
co
m
b
in
ed
to
an
au
to
e
n
co
d
er
co
n
s
id
er
in
g
m
o
d
el
u
n
ce
r
tain
ties
.
U
p
d
ates
on
v
ar
io
u
s
p
ar
am
eter
s
an
d
tim
e
s
ca
les
is
ac
co
m
p
lis
h
ed
th
r
o
u
g
h
th
e
d
u
al
-
ex
ten
d
ed
Kalm
an
f
ilter
.
Fo
r
im
p
r
o
v
in
g
th
e
r
ate
o
f
esti
m
ato
r
,
th
e
s
tu
d
y
u
s
ed
t
h
e
v
a
r
iab
le
f
o
r
g
ettin
g
f
a
cto
r
lim
ited
m
em
o
r
y
r
ec
u
r
s
iv
e
least
s
q
u
ar
es
tech
n
i
q
u
e.
Similar
ly
,
t
h
e
au
th
o
r
s
in
[
4
2
]
,
[
4
3
]
f
o
u
n
d
th
at
elec
tr
o
c
h
em
ical
im
p
ed
a
n
ce
s
p
ec
tr
o
s
co
p
y
is
also
a
p
o
we
r
f
u
l
to
o
l
f
o
r
ac
h
ie
v
in
g
p
r
ec
i
s
e
s
tate
esti
m
atio
n
.
C
o
n
v
er
s
ely
,
in
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
,
th
e
im
p
lem
en
tati
o
n
o
f
elec
tr
o
c
h
em
ical
im
p
ed
a
n
ce
s
p
ec
tr
o
s
co
p
y
(
EIS
)
m
ay
r
eq
u
ir
e
s
p
ec
ialized
eq
u
ip
m
en
t
,
s
o
p
h
is
ticated
an
aly
tical
tech
n
iq
u
es,
an
d
ca
r
ef
u
l
co
n
tr
o
l
o
f
ex
p
er
im
en
tal
co
n
d
it
io
n
s
.
Alter
n
ativ
ely
,
th
e
s
tu
d
y
b
y
[
4
4
]
s
u
g
g
ested
an
ad
ap
tiv
e
f
r
ac
tio
n
al
-
o
r
d
er
s
q
u
a
r
e
r
o
o
t
u
n
s
ce
n
ted
KF
wh
ich
d
y
n
am
ically
u
p
d
ate
s
d
is
tu
r
b
an
ce
s
tatis
tics
in
r
ea
l
-
ti
m
e
ad
d
r
ess
in
g
th
e
p
r
o
b
lem
o
f
d
ev
iatio
n
b
r
o
u
g
h
t
o
n
b
y
im
p
r
o
p
er
n
o
is
e
co
v
ar
ian
ce
m
atr
ices
.
I
n
co
m
p
ar
is
o
n
t
o
o
t
h
er
KFs
as
m
en
tio
n
ed
ab
o
v
e
,
th
e
s
tu
d
ies
b
y
[
4
5
]
,
[
4
6
]
s
u
g
g
est
th
at
cu
b
atu
r
e
K
alm
an
f
ilter
(
C
KF
)
ex
ce
ls
in
h
an
d
lin
g
th
e
co
m
p
lex
ities
o
f
n
o
n
lin
ea
r
d
y
n
am
ics,
p
r
o
v
id
i
n
g
m
o
r
e
r
eliab
le
,
an
d
p
r
ec
is
e
esti
m
at
es.
I
ts
ad
ap
tab
ilit
y
an
d
ef
f
ec
tiv
en
ess
m
ak
e
it
a
v
alu
ab
le
to
o
l
f
o
r
a
p
p
lica
tio
n
s
r
an
g
in
g
f
r
o
m
r
o
b
o
tics
an
d
n
av
ig
atio
n
s
y
s
tem
s
to
s
ig
n
al
p
r
o
ce
s
s
in
g
an
d
co
n
tr
o
l e
n
g
i
n
ee
r
in
g
.
E
v
en
th
o
u
g
h
th
er
e
h
as
b
ee
n
q
u
an
titativ
e
a
n
aly
s
is
o
f
v
a
r
io
u
s
esti
m
atio
n
tech
n
iq
u
es,
n
o
d
etailed
in
v
esti
g
atio
n
o
f
m
o
d
el
u
n
ce
r
t
ain
ties
(
h
y
s
ter
esis
)
,
ca
p
ac
ity
esti
m
atio
n
co
n
ce
r
n
in
g
t
h
e
ag
in
g
ef
f
ec
t,
wh
ich
ar
e
th
e
m
ajo
r
ch
allen
g
es to
b
e
a
d
d
r
ess
ed
f
o
r
e
n
h
an
ce
m
en
t
o
r
o
f
b
atter
y
p
e
r
f
o
r
m
an
ce
,
a
n
d
p
r
ac
t
icality
.
I
n
r
e
g
ar
d
to
th
is
,
ad
v
an
ce
m
e
n
ts
s
h
o
u
ld
c
o
llectiv
ely
aim
to
a
d
d
r
ess
th
ese
co
n
f
r
o
n
ts
co
r
r
elate
d
with
th
e
s
u
p
er
io
r
s
tate
esti
m
atio
n
p
r
o
ce
d
u
r
e
,
ac
h
iev
i
n
g
m
o
r
e
r
eliab
le
an
d
r
o
b
u
s
t
b
atter
y
s
tate
esti
m
atio
n
in
v
ar
io
u
s
ap
p
licatio
n
s
.
I
n
ter
esti
n
g
ly
,
p
r
ev
io
u
s
r
esear
c
h
h
as
n
o
t
ex
p
l
o
r
ed
b
atter
y
m
o
d
elin
g
with
h
y
s
ter
esis
an
d
ag
ein
g
ef
f
ec
ts
in
th
e
esti
m
atio
n
p
r
ac
tice.
I
n
v
iew
o
f
th
ese
s
h
o
r
tco
m
in
g
s
,
C
KF,
as
a
r
o
b
u
s
t
s
tate
esti
m
ato
r
,
is
p
r
o
p
o
s
ed
in
th
is
f
ield
o
f
wo
r
k
.
T
h
e
k
ey
c
o
n
tr
ib
u
ti
o
n
o
f
th
e
ar
ticle
is
as f
o
llo
ws:
-
A
s
tate
-
s
p
ac
e
r
ep
r
esen
tatio
n
o
f
th
e
b
atter
y
m
o
d
el
an
d
m
ath
e
m
atica
l
m
o
d
el
o
f
ca
p
ac
ity
d
eg
r
ad
atio
n
o
r
ag
i
n
g
ef
f
ec
t is m
ad
e
f
o
r
th
e
ef
f
ec
tiv
e
s
tate
esti
m
atio
n
;
-
As
a
s
tate
-
of
-
ar
t
r
o
b
u
s
t
alg
o
r
it
h
m
,
th
e
C
KF
m
eth
o
d
is
d
ev
elo
p
ed
to
o
b
tain
b
etter
ac
cu
r
ac
y
i
n
So
C
esti
m
atio
n
u
n
d
er
ca
p
ac
ity
d
e
g
r
ad
atio
n
o
r
ag
in
g
ef
f
ec
t
; a
n
d
-
C
o
m
p
ar
ativ
e
an
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
C
KF
with
o
th
er
KFs
u
n
d
er
eq
u
i
v
alen
t
n
o
n
lin
ea
r
ities
an
d
ag
in
g
ef
f
ec
t.
T
h
e
r
em
ain
in
g
p
a
p
er
is
o
r
g
an
ized
as
f
o
llo
ws.
Sectio
n
2
f
ir
s
t
d
escr
ib
es
th
e
co
m
p
lete
b
atter
y
m
o
d
el.
Nex
t,
th
e
d
etailed
m
ec
h
an
is
m
f
o
r
ag
in
g
is
p
r
esen
ted
an
d
its
m
ath
em
atica
l
m
o
d
el
h
as
b
ee
n
d
ev
elo
p
ed
f
o
r
ca
p
ac
ity
esti
m
atio
n
.
Sectio
n
3
ex
p
lain
s
co
n
v
en
tio
n
al
an
d
p
r
o
p
o
s
ed
So
C
esti
m
atio
n
m
eth
o
d
o
lo
g
ies
with
its
alg
o
r
ith
m
s
.
I
n
s
ec
tio
n
4
,
th
e
e
f
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
r
o
b
u
s
t
C
KF
tech
n
iq
u
e
is
v
er
if
i
ed
with
co
m
p
a
r
is
o
n
o
f
o
th
e
r
f
ilter
in
g
tec
h
n
iq
u
es.
F
in
ally
,
s
ec
tio
n
5
p
r
o
v
i
d
es a
s
u
m
m
ar
y
o
f
th
e
f
i
n
d
in
g
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f CK
F
a
lg
o
r
ith
m
fo
r
b
a
tter
y
S
o
C
esti
ma
tio
n
w
ith
its
a
g
in
g
effec
t
(
G
.
Gee
th
a
R
a
v
a
li
)
889
2.
B
AT
T
E
RY
M
O
D
E
L
AND
M
O
DE
L
P
ARA
M
E
T
E
RS I
DE
N
T
I
F
I
CAT
I
O
N
2
.
1
.
E
nh
a
nced
s
elf
-
co
rr
ec
t
ing
m
o
del
Dev
elo
p
in
g
a
c
o
n
cise
an
d
ac
cu
r
ate
b
atter
y
m
o
d
el
is
th
e
p
r
e
-
r
eq
u
is
ite
co
n
d
itio
n
th
at
s
ig
n
if
ican
tly
im
p
ac
ts
th
e
p
r
ec
is
io
n
o
f
th
e
So
C
esti
m
atio
n
.
C
o
m
p
ar
ed
to
v
ar
io
u
s
m
o
d
els
av
ailab
le
f
o
r
L
i
th
iu
m
-
io
n
b
atter
ies,
as
d
is
cu
s
s
ed
ea
r
lier
co
n
ce
r
n
i
n
g
s
tab
ilit
y
,
n
o
n
lin
ea
r
ities
,
p
r
ec
is
io
n
,
an
d
less
co
m
p
licated
co
m
p
u
tin
g
in
So
C
esti
m
atio
n
,
th
e
e
n
h
an
ce
d
s
elf
-
co
r
r
ec
tin
g
(
E
SC
)
m
o
d
el
was
d
ev
elo
p
ed
,
as
d
ep
icted
in
Fig
u
r
e
1
.
T
h
e
d
ev
el
o
p
ed
m
o
d
el
in
co
r
p
o
r
ated
p
a
r
am
eter
s
r
elate
d
to
d
if
f
u
s
io
n
,
OC
V
as
a
m
ea
s
u
r
e
o
f
So
C
,
an
d
o
h
m
ic
r
esis
tan
ce
,
in
clu
d
in
g
th
e
h
y
s
ter
esis
ef
f
ec
t
.
Hy
s
ter
es
is
is
a
p
ath
-
d
ep
en
d
en
t
v
o
ltag
e
th
at
d
o
es
n
o
t
d
ec
ay
t
o
ze
r
o
wh
en
th
e
ce
ll
r
ests
,
u
n
lik
e
d
if
f
u
s
io
n
v
o
ltag
es
th
at
ch
an
g
e
with
tim
e.
T
h
e
m
o
d
el
p
ar
am
eter
s
wer
e
d
eter
m
in
ed
u
s
in
g
ex
p
er
im
en
tal
d
ata
f
r
o
m
t
h
e
1
8
6
5
0
-
b
atter
y
ce
ll.
T
o
d
eter
m
in
e
t
h
e
m
o
d
el
p
ar
am
eter
v
alu
es,
th
e
f
u
n
ctio
n
s
w
er
e
ass
o
ciate
d
with
a
to
o
lb
o
x
n
a
m
ed
E
SC
in
Octa
v
e/M
AT
L
AB
wh
ich
p
r
o
v
id
e
s
ac
ce
s
s
to
th
e
m
o
d
el
f
ield
s
(
p
r
o
ce
s
s
OC
V
an
d
p
r
o
ce
s
s
d
y
n
am
ic
)
.
T
ab
le
1
tab
u
lates th
e
b
atter
y
s
p
ec
if
icatio
n
s
.
T
h
e
d
is
cr
ete
f
o
r
m
o
f
m
ath
em
atica
l
eq
u
atio
n
s
is
w
r
itten
f
o
r
th
e
a
b
o
v
e
m
o
d
el
.
I
n
d
is
cr
ete
tim
e,
th
e
ass
u
m
p
tio
n
wa
s
m
ad
e
th
at
th
e
cu
r
r
en
t
r
em
ai
n
s
p
er
s
is
ten
t
wit
h
in
th
e
en
tire
in
ter
v
al
.
E
ac
h
at
tr
ib
u
te
o
f
d
y
n
am
ic
n
atu
r
e
en
s
u
es with
in
(
1
)
an
d
(
2
)
.
[
+
1
]
=
[
]
[
]
+
[
]
[
]
(
1
)
[
[
+
1
]
1
[
+
1
]
ℎ
[
+
1
]
]
=
[
1
0
0
0
0
0
0
[
]
]
[
[
]
1
[
]
ℎ
[
]
]
+
[
−
[
]
∆
/
0
0
0
[
]
−
1
]
[
[
]
(
[
]
)
]
(
2
)
Sin
ce
So
C
(
th
e
b
atter
y
r
esid
u
al/lef
to
v
er
ca
p
ac
ity
)
is
n
’
t
a
p
h
y
s
ical
q
u
an
tity
.
T
h
er
e
f
o
r
e,
So
C
ca
n
b
e
ap
p
r
o
x
im
ated
u
tili
zin
g
t
h
e
b
at
ter
y
-
m
ea
s
u
r
ed
v
alu
es
(
v
o
ltag
e
,
cu
r
r
e
n
t
,
an
d
tem
p
er
atu
r
e)
.
=
;
Z
[
+
1
]
=
Z
[
]
−
∆
t
Q
[
]
(
3
)
C
o
m
p
u
tin
g
ter
m
i
n
al
v
o
ltag
e
o
f
th
e
b
atter
y
as
(
4
)
a
n
d
(
5
)
.
[
]
=
[
]
[
]
+
[
]
[
]
(
4
)
[
]
=
(
[
]
,
[
]
)
+
0
[
]
+
ℎ
[
]
−
1
1
[
]
−
0
[
]
(
5
)
T
h
is
m
ath
em
atica
l
m
o
d
el
was
s
u
b
jecte
d
to
in
teg
r
atio
n
with
f
i
lter
in
g
alg
o
r
ith
m
s
f
o
r
esti
m
atin
g
th
e
b
atter
y
s
tates.
Fig
u
r
e
1
.
B
atter
y
m
o
d
el
T
ab
le
1
.
B
atter
y
ce
ll
p
ar
ticu
la
r
s
B
a
t
t
e
r
y
p
a
r
a
met
e
r
S
p
e
c
i
f
i
c
a
t
i
o
n
Ty
p
e
Li
N
M
C
U
p
p
e
r
/
l
o
w
e
r
c
u
t
-
o
f
f
v
o
l
t
a
g
e
4
.
2
/
2
.
5
V
N
o
mi
n
a
l
v
o
l
t
a
g
e
3
.
6
V
N
o
mi
n
a
l
c
a
p
a
c
i
t
y
2
5
A
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dece
m
b
er
20
2
4
:
8
8
6
-
899
890
2
.
2
.
Ca
pa
ci
t
y
deg
ra
da
t
io
n/a
g
ing
m
o
del
Un
d
er
s
tan
d
in
g
an
d
m
itig
atin
g
th
e
ef
f
ec
ts
o
f
a
g
in
g
is
cr
u
cial
f
o
r
o
p
tim
izin
g
b
atter
y
li
f
esp
an
an
d
m
ain
tain
in
g
r
eliab
le
p
er
f
o
r
m
a
n
ce
.
Ap
ar
t
f
r
o
m
v
ar
io
u
s
ag
in
g
m
ec
h
an
is
m
s
r
ef
er
r
ed
t
o
[
4
7
]
wer
e
tab
u
lated
in
T
ab
le
2
,
t
em
p
er
atu
r
e
,
C
-
r
ate,
d
ep
th
o
f
d
is
ch
ar
g
e,
So
C
,
we
r
e
th
e
ce
n
tr
al
v
ar
iab
les
im
p
er
ili
n
g
th
e
d
ev
elo
p
m
en
t
of
ag
in
g
.
T
o
d
em
o
n
s
tr
ate
th
e
i
m
p
ac
t
o
f
a
g
in
g
,
th
e
m
o
d
el
wa
s
d
ev
elo
p
ed
b
y
i
n
co
r
p
o
r
atin
g
t
h
e
tem
p
er
atu
r
e
an
d
p
o
wer
-
law
r
elatio
n
.
T
h
is
co
m
b
in
atio
n
p
r
o
v
id
es
a
co
m
p
r
eh
en
s
iv
e
ap
p
r
o
ac
h
,
allo
win
g
u
s
to
u
n
d
er
s
tan
d
tem
p
er
atu
r
e
v
ar
iatio
n
s
an
d
th
e
co
m
p
le
x
,
n
o
n
-
lin
ea
r
n
atu
r
e.
T
h
u
s
,
th
e
m
o
d
el
th
at
in
co
r
p
o
r
at
es
th
e
ab
o
v
e
f
ac
to
r
s
h
elp
s
ac
co
u
n
t
f
o
r
th
e
im
p
ac
t
o
f
ag
i
n
g
o
n
ca
p
ac
ity
.
W
ith
th
is
,
th
e
r
elativ
e
ca
p
ac
ity
was
ass
ess
ed
,
in
f
er
r
in
g
th
e
ex
ten
t o
f
a
g
in
g
a
n
d
d
e
g
r
ad
atio
n
th
at
o
cc
u
r
r
ed
.
T
h
e
tem
p
er
atu
r
e
d
ep
en
d
e
n
ce
o
f
r
ea
ctio
n
r
ates b
y
Ar
r
h
en
iu
s
eq
u
atio
n
ca
n
b
e
o
f
th
e
f
o
r
m
as
(
6
)
.
K
(
T
)
=
×
e
xp
(
−
)
(
6
)
Her
e,
k
(
T
)
is
th
e
r
ea
ctio
n
r
at
e
co
n
s
tan
t
at
tem
p
er
at
u
r
e,
is
th
e
p
r
e
-
ex
p
o
n
e
n
tial
f
ac
to
r
d
ep
en
d
s
o
n
c
u
r
r
e
n
t
(
a
s
s
u
m
ed
to
b
e
1
×1
0
−
6
n
m
/s
f
o
r
illu
s
tr
ativ
e
p
u
r
p
o
s
es),
is
th
e
ac
tiv
atio
n
en
er
g
y
f
o
r
c
y
clin
g
ag
in
g
(
in
J
/m
o
l
o
r
k
J
/m
o
l)
,
is
th
e
u
n
iv
e
r
s
al
g
a
s
co
n
s
tan
t (
8
.
3
1
4
J
/m
o
l
\
cd
o
t
p
K)
,
is
th
e
ab
s
o
lu
te
tem
p
e
r
atu
r
e
in
Kelv
in
.
Fo
r
in
s
tan
ce
,
th
e
g
r
o
wth
o
f
th
e
SEI
lay
er
ca
n
o
f
ten
b
e
d
escr
ib
ed
b
y
a
p
o
wer
law
o
f
th
e
f
o
r
m
as (
7
)
.
EI
thic
k
n
e
s
s
=
K
(
T
)
×
N
z
(
7
)
Her
e,
SEI
t
h
ic
k
n
ess
is
th
e
th
ic
k
n
ess
o
f
t
h
e
SEI
lay
er
(
n
an
o
m
eter
s
(
n
m
)
o
v
e
r
tim
e
an
d
cy
cle
co
u
n
t)
,
k
(
T
)
is
th
e
tem
p
er
atu
r
e
-
d
ep
en
d
en
t
r
ate
c
o
n
s
tan
t
f
r
o
m
th
e
Ar
r
h
en
iu
s
eq
u
atio
n
,
N
is
cy
cle
co
u
n
t,
z
is
th
e
p
o
wer
law
ex
p
o
n
e
n
t.
C
ap
ac
ity
lo
s
s
is
ca
lcu
lated
as
(
8
)
.
×
(1
-
K
(
T
)
×
N
z
)
(
8
)
T
h
e
p
ar
a
m
eter
v
alu
es
f
o
r
ca
p
a
city
lo
s
s
ca
lcu
latio
n
ar
e
g
iv
e
n
in
T
ab
le
3
.
T
h
e
b
atter
y
'
s
ca
p
ac
ity
h
as
d
im
in
is
h
ed
to
ar
o
u
n
d
2
0
am
p
e
r
e
-
h
o
u
r
s
(
A
h
)
af
ter
1
0
0
0
cy
cles a
s
s
h
o
wn
in
Fig
u
r
e
2
.
T
ab
le
2
.
Ag
in
g
m
ec
h
a
n
is
m
s
C
a
u
se
Ef
f
e
c
t
Le
a
d
s
t
o
En
h
a
n
c
e
d
b
y
C
o
n
t
i
n
u
o
u
s l
o
w
-
r
a
t
e
e
l
e
c
t
r
o
l
y
t
e
d
e
c
o
m
p
o
si
t
i
o
n
b
u
i
l
d
s SEI
Li
l
o
ss
,
i
mp
e
d
a
n
c
e
r
i
se
C
a
p
a
c
i
t
y
/
p
o
w
e
r
f
a
d
e
S
o
C
,
t
e
mp
e
r
a
t
u
r
e
r
i
se
S
EI
g
r
o
w
t
h
l
e
a
d
i
n
g
t
o
s
u
r
f
a
c
e
a
r
e
a
r
e
d
u
c
t
i
o
n
i
mp
e
d
a
n
c
e
r
i
se
P
o
w
e
r
f
a
d
e
S
o
C
,
t
e
mp
e
r
a
t
u
r
e
r
i
se
C
h
a
n
g
e
s
i
n
p
o
r
o
s
i
t
y
d
u
e
t
o
v
o
l
u
m
e
c
h
a
n
g
e
a
n
d
S
EI
g
r
o
w
t
h
i
mp
e
d
a
n
c
e
r
i
se
P
o
w
e
r
f
a
d
e
I
n
c
r
e
a
se
d
S
o
C
,
c
y
c
l
i
n
g
r
a
t
e
M
e
t
a
l
l
i
c
L
i
p
l
a
t
i
n
g
,
su
b
s
e
q
u
e
n
t
e
l
e
c
t
r
o
l
y
t
e
d
e
c
o
m
p
o
si
t
i
o
n
Li
t
h
i
u
m
(
e
l
e
c
t
r
o
l
y
t
e
)
l
o
ss
C
a
p
a
c
i
t
y
(
p
o
w
e
r
)
f
a
d
e
Lo
w
t
e
m
p
e
r
a
t
u
r
e
,
h
i
g
h
c
h
a
r
g
e
r
a
t
e
s
G
r
a
p
h
i
t
e
e
x
f
o
l
i
a
t
i
o
n
,
g
a
s
e
v
o
l
u
t
i
o
n
,
s
o
l
v
e
n
t
co
-
i
n
t
e
r
c
a
l
a
t
i
o
n
A
c
t
i
v
e
ma
t
e
r
i
a
l
f
a
i
l
u
r
e
,
Li
l
o
ss
C
a
p
a
c
i
t
y
f
a
d
e
O
v
e
r
c
h
a
r
g
e
C
o
n
t
a
c
t
b
/
w
p
a
r
t
i
c
l
e
s
l
o
st
d
u
e
t
o
v
o
l
u
me
c
h
a
n
g
e
s
Lo
ss
o
f
a
c
t
i
v
e
m
a
t
e
r
i
a
l
C
a
p
a
c
i
t
y
f
a
d
e
H
i
g
h
r
a
t
e
,
l
o
w
c
e
l
l
S
O
C
D
e
c
o
m
p
o
si
t
i
o
n
o
f
b
i
n
d
e
r
M
e
c
h
a
n
i
c
a
l
s
t
a
b
i
l
i
t
y
d
e
f
i
c
i
t
,
Li
d
e
f
i
c
i
t
C
a
p
a
c
i
t
y
f
a
d
e
S
o
C
,
t
e
mp
e
r
a
t
u
r
e
r
i
se
G
r
a
p
h
i
t
e
e
x
f
o
l
i
a
t
i
o
n
,
g
a
s
e
v
o
l
u
t
i
o
n
,
s
o
l
v
e
n
t
co
-
i
n
t
e
r
c
a
l
a
t
i
o
n
Li
l
o
ss
,
a
c
t
i
v
e
m
a
t
e
r
i
a
l
d
e
f
i
c
i
t
C
a
p
a
c
i
t
y
f
a
d
e
O
v
e
r
c
h
a
r
g
e
P
h
a
se
t
r
a
n
s
i
t
i
o
n
s
C
r
a
c
k
i
n
g
o
f
a
c
t
i
v
e
p
a
r
t
i
c
l
e
s
C
a
p
a
c
i
t
y
f
a
d
e
H
i
g
h
r
a
t
e
s,
h
i
g
h
/
l
o
w
S
O
C
S
t
r
u
c
t
u
r
a
l
d
i
so
r
d
e
r
i
n
g
Li
s
i
t
e
s l
o
s
t
a
n
d
L
i
t
r
a
p
p
e
d
C
a
p
a
c
i
t
y
f
a
d
e
H
i
g
h
r
a
t
e
s,
h
i
g
h
/
l
o
w
S
O
C
M
e
t
a
l
d
i
ss
o
l
u
t
i
o
n
a
n
d
/
o
r
e
l
e
c
t
r
o
l
y
t
e
M
i
g
r
a
t
i
o
n
o
f
so
l
u
b
l
e
s
p
e
c
i
e
s
C
a
p
a
c
i
t
y
f
a
d
e
H
i
g
h
/
l
o
w
S
O
C
,
h
i
g
h
t
e
m
p
e
r
a
t
u
r
e
D
e
c
o
m
p
o
si
t
i
o
n
R
e
p
r
e
c
i
p
i
t
a
t
i
o
n
o
f
n
e
w
p
h
a
s
e
s,
f
o
r
m
su
r
f
a
c
e
l
a
y
e
r
P
o
w
e
r
f
a
d
e
El
e
c
t
r
o
l
y
t
e
d
e
c
o
m
p
o
si
t
i
o
n
G
a
s e
v
o
l
u
t
i
o
n
H
i
g
h
t
e
m
p
e
r
a
t
u
r
e
B
i
n
d
e
r
d
e
c
o
m
p
o
si
t
i
o
n
,
o
x
i
d
a
t
i
o
n
o
f
c
o
n
d
u
c
t
i
v
e
a
g
e
n
t
C
o
n
n
e
c
t
i
v
i
t
y
l
o
ss
P
o
w
e
r
f
a
d
e
C
o
r
r
o
si
o
n
o
f
c
u
r
r
e
n
t
c
o
l
l
e
c
t
o
r
C
o
n
n
e
c
t
i
v
i
t
y
l
o
ss
P
o
w
e
r
f
a
d
e
H
i
g
h
S
O
C
T
ab
le
3
.
Par
am
eter
v
alu
es f
o
r
ca
p
ac
ity
d
eg
r
a
d
atio
n
m
o
d
el
A
E
a
/R
z
0
.
3
6
8
7
1
4
7
2
0
.
6
4
0
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f CK
F
a
lg
o
r
ith
m
fo
r
b
a
tter
y
S
o
C
esti
ma
tio
n
w
ith
its
a
g
in
g
effec
t
(
G
.
Gee
th
a
R
a
v
a
li
)
891
Fig
u
r
e
2
.
Deg
r
ad
atio
n
in
ca
p
a
city
o
b
s
er
v
ed
in
a
L
i
-
io
n
ce
ll a
f
ter
u
n
d
er
g
o
i
n
g
1
0
0
0
cy
cles
3.
M
E
T
H
O
DO
L
O
G
Y
E
v
er
y
a
p
p
r
o
ac
h
im
p
lem
en
ts
a
d
if
f
er
en
t
m
eth
o
d
o
lo
g
y
to
ev
al
u
ate
th
e
So
C
p
er
f
o
r
m
a
n
ce
.
Alt
er
n
ativ
e
to
th
e
co
n
v
en
tio
n
al
a
p
p
r
o
ac
h
es
d
i
s
cu
s
s
ed
,
KF
m
ak
es
it
a
to
p
c
h
o
i
ce
f
o
r
r
ea
l
-
tim
e
s
tate
esti
m
atio
n
f
o
r
its
o
p
tim
ality
,
ad
ap
tab
ilit
y
,
ef
f
icien
cy
,
r
o
b
u
s
tn
ess
,
v
er
s
atility
,
ab
ilit
y
to
h
a
n
d
le
s
en
s
o
r
d
ata,
an
d
well
-
estab
lis
h
ed
m
ath
em
atica
l
th
eo
r
y
.
KF
is
a
s
p
ec
ial
ca
s
e
o
f
s
eq
u
en
tial
p
r
o
b
ab
ilis
tic
in
f
er
en
ce
,
y
ield
in
g
an
o
p
tim
al
s
tate
esti
m
ate
th
r
o
u
g
h
t
h
e
m
in
im
u
m
m
ea
n
-
s
q
u
a
r
ed
er
r
o
r
ap
p
r
o
ac
h
.
Ho
wev
er
,
its
r
elia
n
ce
o
n
a
Gau
s
s
ian
d
is
tr
ib
u
tio
n
ass
u
m
p
tio
n
p
o
s
ed
ch
allen
g
es
wh
en
co
n
f
r
o
n
te
d
with
n
o
n
-
Gau
s
s
ian
d
is
tr
ib
u
tio
n
s
,
a
co
m
m
o
n
o
cc
u
r
r
e
n
ce
in
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
[
4
8
]
.
As
b
atter
ies
wer
e
s
u
b
ject
ed
to
non
-
lin
ea
r
c
h
ar
ac
ter
is
tics
,
it
was
cr
itical
f
o
r
m
o
d
els
r
ela
tin
g
to
t
h
em
to
also
b
e
o
f
a
n
o
n
-
lin
ea
r
n
atu
r
e.
A
n
o
n
-
lin
ea
r
r
elatio
n
s
h
ip
b
etwe
e
n
th
e
So
C
an
d
r
esu
ltan
t
v
o
lta
g
e
was
o
b
s
er
v
ed
in
r
ec
h
ar
g
ea
b
le
b
atter
ies,
r
en
d
er
i
n
g
th
e
en
tire
p
r
o
p
ag
atio
n
p
o
te
n
tially
in
co
m
p
atib
le
with
a
Gau
s
s
ian
en
v
ir
o
n
m
en
t.
3
.
1
.
No
n
-
lin
ea
r
K
F
t
ec
hn
iqu
es
Un
lik
e
lin
ea
r
Kalm
an
f
ilter
s
,
wh
ich
we
r
e
s
p
ec
if
ically
d
esig
n
ed
f
o
r
lin
ea
r
s
y
s
tem
s
,
n
o
n
-
lin
ea
r
Kalm
an
f
ilter
s
,
we
r
e
m
o
r
e
f
lex
ib
le
a
n
d
ca
p
ab
le
o
f
ac
c
o
m
m
o
d
atin
g
n
o
n
-
lin
ea
r
r
elatio
n
s
h
ip
s
[
4
9
]
.
I
n
t
h
e
p
r
esen
ce
o
f
n
o
n
-
lin
ea
r
ities
,
th
ese
f
ilter
s
co
n
tr
i
b
u
te
d
to
en
h
a
n
cin
g
th
e
p
er
f
o
r
m
an
ce
an
d
r
eliab
ilit
y
o
f
B
MS
.
Dif
f
er
en
t
n
o
n
-
lin
ea
r
v
ar
ian
ts
f
o
r
s
tate
esti
m
atio
n
w
er
e
ap
p
lied
to
th
e
d
e
v
elo
p
e
d
b
atter
y
m
o
d
el
with
its
ag
in
g
af
f
ec
t.
3
.
1
.
1
.
E
x
t
ended K
F
E
x
ten
d
ed
Kalm
an
f
ilter
(
E
KF
)
,
an
an
aly
tical
lin
ea
r
izatio
n
o
f
th
e
s
y
s
tem
m
o
d
el
u
n
d
er
ev
er
y
tim
e
in
s
tan
ce
.
Similar
to
KF,
E
KF
f
o
llo
wed
t
h
e
s
am
e
wo
r
k
in
g
p
r
in
cip
le
b
u
t
em
p
lo
y
ed
a
lin
e
ar
izatio
n
ap
p
r
o
ac
h
,
o
p
er
atin
g
th
r
o
u
g
h
a
two
-
s
tep
esti
m
atio
n
p
r
o
ce
s
s
s
h
o
wn
in
Fig
u
r
e
3
.
Gen
er
alizin
g
th
e
n
o
n
lin
ea
r
ca
s
e
with
s
y
s
tem
d
y
n
am
ics
:
=
(
−
1
,
−
1
,
−
1
)
(
9
)
=
ℎ
(
,
,
)
(
1
0
)
e
s
tim
ato
r
p
r
o
v
id
es
an
o
u
tp
u
t
s
tate
esti
m
ate
̂
+
,
er
r
o
r
co
v
ar
ia
n
c
e
esti
m
ate
∑
̃
,
+
,
h
o
we
v
er
,
ex
is
ts
h
ig
h
ce
r
tain
ty
th
at
th
e
tr
u
e
v
alu
e
f
alls
with
in
̂
+
±
3
√
dia
g
(
∑
̃
,
+
)
(
b
o
u
n
d
s
)
a
n
d
e
x
p
ec
tin
g
u
n
t
il
s
u
b
s
eq
u
en
t
in
ter
v
al
co
m
es,
u
p
d
atin
g
k
an
d
p
r
o
ce
ed
in
g
to
s
tate
p
r
ed
ictio
n
s
tep
.
Hen
ce
,
t
h
is
d
em
o
n
s
tr
ates
a
r
ec
u
r
s
iv
e
p
r
o
ce
s
s
.
3.
1
.2
.
Cent
ra
l dif
f
er
ence
K
F
C
en
tr
al
d
if
f
er
e
n
ce
Kalm
an
f
ilt
er
(
C
DKF
)
,
a
s
tatis
tical
o
r
e
m
p
ir
ical
lin
ea
r
izatio
n
o
f
th
e
s
y
s
tem
m
o
d
el
f
o
r
e
v
er
y
tim
e
in
s
tan
ce
.
Giv
en
an
i
n
p
u
t
r
an
d
o
m
v
ar
iab
le
x
∈
R^
n
an
d
x
~
(
μ
,
∑),
w
h
er
e
μ
o
r
x
̅
o
r
X₀
r
e
p
r
esen
ts
th
e
m
ea
n
an
d
∑ is
th
e
co
v
a
r
ia
n
ce
,
th
e
g
e
n
er
atio
n
o
f
p
+
1
=
2
n
+
1
(
with
n
b
ein
g
t
h
e
s
y
s
tem
d
im
en
s
io
n
)
s
ig
m
a
p
o
in
ts
en
tail th
e
cr
ea
tio
n
o
f
a
m
atr
ix
with
a
s
p
ec
if
ied
ess
en
tial.
C
en
tr
al
d
if
f
er
en
ce
tr
an
s
f
o
r
m
atio
n
:
x
̅
or
X
0
=
X
̂
(
k
|
k
)
(
1
1
)
f
o
r
i=1
,
.
.
.
,
n
X
i
(
k
|
k
)
=
(
X
0
+
γ
√
∑
x
̃
)
i
(
12)
f
o
r
i=n
+1
,
.
.
.
,
2
n
X
i
(
k
|
k
)
=
(
X
0
−
γ
√
∑
x
̃
)
i
−
n
(
13)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dece
m
b
er
20
2
4
:
8
8
6
-
899
892
w
h
er
e,
X
̂
(
k
|
k
)
is
a
v
ec
to
r
o
f
len
g
th
n
f
o
r
wh
ich
th
e
s
ig
m
a
p
o
in
ts
ar
e
co
m
p
u
ted
,
∑
x
̃
is
its
co
v
ar
ian
ce
m
atr
ix
an
d
an
d
a
r
e
w
e
i
g
h
ts
ass
o
c
i
a
te
d
w
ith
t
h
e
s
i
g
m
a
p
o
i
n
t
s
f
o
r
e
s
t
i
m
a
ti
n
g
t
h
e
m
e
a
n
v
e
c
t
o
r
s
a
n
d
c
o
v
a
r
i
an
c
e
m
a
t
r
i
c
es
,
r
e
s
p
e
c
t
i
v
el
y
.
(
γ
√
∑
x
̃
)
i
s
t
h
e
i
th
c
o
l
u
m
n
o
f
t
h
e
m
a
t
r
i
x
s
q
u
a
r
e
r
o
o
t
,
e
.
g
.
,
lo
w
e
r
t
r
i
a
n
g
u
l
a
r
C
h
o
l
e
s
k
y
f
a
ct
o
r
i
z
a
t
i
o
n
.
Valu
es in
weig
h
ts
u
s
ed
b
y
C
DKF
ar
e
(
1
4
)
-
(
1
7
)
.
γ
=
h
(
1
4
)
w
0
(
m
)
=
h
2
−
n
h
2
(
1
5
)
w
0
(
c
)
=
h
2
−
n
h
2
(
1
6
)
f
o
r
i=1
,
.
.
.
,
n
w
i
(
c
)
=
w
i
(
m
)
=
1
2
h
2
(
17)
T
h
u
s
,
th
e
en
s
em
b
le
o
f
s
ig
m
a
p
o
in
ts
is
p
r
o
d
u
ce
d
as o
u
tlin
ed
(
1
8
)
.
=
{
0
,
(
0
+
√
∑
̃
)
,
(
0
−
√
∑
̃
)
}
(1
8
)
̂
(
|
)
is
co
m
p
u
ted
f
r
o
m
th
e
s
ig
m
a
p
o
in
ts
g
en
er
ate
d
,
∑
̃
is
co
v
ar
ian
ce
,
an
d
weig
h
ts
r
elate
d
to
m
ea
n
an
d
co
v
ar
ian
ce
a
r
e
,
.
√
∑
̃
g
iv
es
th
e
f
ac
to
r
izatio
n
u
n
d
er
th
e
l
o
wer
-
tr
ia
n
g
u
lar
-
C
h
o
lesk
y
d
iv
is
io
n
.
Her
e
h
=
√3
;
tu
n
in
g
p
ar
am
eter
.
Fig
u
r
e
3
.
I
m
p
lem
en
tatio
n
f
lo
w
ch
ar
t o
f
KF,
E
KF a
lg
o
r
ith
m
3.
1
.
3
.
Uns
ce
nte
d/S
ig
m
a
po
in
t
K
F
U
n
s
ce
n
ted
K
alm
an
f
ilter
(
UK
F
)
/
s
ig
m
a
p
o
in
t
K
alm
an
f
ilter
(
SP
KF
)
,
a
s
tatis
tical
lin
ea
r
izati
o
n
s
y
s
tem
.
Sig
m
a
p
o
in
t
s
(
a
d
eter
m
in
is
tic
s
am
p
le
p
o
in
ts
)
wer
e
ch
o
s
en
to
p
r
ec
is
ely
esti
m
ate
th
e
s
tatis
t
ic
s
o
f
th
e
p
r
o
p
ag
atin
g
m
eth
o
d
.
Un
s
ce
n
te
d
tr
an
s
f
o
r
m
atio
n
:
X
0
=
X
̂
(
k
|
k
)
(
1
9
)
f
o
r
i=1
,
.
.
.
,
n
X
i
(
k
|
k
)
=
(
X
0
+
γ
√
∑
x
̃
)
i
(
20)
f
o
r
i=n
+1
,
.
.
.
,
2
n
X
i
(
k
|
k
)
=
(
X
0
−
γ
√
∑
x
̃
)
i
−
n
(
21)
w
h
er
e,
X
̂
(
k
|
k
)
is
a
v
ec
to
r
o
f
len
g
th
n
f
o
r
wh
ich
th
e
s
ig
m
a
p
o
in
ts
ar
e
co
m
p
u
ted
,
∑
x
̃
is
its
co
v
ar
ian
ce
m
atr
ix
an
d
an
d
ar
e
weig
h
ts
ass
o
ciate
d
with
th
e
s
ig
m
a
p
o
i
n
ts
f
o
r
est
im
atin
g
th
e
m
ea
n
v
ec
to
r
s
an
d
co
v
ar
ia
n
ce
m
atr
ices,
r
esp
ec
tiv
ely
.
(
√
(
n
+
λ
)
(
∑
x
̃
)
is
th
e
i
th
co
lu
m
n
o
f
th
e
m
atr
i
x
s
q
u
ar
e
r
o
o
t,
e.
g
.
,
lo
wer
tr
ian
g
u
lar
C
h
o
lesk
y
f
ac
to
r
izatio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f CK
F
a
lg
o
r
ith
m
fo
r
b
a
tter
y
S
o
C
esti
ma
tio
n
w
ith
its
a
g
in
g
effec
t
(
G
.
Gee
th
a
R
a
v
a
li
)
893
W
eig
h
t v
alu
es f
o
r
UKF/SP
KF
ar
e
(
2
2
)
-
(
2
5
)
.
γ
=
√
n
+
λ
(
2
2
)
w
0
(
m
)
=
λ
n
+
λ
(
2
3
)
w
0
(
c
)
=
λ
(
n
+
λ
)
+
(
1
−
α
2
+
β
)
(
2
4
)
f
o
r
i=1
,
.
.
.
,
n
w
i
(
c
)
=
w
i
(
m
)
=
1
2
(
n
+
λ
)
(
25)
W
h
e
r
e
,
=
2
(
+
)
−
,
wi
th
in
t
h
e
r
an
g
e
o
f
(
10
−
2
≤
≤
1
)
a
n
d
{
0
,
3
,
−
}
.
I
n
th
e
g
i
v
e
n
c
o
n
te
x
t
,
λ
s
er
v
es
as
t
h
e
s
ca
l
in
g
p
a
r
a
m
et
e
r
,
k
r
e
p
r
ese
n
ts
s
e
c
o
n
d
a
r
y
s
ca
li
n
g
p
ar
am
ete
r
,
a
n
d
t
o
i
n
t
eg
r
a
te
p
r
e
ce
d
i
n
g
r
e
ali
za
t
io
n
r
e
g
a
r
d
i
n
g
th
e
x
p
r
o
p
ag
ati
o
n
,
β
w
as
em
p
l
o
y
e
d
.
A
d
d
iti
o
n
all
y
,
α
p
la
y
s
a
c
r
u
ci
al
r
o
le
i
n
d
et
er
m
i
n
i
n
g
p
r
o
p
ag
ati
o
n
ar
o
u
n
d
t
h
e
m
ea
n
x
̄
(
t
y
p
i
ca
ll
y
a
r
o
u
n
d
1
e
-
3
)
.
I
n
g
en
er
al
,
k
a
n
d
β
wer
e
u
s
u
al
ly
c
h
o
s
e
n
as
0
a
n
d
2
r
esp
ec
t
iv
el
y
.
T
h
e
p
a
r
a
m
e
te
r
s
f
o
r
t
u
n
i
n
g
t
h
e
Ga
u
s
s
ian
p
r
o
b
a
b
ili
ty
d
e
n
s
it
y
f
u
n
ct
io
n
w
er
e
s
e
lec
te
d
as
f
o
l
lo
ws:
β=2
,
α
=
0
.
0
0
1
,
a
n
d
k
=
0
.
Fi
g
u
r
e
4
i
ll
u
s
tr
at
es
t
h
e
f
l
o
w
d
ia
g
r
am
o
f
C
DFK
,
UKF/
SP
KF
a
lg
o
r
it
h
m
.
B
y
i
n
co
r
p
o
r
ati
n
g
t
h
e
w
ei
g
h
ts
as
{
,
(
)
,
(
)
}
;
(
)
,
(
)
p
o
s
s
ess
r
ea
l s
ca
l
ar
q
u
a
n
tit
ies
,
w
ei
g
h
te
d
m
o
m
e
n
ts
we
r
e
c
o
m
p
u
te
d
as
(
2
6
)
a
n
d
(
2
7
)
.
0
=
∑
(
)
2
=
0
(
2
6
)
an
d
∑
̃
=
∑
(
)
(
−
̅
)
(
−
̅
)
2
=
0
(
2
7
)
F
o
l
l
o
w
e
d
b
y
t
h
e
p
r
o
p
a
g
a
t
i
o
n
o
v
e
r
s
i
g
m
a
p
o
i
n
t
s
t
h
r
o
u
g
h
t
h
e
f
u
n
c
t
i
o
n
o
f
n
o
n
l
i
n
e
a
r
i
t
y
,
w
h
e
r
e
in
t
r
a
n
s
f
o
r
m
e
d
s
e
t
o
f
s
i
g
m
a
p
o
i
n
ts
a
s
Ỿ
is
o
b
t
a
i
n
e
d
.
T
h
e
n
,
c
o
m
p
u
t
i
n
g
o
u
t
p
u
t
f
i
r
s
t
s
ta
t
i
s
t
i
c
al
m
o
m
e
n
t
s
o
f
Ỿ
t
r
a
n
s
f
o
r
m
e
d
p
o
i
n
t
s
as
s
ta
t
e
d
:
Ỿ
=
(
)
(
2
8
)
0
=
∑
(
)
Ỿ
2
=
0
(
2
9
)
an
d
∑
̃
=
∑
(
)
(
Ỿ
−
̅
)
(
Ỿ
−
̅
)
2
=
0
(
3
0
)
So
m
e
o
f
t
h
e
th
eo
r
etica
l
d
if
f
e
r
en
ce
s
in
th
e
f
u
n
ctio
n
al
p
r
o
ce
s
s
o
f
NKFs
wer
e
s
u
m
m
ar
ized
in
T
ab
le
4
.
Desp
ite
lim
itatio
n
s
,
E
KF
was
s
en
s
itiv
e
to
th
e
ch
o
ice
o
f
in
itial
co
n
d
itio
n
s
,
an
d
i
n
co
r
r
ec
t
in
itializatio
n
o
r
p
o
o
r
o
b
s
er
v
ab
ilit
y
c
o
u
ld
lead
t
o
c
o
n
v
er
g
e
n
ce
is
s
u
es,
p
o
te
n
tially
d
iv
er
g
in
g
o
r
c
o
n
v
er
g
in
g
to
a
lo
ca
l
m
in
im
u
m
.
I
n
co
n
tr
ast,
UKF's
ef
f
ec
tiv
en
ess
r
eli
ed
o
n
th
e
p
r
o
p
er
p
lace
m
en
t
o
f
s
ig
m
a
p
o
in
ts
,
an
d
as
t
h
e
s
tate
d
im
en
s
io
n
in
cr
ea
s
ed
,
th
e
g
r
o
win
g
n
u
m
b
er
o
f
s
ig
m
a
p
o
in
ts
co
u
ld
im
p
ac
t
ef
f
icien
cy
.
Alth
o
u
g
h
U
KF
av
o
id
ed
E
KF'
s
lin
ea
r
izatio
n
er
r
o
r
s
,
th
e
c
h
o
ic
e
o
f
s
ig
m
a
p
o
in
ts
i
n
tr
o
d
u
ce
d
ap
p
r
o
x
im
atio
n
er
r
o
r
s
,
lead
i
n
g
to
i
n
ac
cu
r
ac
ies
i
n
ce
r
tain
s
ce
n
ar
io
s
.
C
o
n
s
eq
u
en
tly
,
th
e
aim
was
to
ad
d
r
ess
s
o
m
e
o
f
th
e
lim
itatio
n
s
as
s
o
ciate
d
w
ith
o
th
er
ad
v
an
ce
d
NKF.
T
h
u
s
,
p
r
o
p
o
s
ed
c
u
b
atu
r
e
KF a
s
a
r
o
b
u
s
t e
s
tim
ato
r
f
o
r
So
C
esti
m
atio
n
.
3.
1
.4
.
Cuba
t
ure
K
F
:
pro
po
s
ed
ro
bu
s
t
s
t
a
t
e
-
estim
a
t
o
r
C
KF
,
a
B
ay
esian
f
ilter
in
g
alg
o
r
ith
m
d
esig
n
e
d
f
o
r
n
o
n
lin
ea
r
s
y
s
tem
s
.
C
KF
em
p
lo
y
ed
a
cu
b
atu
r
e
r
u
le
,
in
s
tead
o
f
lin
ea
r
izatio
n
,
f
o
r
ac
cu
r
ate
p
r
o
p
ag
atio
n
o
f
th
e
s
y
s
tem
'
s
co
v
ar
ian
ce
.
T
h
e
co
m
p
u
tatio
n
al
b
u
r
d
e
n
ass
o
ciate
d
with
C
KF
was
co
m
p
ar
ativ
ely
lig
h
ter
s
in
ce
it
e
m
p
lo
y
ed
o
n
ly
2
n
cu
b
atu
r
e
p
o
in
ts
(
wh
er
e
n
is
t
h
e
s
y
s
tem
d
im
en
s
io
n
)
,
wh
ile
UKF
u
tili
ze
d
2
n
+1
s
ig
m
a
p
o
in
t
s
f
o
r
s
tate
an
d
co
v
ar
ia
n
ce
p
r
o
p
ag
atio
n
.
C
u
b
atu
r
e
tr
an
s
f
o
r
m
atio
n
:
f
o
r
i=1
,
.
.
.
,
n
X
i
(
k
|
k
)
=
(
X
0
+
γ
√
∑
x
̃
)
i
(
31
)
f
o
r
i=n
+1
,
.
.
.
,
2
n
X
i
(
k
|
k
)
=
(
X
0
−
γ
√
∑
x
̃
)
i
−
n
(
32)
f
o
r
i=1
,
.
.
.
,
n
w
i
=
1
2n
(
3
3
)
I
n
th
is
c
o
n
tex
t,
Q(
k
)
an
d
R
(
k
)
r
ep
r
esen
ted
th
e
m
atr
ices
o
f
co
v
a
r
ian
ce
f
o
r
p
r
o
ce
s
s
an
d
s
en
s
o
r
n
o
is
es,
r
esp
ec
tiv
ely
.
Utilizin
g
th
e
wei
g
h
ted
esti
m
ated
co
v
ar
ian
ce
m
atr
ix
,
b
o
t
h
UKF
an
d
C
KF
co
n
v
er
s
io
n
s
g
en
er
ate
d
s
am
p
le
in
d
icate
s
.
No
tab
ly
,
f
o
r
C
KF,
all
p
o
in
ts
,
in
c
lu
d
in
g
th
e
ce
n
ter
p
o
i
n
t,
wer
e
ass
ig
n
ed
eq
u
al
weig
h
t,
r
esu
ltin
g
in
a
to
tal
o
f
2
n
p
o
in
ts
u
s
ed
.
T
h
is
u
n
if
o
r
m
weig
h
tin
g
s
im
p
lifie
d
th
e
s
ig
m
a
p
o
in
ts
an
d
co
v
ar
ia
n
ce
ca
lcu
latio
n
s
in
C
KF,
en
s
u
r
in
g
a
co
n
s
is
ten
t
tr
ea
tm
en
t
ac
r
o
s
s
all
p
o
in
ts
.
C
K
F
d
o
es
n
o
t
in
v
o
lv
e
as
m
an
y
tu
n
in
g
p
a
r
am
eter
s
as
UKF.
T
h
e
s
elec
tio
n
o
f
cu
b
atu
r
e
p
o
in
ts
is
o
f
ten
s
tr
aig
h
tf
o
r
war
d
,
m
a
k
in
g
C
KF
a
m
o
r
e
p
a
r
am
e
ter
-
f
r
ee
alter
n
ativ
e,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dece
m
b
er
20
2
4
:
8
8
6
-
899
894
s
im
p
lify
in
g
th
e
im
p
lem
en
tatio
n
,
an
d
r
ed
u
cin
g
th
e
n
ee
d
f
o
r
p
ar
am
eter
tu
n
in
g
.
Fig
u
r
e
5
g
iv
e
s
th
e
f
lo
w
d
iag
r
am
o
f
C
KF a
lg
o
r
ith
m
.
Fig
u
r
e
4
.
Flo
w
d
ia
g
r
am
o
f
C
DKF
an
d
UKF/SP
K
F a
lg
o
r
ith
m
T
ab
le
4
.
T
h
eo
r
etica
l c
o
m
p
ar
i
s
o
n
o
f
n
o
n
-
lin
ea
r
KFs
f
o
r
esti
m
atin
g
So
C
S
y
st
e
m
A
p
p
l
i
c
a
b
i
l
i
t
y
A
ssu
mp
t
i
o
n
s
Li
mi
t
a
t
i
o
n
s
C
o
m
p
u
t
a
t
i
o
n
a
l
C
o
m
p
l
e
x
i
t
y
R
a
t
e
o
f
e
st
i
mat
e
EK
F
M
o
d
e
r
a
t
e
n
o
n
l
i
n
e
a
r
sy
st
e
ms
,
G
a
u
s
si
a
n
Ta
y
l
o
r
-
s
e
r
i
e
s
e
x
p
a
n
si
o
n
t
o
l
i
n
e
a
r
i
z
e
s
y
st
e
m
e
q
u
a
t
i
o
n
s
f
o
r
c
o
v
a
r
i
a
n
c
e
s
Li
n
e
a
r
i
z
e
s
t
h
e
sy
s
t
e
m
a
t
e
a
c
h
st
e
p
,
ma
y
l
e
a
d
t
o
i
n
a
c
c
u
r
a
c
i
e
s
i
n
h
i
g
h
l
y
n
o
n
l
i
n
e
a
r
sy
s
t
e
ms
M
o
d
e
r
a
t
e
H
i
g
h
C
D
K
F
/
U
K
F
/
S
P
K
F
H
i
g
h
l
y
n
o
n
l
i
n
e
a
r
sy
st
e
ms
,
G
a
u
s
si
a
n
2
n
+
1
s
i
g
ma
p
o
i
n
t
s
,
a
v
o
i
d
s
l
i
n
e
a
r
i
z
a
t
i
o
n
u
si
n
g
c
a
r
e
f
u
l
l
y
c
h
o
s
e
n
si
g
ma
p
o
i
n
t
s
R
e
q
u
i
r
e
s
t
u
n
i
n
g
o
f
sc
a
l
i
n
g
p
a
r
a
m
e
t
e
r
s,
i
n
c
r
e
a
se
d
c
o
m
p
u
t
a
t
i
o
n
a
l
c
o
m
p
l
e
x
i
t
y
c
o
m
p
a
r
e
d
t
o
E
K
F
M
o
d
e
r
a
t
e
t
o
h
i
g
h
H
i
g
h
C
K
F
H
i
g
h
l
y
n
o
n
l
i
n
e
a
r
,
n
o
n
-
g
a
u
ssi
a
n
2
n
c
u
b
a
t
u
r
e
p
o
i
n
t
s
,
u
t
i
l
i
z
e
s
d
e
t
e
r
mi
n
i
st
i
c
c
u
b
a
t
u
r
e
samp
l
i
n
g
t
e
c
h
n
i
q
u
e
C
a
n
b
e
c
o
m
p
u
t
a
t
i
o
n
a
l
l
y
i
n
t
e
n
si
v
e
,
e
s
p
e
c
i
a
l
l
y
i
n
h
i
g
h
-
d
i
m
e
n
s
i
o
n
a
l
s
t
a
t
e
sp
a
c
e
s
H
i
g
h
V
e
r
y
h
i
g
h
Fig
u
r
e
5
.
Flo
w
d
ia
g
r
am
o
f
C
KF a
lg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f CK
F
a
lg
o
r
ith
m
fo
r
b
a
tter
y
S
o
C
esti
ma
tio
n
w
ith
its
a
g
in
g
effec
t
(
G
.
Gee
th
a
R
a
v
a
li
)
895
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
Usi
n
g
th
e
d
ev
elo
p
ed
b
atter
y
m
o
d
el
in
clu
d
in
g
a
g
in
g
ef
f
ec
t,
th
ese
f
ilter
in
g
tech
n
i
q
u
es
ar
e
im
p
lem
en
ted
an
d
s
im
u
lated
in
Octa
v
e/M
A
T
L
AB
s
o
f
twar
e.
B
ased
o
n
t
h
e
m
etr
ics
:
r
o
o
t
m
ea
n
s
q
u
ar
e
e
r
r
o
r
,
m
ea
n
ab
s
o
l
u
te
er
r
o
r
,
an
d
m
ax
im
u
m
er
r
o
r
,
th
e
p
er
f
o
r
m
an
ce
is
ass
ess
ed
.
L
et
N
b
e
th
e
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
,
̂
[
]
b
e
th
e
esti
m
ated
b
atter
y
s
tate
,
an
d
[
]
b
e
th
e
tr
u
e
(
ac
t
u
al)
b
atter
y
s
tate.
R
o
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
is
a
m
ea
s
u
r
e
o
f
th
e
av
er
a
g
e
m
ag
n
itu
d
e
o
f
th
e
er
r
o
r
s
b
etwe
e
n
p
r
ed
icted
v
alu
es a
n
d
ac
tu
al
v
alu
es in
a
d
ataset.
R
MS
=
√
1
∑
(
[
]
−
̂
[
]
)
2
=
1
(
34
)
M
ax
im
u
m
er
r
o
r
(
MA
X
)
r
ep
r
e
s
en
ts
th
e
m
ax
im
u
m
d
ev
iatio
n
o
r
d
if
f
er
e
n
ce
b
etwe
en
p
r
e
d
icted
v
alu
es
an
d
ac
tu
al
v
alu
es in
a
d
ataset.
MA
E
=
1
∑
|
[
]
−
̂
[
]
|
=
1
,
an
d
(
35
)
M
ea
n
ab
s
o
lu
te
er
r
o
r
(
MA
E
)
is
a
m
ea
s
u
r
e
o
f
th
e
a
v
er
ag
e
m
ag
n
itu
d
e
o
f
th
e
er
r
o
r
s
b
etwe
en
p
r
ed
icted
v
alu
es a
n
d
ac
tu
al
v
alu
es in
a
d
ataset.
Un
li
k
e
R
MSE
,
MA
E
d
o
es n
o
t sq
u
ar
e
th
e
er
r
o
r
s
,
m
ak
in
g
it less
s
en
s
itiv
e
to
o
u
tlier
s
.
MA
X
=
ma
x
|
[
]
−
̂
[
]
|
(
36
)
Fig
u
r
e
s
6
an
d
7
in
d
icate
th
e
esti
m
atio
n
an
aly
s
is
f
o
r
ex
ten
d
ed
E
KF
an
d
C
DKF
alg
o
r
i
th
m
s
.
T
h
e
r
ep
r
esen
tatio
n
in
clu
d
es
a
b
lac
k
s
o
lid
lin
e
d
e
n
o
tin
g
th
e
esti
m
ate,
a
g
r
ee
n
s
o
lid
lin
e
illu
s
tr
atin
g
th
e
tr
u
e
So
C
v
er
s
u
s
tim
e,
an
d
r
ed
lin
es
in
d
ic
atin
g
th
e
So
C
b
o
u
n
d
s
.
T
h
e
ca
l
cu
latio
n
o
f
er
r
o
r
v
er
s
u
s
tim
e
in
v
o
lv
es
d
eter
m
i
n
in
g
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
tr
u
e
v
alu
e
an
d
th
e
esti
m
ate,
co
n
s
i
d
er
in
g
its
b
o
u
n
d
s
.
T
o
m
ain
tain
a
f
air
co
m
p
ar
is
o
n
,
an
id
en
tical
r
an
d
o
m
in
p
u
t
is
ap
p
lied
to
b
o
th
f
ilter
s
.
E
KF
a
n
d
C
DKF
alg
o
r
ith
m
s
'
r
esu
lt
s
in
d
icate
th
at
er
r
o
r
s
s
u
r
p
ass
th
e
b
o
u
n
d
s
in
E
KF
(
R
MSE
:
0
.
4
2
3
0
8
%)
b
u
t
s
tay
with
in
b
o
u
n
d
s
in
C
DKF
(
R
MSE
:
0
.
5
1
5
4
3
%)
f
o
r
th
e
ex
ec
u
ted
iter
atio
n
s
.
Fig
u
r
e
8
in
d
icate
s
th
e
esti
m
atio
n
an
aly
s
is
f
o
r
UKF/SP
KF
alg
o
r
ith
m
.
Up
o
n
e
x
am
in
at
io
n
o
f
th
e
v
is
u
aliza
tio
n
,
a
clea
r
u
n
d
er
s
tan
d
in
g
o
f
th
e
er
r
o
r
m
ag
n
itu
d
e
i
n
co
m
p
ar
is
o
n
t
o
th
e
tr
u
e
So
C
em
er
g
es
with
R
MSE
o
f
0
.
5
7
1
9
9
%
,
h
ig
h
li
g
h
tin
g
th
e
ef
f
ec
tiv
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
SP
KF.
D
u
e
t
o
t
h
e
i
n
c
r
ea
s
e
d
n
u
m
b
e
r
o
f
s
i
g
m
a
p
o
i
n
ts
,
a
c
o
m
p
u
t
a
t
i
o
n
a
l
b
u
r
d
e
n
o
c
c
u
r
r
e
d
,
a
l
o
n
g
w
i
t
h
t
u
n
i
n
g
c
h
a
l
l
e
n
g
es
f
o
r
t
h
e
p
a
r
a
m
e
t
e
r
s
,
m
a
k
i
n
g
t
h
e
f
i
l
t
e
r
l
es
s
e
f
f
i
c
i
e
n
t
.
(
a)
(
b
)
Fig
u
r
e
6
.
E
KF a
lg
o
r
ith
m
r
esu
l
ts
f
o
r
(
a)
So
C
esti
m
atio
n
an
d
(
b
)
So
C
esti
m
atio
n
er
r
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.