TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 2, Februa
ry 20
15, pp. 292 ~ 299
DOI: 10.115
9
1
/telkomni
ka.
v
13i2.687
6
292
Re
cei
v
ed O
c
t
ober 2
0
, 201
4; Revi
se
d Novem
b
e
r
19, 2014; Accept
ed De
cem
b
e
r
12, 2014
Robust SINS/GNSS Integration Method for High
Dynamic Applications
Falin Wu
1
, Heng
y
a
ng Zhao
1
*, Yan Zhao
1
, Haibo Z
hong
2
1
School of Instrumentati
on Sci
ence a
nd Opto
-e
lectro
nics En
gin
eeri
ng, Bei
h
ang U
n
ivers
i
t
y
,
Beiji
ng 1
0
0
191
, China
2
Space Star T
e
chno
log
y
C
o
. L
t
d, Beijin
g, 100
086, Ch
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: heng
ya
n
g17
8@1
63.com
A
b
st
r
a
ct
As high dy
namic movement is
always accompanied
by color
ed no
ise which lacks of
m
a
them
atic
al
mo
de
l, traditi
o
nal K
a
l
m
an fi
lterin
g b
a
sed
o
n
an
assu
mp
ti
o
n
of w
h
ite Ga
u
ssian
no
ise
al
w
a
ys faces ser
i
ous
diver
genc
e. T
o
en
hanc
e th
e p
e
rformanc
e i
n
hig
h
dy
na
mi
c
e
n
viro
nment w
i
t
h
u
n
certai
n co
l
o
red
no
ise, a
ki
nd
of
rob
u
st
filteri
ng base
d
on H
-
infinity
t
e
chn
o
l
ogy is
d
e
vel
o
p
ed.
State mod
e
l of
the
al
gorit
hm is
deriv
ed
fr
o
m
SINS error
pro
pag
atio
n. Both
pos
ition
a
nd
velocity
errors
are
used
as t
h
e
me
asure
m
en
ts. A simul
a
tio
n
system
which
includes a tri-
axial tu
rnt
able and a GNSS
signal sim
u
lator
is used t
o
verif
y
the integration
desi
gn
un
der
h
i
gh
dyn
a
m
ic
en
viron
m
e
n
t. Si
mulati
on r
e
su
lts
prove
d
th
at b
o
th the
acc
u
racy
an
d r
obustn
es
s
of the integr
ati
on des
ig
n hav
e
been i
m
prove
d
sign
ificantly.
Ke
y
w
ords
: SINS/GNSS inte
gratio
n, hig
h
d
y
na
mic, H-infi
n
i
ty Kalman filte
r
ing
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Strapdo
wn In
ertial
Navigati
on System
(S
INS)
is a
kind
of dea
d reckoning
method
based
on Inertial M
easurement Unit (IMU) [1]. As t
he navigation error will get accumulated, the
precisi
on of IMU determines the navigation effe
ct mainly. Global Navigation Satellite System
(G
NSS)
is a kind of
high p
r
eci
s
io
n
po
siti
oning sol
u
tio
n
whi
c
h co
uld
provide po
sition
an
d
velo
city
informatio
n b
y
a sin
g
le
re
ceiver [2]. But the
u
s
ag
e
of GNSS i
s
limited be
ca
u
s
e of th
e
sig
nal
attenuation in
urban
canyo
n
or situation
with st
ron
g
electroma
gne
tic in
terference. Furthermore,
the lo
w o
u
tp
ut rate
of
G
N
SS limits its u
s
a
g
e
in
high
dynami
c
e
n
viro
nme
n
t. SINS/GNSS
integratio
n mi
xes thei
r a
d
vant
age
s
and
disa
dvantag
e
s
respe
c
tively whe
r
e th
e
Kalman filteri
n
g
(KF) is
c
o
mmonly us
ed [3, 4].
High
dynami
c
m
o
vement
is
always
a
c
compa
n
ied
with u
n
certai
n colored
no
ise [5].
Ho
wever, tra
d
itional Kalm
an filter reli
es
on the
a
s
sumption th
at both pro
c
ess noi
se a
nd
measurement
noise are uncorrel
at
ed white Gaussian
noise whi
c
h
will
result in the divergent of
navigation re
sults. Te
chn
o
logie
s
su
ch
as
robu
st filtering ha
s b
een develo
p
ed to enhan
ce
navigation p
e
r
forma
n
ce un
der hi
gh dyn
a
mic e
n
viron
m
ent
[6, 7].
H-infinity filtering i
s
a ki
nd
of
robu
st filterin
g technol
ogy
which
could
retard f
ilteri
ng diverg
ence effectively
in colo
red no
ise
environ
ment
[8]. There
is no
req
u
ire
m
ent of
noi
se pri
o
ri
kno
w
led
ge
but j
u
st h
a
ving fi
nite
boun
ded
ene
rgie
s. H-infini
ty filtering ba
sed
on tra
d
itional Kalm
an
filtering do
es
not de
stroy t
he
linearity and
only need the
transfo
rmatio
n of the covariance matrix cal
c
ulatio
n.
In this pap
er, a kind of
H-infinity Kal
m
an
filter al
gorithm fo
r SINS/GNSS integrate
d
navigation
sy
stem i
s
d
e
si
g
ned. Th
e p
r
o
c
e
s
s mod
e
l i
s
b
a
sed o
n
S
I
NS erro
r p
r
o
pagatio
n. Errors
of both
po
sition a
nd vel
o
ci
ty are
use
d
a
s
m
easurem
ents
. H-infinity
filteri
n
g
w
a
s
us
e
d
to
en
h
anc
e
sy
st
em
rob
u
s
t
n
e
ss.
A
t
la
st
,
a com
p
a
r
ison
of
H-i
n
finity Kalman
filtering wit
h
the traditio
nal
Kalman filteri
ng ha
s bee
n dra
w
n u
s
ing
a hard
w
a
r
e
-
in
-the–lo
op si
m
u
lation sy
ste
m
.
2. Integra
t
ion Design
Structu
r
e of the integration
des
ig
n is sho
w
n in Figu
re
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
u
st SINS/GNSS Integration Method
for
High
Dyna
m
i
c Applicati
ons (Falin
Wu)
293
Figure 1. Integration
stru
ct
ure
SINS algorith
m
is appli
ed
based on gy
roscop
e ang
ul
ar velo
city
b
ib
and accel
e
ro
m
e
te
r
specific force
b
f
which a
c
qui
red from IMU. Errors
between SINS an
d GNSS re
ce
iver outputs
are
used as
measurement
s of the
filter.
Filter estimation output
s
will modify the SINS outputs
whi
c
h
u
s
e
d
as
the
final outputs and feedba
ck
to
t
he next SINS iteration at
the same ti
me.
Be
s
i
d
e
th
es
e,
L
,
λ
and
h
are
latitude, lon
g
itude a
nd
al
titude with
L
,
and
h
a
s
the
er
rors
.
e/
n/
u
v
are v
e
locitie
s
in
ge
ogra
phi
c
coo
r
dinate
(i.e., east, no
rth an
d up
) with
e/
n
/
u
v
as the
er
rors
.
,
and
a
r
e
craft attitude (i.e., y
a
w, pit
c
h
an
d roll
) from
t
frame (T
rue
frame
or
navigation frame)
coo
r
din
a
te to
b
fram
e (Body fram
e or craft frame) coordina
te.
e/
n
/
u
Φ
are
misalig
nment
angle
s
from
t
frame to
c
frame (Com
p
u
ter fram
e)
coordi
nate [9].
x
/y
/
z
v
are
velocitie
s
in e
a
rth fixed coo
r
dinate a
s
pa
rts of GNSS receive
r
outpu
ts.
2.1. Process
Model
Process mod
e
l of the SINS/GNSS integration i
s
:
XF
X
G
W
&
(1)
whe
r
e
X
is the estimation
state variable
with cova
rian
ce matrix
P
.
22
2
2
2
2
2
2
2
2
2
2
2
2
2
d
i
a
g
,
, ,
,
,
,
,
,
,
,
,
,
,
,
en
u
e
n
u
x
y
z
x
y
z
T
en
u
e
n
u
x
y
z
x
y
z
ΦΦ
Φ
vv
v
L
h
ΦΦ
Φ
vv
v
L
h
X
P
(2)
Whe
r
e
2
e/
n/
u
Φ
,
2
e/
n/
u
v
an
d
2
/
L
/h
are varia
n
ce of mi
sali
gnment an
gl
es, velocity errors an
d
positio
n e
r
rors.
x
/y
/
z
and
x
/y
/
z
are gyrosco
p
e
drift a
n
d
a
c
cele
rom
e
ter
bias at
b
frame
coo
r
din
a
te wi
th variance
2
x/
y
/
z
and
2
x/
y
/
z
.
W
is additive ze
ro mea
n
whit
e Gau
ssi
an n
o
ise of the IM
U with covari
ance matrix
Q
.
2
2
222
2
d
i
a
g
,
, ,
, ,
gx
g
y
g
z
ax
ay
az
gx
gy
gz
ax
ay
az
T
W
Q=
(3)
W
h
er
e
g
x/
g
y
/
g
z
and
ax
/
a
y
/
az
are gy
ro
sco
pe a
n
d
a
ccel
e
rom
e
ter noi
se
process
with va
rian
ce
2
g
x/
g
y
/
g
z
and
2
ax
/
a
y
/
az
.
Process noi
se input matrix
G
is given as:
33
33
33
3
3
33
33
33
33
33
33
T
0000
I
G
000
I
0
(4)
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 292 – 299
294
State tran
sition mat
r
ix
F
co
uld be
extra
c
t
ed fro
m
p
r
op
agation
of mi
salig
nment
a
ngle
s
,
velocity errors, positio
n erro
rs a
nd IMU
errors whi
c
h
can b
e
expre
s
sed a
s
belo
w
[10].
2
(
s
in
ta
n
)
(
c
o
s
)
(
s
in
ta
n
)
+
s
in
(c
o
s
)
t
a
n
(c
o
s
s
e
c
)
ee
n
ei
e
n
i
e
u
e
nn
m
en
e
ei
e
e
u
i
e
n
nm
n
en
e
e
ui
e
e
n
i
e
nm
n
n
vv
v
LL
L
Rh
Rh
R
h
vv
v
LL
L
L
Rh
R
h
Rh
vv
v
v
LL
L
L
L
Rh
R
h
Rh
Rh
u
&
&
&
(5)
2
2
(t
a
n
)
(2
s
i
n
t
a
n
)
(
2
c
o
s
)
ta
n
(2
c
o
s
s
e
c
2
s
i
n
)
2(
si
n
t
an
)
nu
en
u
u
n
e
mm
ee
ie
n
i
e
u
nn
en
e
u
en
ie
n
i
e
u
e
n
n
eu
n
nu
e
e
u
i
e
e
n
nm
vv
vf
f
L
v
Rh
Rh
vv
LL
v
L
v
Rh
R
h
vv
v
v
vv
L
Lv
L
L
v
L
h
Rh
Rh
vv
v
vf
f
L
L
v
v
Rh
R
h
R
&
&
2
2
ta
n
(2
c
o
s
s
e
c
)
2
2(
cos
)
2
s
in
2
s
in
u
m
ee
u
e
ie
e
n
nm
n
en
ue
n
n
e
i
e
e
u
nm
ie
e
i
e
e
u
v
h
vv
v
+
v
L
LL
v
L
h
Rh
R
h
Rh
vv
vf
f
L
v
v
Rh
R
h
Lv
L
L
v
h
&
(6)
se
c
s
e
c
ta
n
nn
mm
n
ee
e
nn
m
n
u
vv
L=
h
Rh
Rh
R
h
vv
v
λ
=L
L
L
L
h
Rh
Rh
R
h
Rh
h=
v
&
&
&
(7)
x
/
y
/z
g
x
/g
y
/
g
z
x
/y
/
z
a
x
/
a
y
/
a
z
&
&
(8)
Whe
r
e
e/
n
/
u
f
,
e/
n/
u
and
e/
n
/
u
denote the
specifi
c
force,
gyrosco
pe d
r
i
ft and accele
rometer
bias
at
t
frame, res
p
ec
tively.
ie
is the rotation
al angul
ar ve
locity of the earth.
m
R
and
n
R
u
s
ed
above are ra
dius of me
ridi
an plan
e and
prime
verti
c
al
plane which can b
e
cal
c
ul
ated as:
2
2
12
3
s
i
n
1s
i
n
e
m
e
n
R
R
ee
L
R
R
eL
(9)
Whe
r
e
e
R
repre
s
ent
s the radi
us of the ea
rth and
e
is
the earth ec
centrity.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
u
st SINS/GNSS Integration Method
for
High
Dyna
m
i
c Applicati
ons (Falin
Wu)
295
2.2. Measure
ment Model
Measurement
model is b
a
se
d on po
sition error a
nd velocity error at geo
grap
hical
coo
r
din
a
te which
can b
e
e
x
presse
d as:
ZH
X
V
(10
)
Whe
r
e
Z
is the measu
r
em
en
t given as:
Z
T
en
u
T
e
,
S
I
NS
e
,
G
N
SS
n,
SI
NS
n,
GN
SS
u
,
SINS
u,
GNSS
SI
N
S
GN
SS
SI
N
S
GNSS
SI
N
S
GNSS
vv
v
L
h
vv
v
v
v
v
L
L
h
h
(11
)
The
GNSS
receive
r
h
a
s velocity o
u
tput
s at
ea
rth E
C
EF
(Earth
Cente
r
ed
Earth Fixed)
c
o
or
d
i
na
te
a
s
x
/y
/
z
,
G
N
S
S
v
which h
a
ve to be tran
sferred into geo
graphi
cal coord
i
nate as
e
/
n
/
u,
G
N
SS
v
.
cos
s
in
0
22
co
s
s
i
n
c
o
s
c
o
s
s
i
n
22
2
2
2
sin
s
in
sin
c
os
c
o
s
22
2
2
2
e,
GN
S
S
n,
G
N
SS
u,
G
N
SS
λλ
v
vL
λ
L
λ
L
v
L
λ
L
λ
L
x,
GN
S
S
y,
G
N
S
S
z,
G
N
S
S
v
v
v
(12
)
The mea
s
u
r
e
m
ent matrix is given a
s
:
33
33
3
3
3
3
33
33
33
33
3
3
33
0I
0
0
0
H
00
I
0
0
(13
)
V
is ze
ro mea
n
white Gau
s
si
an noi
se with
covari
an
ce m
a
trix
R
.
22
22
2
2
2
2
2
2
2
2
d
i
a
g
, , ,
,
,
d
i
a
g
,
,
,
,
,
en
u
h
h
h
h
v
en
u
h
h
v
h
h
v
v
v
v
L
h
v
v
v
pe
pe
p
vv
v
L
h
v
v
v
p
e
p
e
p
RR
RR
v
TT
V
R
(14
)
Whe
r
e
e/
n/
u
v
are GNSS velocity measurement
noise
s at ge
ogra
phi
cal co
ordin
a
te whi
c
h can al
so
be expresse
d
as ho
ri
zontal
and verti
c
al
noise
h
v
and
v
v
w
i
th var
i
ances
of
2
h
v
and
2
v
v
.
/
L
/h
are
GNSS
g
eographi
cal
p
o
sition
mea
s
urem
ent n
o
ises
t
r
an
sferre
d from
ho
rizo
ntal an
d verti
c
al
noise
h
p
and
v
p
with variances
of
2
h
p
and
2
v
p
.
2.3. H-infinity
Kalman Filter
Discretizatio
n
of the process model a
nd
measurement
model is represe
n
ted a
s
:
11
/
kk
k
k
k
k
kk
k
k
XX
W
ZH
X
V
(15
)
A
ssu
me
K
F
T
is the cal
c
ulatio
n perio
d of the Kalman filter.
and
are give
n as:
2
2
KF
KF
KF
T
TT
Ι
F
GF
(16)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 292 – 299
296
A
ssu
me
ˆ
k
X
is t
he
state e
s
timation
with v
a
rian
ce
k
P
, the recursio
n alg
o
rithm of th
e
H-
infinity filtering can b
e
expressed a
s
:
,1
2
1
11
/
1
/
1
/
,
1
/
1
11
1
1
1
1
11
/
1
1
1
1
/
0
0
ˆˆ
ˆ
k
TT
ek
k
k
k
k
k
TT
T
T
T
k
k
k
k
kk
k
k
kk
k
k
k
k
kk
k
TT
kk
k
k
k
k
k
k
kk
k
k
k
k
kk
-
ek
H
R
RP
H
L
IL
H
PP
Q
P
H
L
R
P
L
KP
H
H
P
H
R
XX
K
Z
H
X
(17)
Whe
r
e
k
L
I
an
d
1
21
max
e
i
g
T
kk
k
PH
H
.
ma
x
e
i
g
M
mean
s th
e m
a
ximum ei
ge
nvalu
e
of matrix
M
.
1
is a paramete
r
use
d
to gu
arante
e
the positiven
ess
of
k
P
and control the
tradeoff between ro
bu
stne
ss a
nd preci
s
i
on [11]. The value of
is set
as 10 in this
system.
4. Validation and Analy
s
is
To verify the
integration
desi
gn, a h
a
r
dw
are-in
-the
-loop
sim
u
lati
on sy
stem h
a
s b
een
develop
ed [1
2]. The
syste
m
in
clude
s a
IMU, a
G
N
S
S
re
ceive
r
, a
trajecto
ry
sim
u
lator, a
tri
-
axial
turntable, a G
N
SS sign
al si
mulator a
nd a
nav
igation compute
r
as
shown in Figu
re 2.
Figure 2. Simulation sy
ste
m
stru
cture
Figure 3. Time synchro
n
ization diag
ram
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
u
st SINS/GNSS Integration Method
for
High
Dyna
m
i
c Applicati
ons (Falin
Wu)
297
The sy
stem
is built o
n
ann
ular fi
ber-
opti
c
co
mmuni
cation
netwo
rk to
ensure
instanta
neity [13]. The IMU co
ntain
s
a
tri-axia
l fiber-optic
gyro
scope an
d a tri
-
axial pen
dul
ous
integratin
g a
c
celeromete
r with
output
freq
uen
cy
of 100
Hz. T
he G
N
SS
receive
r
outp
u
ts
navigation data and PPS (Pulses Pe
r Second) [14] at frequency
of 10Hz. The
accelerom
e
ter
outputs de
sired a
c
cele
rati
on u
nde
r ext
e
rnal
current
inje
ction
whi
c
h
co
mes form thre
e el
ect
r
ic
isolate
d
cha
n
nels on the
DC po
we
r bo
ard [15].
Impulse counte
r
board is use
d
to receive
and
transfo
rm co
ntinuou
s imp
u
lse
s
co
me from the IMU [16]. The navigation com
puter is u
s
ed
to
receive and
synchroni
ze d
a
ta as sho
w
n
in Figure 3 a
nd implem
ent
the integratio
n algorith
m
.
The b
a
si
c SI
NS alg
o
rithm
will
be
done
firstly
when
the IMU data
ha
s b
een
a
c
qui
red.
Assu
me the
SINS has out
put of
,
SI
N
S
IM
U
m
xt
and
,1
SI
N
S
I
M
U
m
xt
at time
,
I
MU
m
t
and
,1
IM
U
m
t
. S
o
navigation re
sults at time
,
P
PS
k
t
is availabl
e by applying bin
o
mial
interpol
ation [17]. GNSS data at
time
,
P
PS
k
t
could b
e
recko
ned b
y
the followin
g
operation.
,1
,
,,
,
,
,1
,
,,
,,
,
S
I
N
S
IM
U
m
S
I
N
S
IM
U
m
S
I
NS
PPS
k
S
I
N
S
I
M
U
m
PPS
k
I
M
U
m
IM
U
m
I
M
U
m
SI
N
S
SI
N
S
I
M
U
n
S
I
N
S
P
P
S
k
G
N
S
S
I
M
U
n
G
N
S
S
P
P
S
k
S
I
N
S
G
NS
S
G
NS
S
k
S
I
NS
tt
tt
t
t
tt
tt
tt
t
xx
xx
xx
x
xx
x
x
x
(18)
Initial value of matrix
0
ˆ
X
and
0
P
, along
side
with the matrix
Q
and
R
are set a
s
belo
w
.
0
22
2
0
2
2
222
2
2
ˆ
0
.
0
0
1
0
.
0
0
1
0
.
0
0
1
0000
0
0
0.
05
0.
05
0
.
0
5
50
5
0
5
0
di
ag
0.
00
1
,
0
.
0
0
1
,
0.
001
,
0
.
0
1
,
0.
0
1
,
0.
0
1
,
1
,
1
,
1
,
0
.
0
1
,
T
ee
ms
ms
ms
m
h
h
h
ggg
m
s
ms
ms
m
R
m
R
m
h
X
P
ooo
o
o
oo
o
oo
o
o
22
222
222
222
222
2
2
2
0
.
0
1
,
0
.
0
1
,
1
0
, 1
0
, 1
0
dia
g
0.01
,
0.01
,
0
.
0
1
,
1
0
,
1
0
,
1
0
d
i
ag
0
.
0
1
,
0.
0
1
,
0.
0
1
,
0
.
1
,
0.
1
,
0.
1
ee
h
h
ggg
h
h
h
ggg
m
s
ms
ms
m
R
m
R
m
Q
R
oo
ooo
(19)
Comp
arative experim
ents
of H-infinity Kalm
an filteri
ng and tra
d
itional Kalman
filtering
unde
r high
dynamic e
n
v
ironme
n
t have been
c
ondu
cted u
s
ing the sim
u
lation sy
ste
m
.
Comp
ari
s
o
n
s of attitude error, velo
city erro
r and p
o
siti
on error a
r
e
shown in Figu
re 4.
Attitude erro
r mainly ca
used by colored
noise of IMU unde
r hig
h
d
y
namic e
n
vironment.
Comp
ari
s
o
n
of attitude errors in
dicates
that the
H-infi
nity filtering coul
d provide
high ro
bu
stne
ss
to some exte
nt. IMU noise
and GNSS receive
r
noi
se
affect velocity and positio
n errors main
ly,
expeci
a
lly the
up
axis
re
sul
t
s a
s
the
hei
g
h
t ch
ann
el of
both SINS
an
d G
N
SS hav
e lo
w p
r
e
c
isi
o
n.
Comp
ari
s
o
n
of velocity erro
r and p
o
sition erro
r
in
dicate that H-infinity filtering ha
s bet
ter
inhibition
of u
p
velocity an
d altitude e
r
ror dive
rge
n
cy
,
along
side with
a
mod
e
st improvem
ent at
both velocity and po
sition
errors.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 292 – 299
298
(a) Attitude error
(b) Velo
city
erro
r
(c
) Position e
rro
r
Figure 4. Nav
i
gation erro
r compa
r
ison
5. Conclusio
n
This
pap
er
p
r
esents a
ki
nd of
H-i
n
fin
i
ty Kalman filtering
algo
rithm for SI
NS/GNSS
integratio
n
m
e
thod und
er high dynami
c
enviro
n
me
nt. Both de
sign
s of th
e p
r
o
c
ess mo
del
a
nd
the me
asure
m
ent mo
del
are
linea
r,
which
ap
plys
to
Ka
lman
filte
r
in
g or
an
y
o
t
h
e
r
lin
e
a
r
fu
s
i
on
techn
o
logie
s
.
A brief desig
n of H-infinity filter
ing deriv
ed from tradit
i
onal Kalman
filtering is u
s
ed
to enhan
ce
the robu
stne
ss p
e
rfo
r
ma
nce. Co
mpa
r
ative experi
m
ents un
de
r high dyna
mic
environ
ment based on a hard
w
a
r
e
-
in-t
he-lo
op sim
u
lation system
proved that
the H-infinity
Kalman filteri
ng ha
s better
robu
stne
ss
than tradition
al Kalman filteri
ng.
Ackn
o
w
l
e
dg
ements
The re
se
arch
is partial su
pporte
d by t
he Ope
n
Re
sea
r
ch Fun
d
of the Academy of
Satellite Applicatio
n un
der g
r
ant
No.20
14_
CX
JJ-DH_
07,
and the Sc
ientific Re
se
arch
Found
ation fo
r the Retu
rne
d
Oversea
s
Chine
s
e
Sch
o
l
a
rs, State Ed
ucatio
n Minist
ry, China.
Referen
ces
[1]
T
i
tterton DH, W
e
ston JL.
Strapd
ow
n Inerti
al Nav
i
gati
on
T
e
chno
logy
. T
he Institutio
n of Electrica
l
Engi
neers. 2
0
0
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
u
st SINS/GNSS Integration Method
for
High
Dyna
m
i
c Applicati
ons (Falin
Wu)
299
[2]
Kapl
an ED, H
egart
y
CJ. Un
derstan
din
g
GPS: Principl
es
and App
licati
ons.
ARTECH
HOUSE, INC
.
200
6.
[3]
Grew
al M, Andre
w
s A.
Ka
l
m
a
n
F
ilteri
ng:
T
heory a
nd P
r
actice Usi
ng
MAT
L
AB
. Wiley
-
IEEE Press
.
200
8.
[4]
Groves PD. Principles
of GNSS, Inertial,
a
nd Mu
ltise
n
sor
Integrat
ed Navigation S
y
stems.
ARTECH
HOUSE, IN
C. 200
8.
[5]
Qi W-J, Heil
on
gjia
ng
U, Zha
n
g
P, Ni
e G-H,
De
n
g
Z
-
L. R
o
b
u
st W
e
ig
hted
Measur
ement
F
u
sion
Kalm
a
n
Predictors
w
i
t
h
Uncerta
i
n
Noise V
a
ria
n
c
es.
T
E
LKOMNIKA Indon
es
ian Jo
urna
l of Electrica
l
Engi
neer
in
g
. 2014; 12(
6); 469
2-47
04.
[6]
Xi
e
L, So
h YC.
Ro
bust K
a
lma
n
filter
ing for
uncertain s
y
stems.
Systems
&
Co
ntrol
Letter
s
. 199
4; 2
2
(2);
123-
129.
[7]
Xi
e L, So
h YC,
De Souz
a CE.
Robust K
a
lma
n
filterin
g for u
n
certai
n discr
e
t
e-time s
y
stem
s.
Automatic
Control, IEEE
Transactions on
. 1994; 3
9
(6); 131
0-13
14.
[8]
Simon D. Optimal Stat
e Estimation: Kalman, H
∞
, and No
n
line
a
r Appr
oac
hes. Ne
w
York:
W
ile
y
.
20
06.
[9]
Benso
n
DO. A Compar
iso
n
o
f
T
w
o Ap
pro
a
c
hes to
Pur
e
-In
e
rtial a
nd
Dop
p
ler-In
e
rtial Err
o
r Anal
ys
is.
Aerospace and Electronic Sys
t
em
s, IEEE Transactions on
. 1
975; AES-1
1
(4
); 447-45
5.
[10]
Z
hou W
,
D
a
li
a
n
Un
ivers
i
t
y
Of T
,
Ma H, W
u
S,
Meng
N. IN
S/GPS Integrat
ed N
a
vi
gatio
n
T
e
chnolog
y f
o
r
H
y
pers
onic UA
V.
T
E
LKOMNIKA Indon
esia
n Journ
a
l of Elec
trical Eng
i
ne
eri
n
g
. 201
4; 12(1)
; 398-40
5.
[11]
Li W
,
Jia Y.
H-infin
i
t
y
filteri
ng for
a cl
as
s
of no
nli
n
e
a
r
discrete-tim
e
s
y
stems
base
d
on
unsc
ented
transform.
Sign
al Process
i
ng
.
201
0; 90(1
2
); 3301-
330
7.
[12]
Lei
HR, C
h
e
n
S, Cha
n
g
Y,
W
ang
L. Res
earch
on
the
Hard
w
a
re-i
n-th
e-Lo
op S
i
mul
a
tion for
Hig
h
D
y
namic
SINS
/GNSS Integra
t
ed N
a
vig
a
tio
n
S
y
stem.
Adva
nced
Materi
als
Res
earch
. 20
13;
8
46-
847
;
378-
382.
[13]
Z
hao K-R, Xu S, Ye Q, Li Y.
Desig
n
an
d rea
l
i
z
a
t
io
n of flight
simu
latio
n
sys
tem b
a
sed o
n
Virtual R
eal
ity
techno
lo
gy
. Co
ntrol a
nd D
e
cis
i
on
Confer
enc
e (CCD
C), 2
0
1
1
Ch
ines
e. Mia
n
y
an
g, Chi
na.
201
1; 43
61-
436
4.
[14]
Niu
X
,
Yan K,
Zhang T
,
Zhang Q, Zhang
H, Li
u J. Qualit
y
evaluat
ion of
the pulse
per second (PPS)
signals from commercial GNS
S
receivers.
GPS Solutions
. 201
4; 1-10.
[15]
Li G, Mu J,
Xu H. Meas
ure
m
ent stud
y fo
r accel
e
romet
e
r bas
ed
on i
n
jecti
on c
u
rren
t.
Journal o
f
Astronautic Me
trology a
nd Me
asure
m
ent
. 20
00; 20; 6-7.
[16]
Xi
e W
,
Cai Y, Yao J, Xin
C
.
Design and im
plem
entation of t
he LIMU puls
e
counting system
. IE
T
Confer
ence Pr
ocee
din
g
s. Xia
m
en, Chi
na. 20
12; 778-
78
1.
[17]
Z
hang
P, Gu J,
Mili
os EE, H
u
ynh P.
Navi
gati
o
n w
i
th IMU/GPS/digita
l co
mp
ass w
i
th u
n
sce
nted K
a
l
m
a
n
filter
. Mechatr
onics and A
u
tomation, IEEE Internatio
nal
Confer
ence. Niagara Falls, Ont., Canada.
200
5; 3; 1497-
150
2.
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