I
nte
rna
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n
(
I
J
RA
)
Vo
l.
4
,
No
.
4
,
Dec
em
b
er
2
0
1
5
,
p
p
.
2
43
~2
53
I
SS
N:
2089
-
4856
243
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
J
RA
Integ
ra
tion a
nd
S
i
m
ula
tions
of INS
/G
NSS
Sys
te
m
U
s
ing
t
he
Appro
a
ch of
Ca
rrier
P
ha
se M
ea
sure
m
ents
K
ha
n B
a
ds
ha
h
,
Q
in Yo
ng
y
u
a
n
S
c
h
o
o
l
o
f
A
u
to
m
a
ti
o
n
,
N
o
rth
w
e
ste
rn
P
o
ly
tec
h
n
ica
l
Un
iv
e
rsity
X
i’an
,
Ch
in
a
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
l
1
1
,
2
0
1
5
R
ev
i
s
ed
Oct
2
7
,
2
0
1
5
A
cc
ep
ted
No
v
1
2
,
2
0
1
5
T
h
is
p
a
p
e
r
d
isc
u
ss
e
s
th
e
te
c
h
n
iq
u
e
s
o
f
a
tt
it
u
d
e
,
v
e
lo
c
it
y
a
d
p
o
siti
o
n
e
sti
m
a
ti
o
n
f
ro
m
G
NSS
c
a
rrier
p
h
a
se
m
e
a
su
re
m
e
n
ts,
a
n
d
in
v
e
s
ti
g
a
tes
th
e
p
e
rf
o
r
m
a
n
c
e
o
f
th
e
lo
w
e
r
p
re
c
isio
n
M
EM
S
b
a
se
d
IN
S
/G
NSS
sy
s
tem
b
a
se
d
o
n
c
a
rrier
p
h
a
se
m
e
a
su
re
m
e
n
ts.
Do
u
b
le
d
if
fe
re
n
c
e
d
c
a
rr
ier
p
h
a
se
m
e
a
su
re
m
e
n
ts
p
ro
v
id
e
m
o
re
a
c
c
u
ra
te
v
e
lo
c
it
y
a
n
d
p
o
siti
o
n
e
sti
m
a
ti
o
n
c
o
m
p
a
re
d
to
c
o
d
e
a
n
d
Do
p
p
ler
m
e
a
su
re
m
e
n
ts.
Ho
w
e
v
e
r,
in
teg
e
r
a
m
b
ig
u
it
y
is
re
q
u
ired
t
o
b
e
re
m
o
v
e
d
f
o
r
p
re
c
ise
p
o
siti
o
n
i
n
g
.
M
u
lt
i
p
les
a
n
ten
n
a
e
a
p
p
ro
a
c
h
is
u
se
d
t
o
d
e
riv
e
th
e
a
tt
it
u
d
e
in
f
o
r
m
a
ti
o
n
f
ro
m
c
a
rrier
p
h
a
se
m
e
a
su
re
m
e
n
ts
in
o
rd
e
r
to
c
o
n
tro
l
th
e
larg
e
in
it
ial
m
is
a
li
g
n
m
e
n
t
a
n
g
les
f
o
r
in
it
ializa
ti
o
n
o
f
th
e
in
teg
ra
ti
o
n
p
r
o
c
e
ss
o
r
to
u
ti
l
ize
d
u
rin
g
b
e
n
ig
n
d
y
n
a
m
ics
.
L
e
v
e
r
a
r
m
e
ff
e
c
t
is
c
o
n
sid
e
re
d
to
c
o
m
p
e
n
sa
te
f
o
r
th
e
se
p
a
ra
ti
o
n
o
f
G
NSS
a
n
ten
n
a
a
n
d
IM
U
lo
c
a
ti
o
n
.
T
h
e
d
e
riv
e
d
t
h
re
e
G
NSS
o
b
se
rv
a
b
les
a
re
u
se
d
to
c
o
rre
c
t
th
e
INS
th
ro
u
g
h
o
p
ti
m
a
l
Ka
l
m
a
n
f
il
teri
n
g
in
a
c
lo
se
d
lo
o
p
.
S
im
u
lati
o
n
re
su
l
ts
in
d
ica
tes
th
e
e
ff
e
c
ti
v
e
n
e
ss
o
f
th
e
in
teg
ra
ted
s
y
ste
m
f
o
r
a
irb
o
rn
e
a
s
w
e
ll
a
s
f
o
r
lan
d
n
a
v
ig
a
ti
o
n
v
e
h
icle
s.
K
ey
w
o
r
d
:
C
ar
r
ier
P
h
ase
Do
p
p
ler
GNSS
I
NS
Kal
m
a
n
Fil
ter
i
n
g
MEMS
P
s
eu
d
o
R
an
g
e
Si
m
u
latio
n
Co
p
y
rig
h
t
©
201
5
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Kh
a
n
B
ad
s
h
ah
,
S
c
h
o
o
l
o
f
A
u
to
m
a
ti
o
n
,
No
rth
w
e
ste
rn
P
o
ly
tec
h
n
ica
l
Un
iv
e
rsit
y
X
i’an
,
S
h
a
a
n
x
i
7
1
0
0
7
2
,
C
h
in
a
.
E
m
ail:
k
h
a
n
_
p
h
y
s@
y
a
h
o
o
.
c
o
m
1.
I
NT
RO
D
UCT
I
O
N
ME
MS
b
ased
in
er
tial
s
e
n
s
o
r
s
h
av
e
e
n
ab
led
th
e
u
s
e
o
f
i
n
er
ti
al
tech
n
o
lo
g
y
i
n
m
an
y
ap
p
lic
atio
n
s
t
h
at
w
er
e
n
o
t
f
ea
s
ib
le
i
n
t
h
e
p
ast
d
u
e
to
s
ize
a
n
d
co
s
t
co
n
s
tr
ain
ts
.
Ho
w
e
v
er
,
d
u
e
to
i
m
m
at
u
r
it
y
o
f
th
i
s
tec
h
n
o
lo
g
y
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
e
s
e
n
s
o
r
s
is
li
m
i
ted
w
h
ic
h
r
eq
u
ir
e
s
s
o
m
e
n
o
n
-
tr
ad
itio
n
al
al
g
o
r
ith
m
s
f
o
r
i
m
p
r
o
v
i
n
g
th
eir
p
er
f
o
r
m
a
n
ce
a
n
d
r
eliab
ilit
y
[
1
]
.
No
w
ad
a
y
s
a
s
i
n
g
le
-
c
h
ip
GNS
S
r
ec
eiv
er
ar
e
a
v
aila
b
le
in
t
h
e
m
ar
k
et
,
w
h
ic
h
ar
e
b
ei
n
g
in
cr
ea
s
in
g
l
y
u
til
iz
ed
in
m
an
y
n
a
v
ig
a
tio
n
ap
p
licatio
n
s
[
2
]
.
T
h
e
in
te
g
r
at
io
n
o
f
GNS
S
a
n
d
ME
MS
I
NS
o
f
f
er
s
a
v
er
y
lo
w
co
s
t,
lig
h
t
w
ei
g
h
t
an
d
s
u
f
f
icie
n
tl
y
ac
c
u
r
ate
an
d
r
eliab
le
s
o
lu
tio
n
f
o
r
n
av
ig
at
io
n
ap
p
licatio
n
s
[
3
]
.
T
h
er
e
ar
e
th
r
ee
m
ai
n
o
b
s
er
v
ab
les r
elate
d
to
th
e
GN
SS
ca
lled
p
s
e
u
d
o
-
r
an
g
e,
ca
r
r
ier
p
h
ase
an
d
Do
p
p
ler
m
ea
s
u
r
e
m
e
n
ts
.
T
h
es
e
o
b
s
er
v
ab
les
ar
e
u
s
ed
as
a
p
er
io
d
ic
u
p
d
ates
to
th
e
I
NS
f
o
r
er
r
o
r
esti
m
atio
n
u
s
i
n
g
th
e
tec
h
n
iq
u
e
o
f
o
p
ti
m
a
l
Kal
m
a
n
f
il
ter
in
g
.
GNSS
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
ts
p
r
o
v
id
e
v
er
y
ac
c
u
r
ate
attitu
d
e,
v
elo
cit
y
a
n
d
p
o
s
itio
n
d
ata
co
m
p
ar
ed
to
th
e
co
d
e
p
h
ase
an
d
Do
p
p
ler
m
ea
s
u
r
e
m
en
ts
.
T
h
e
a
ttit
u
d
e
d
eter
m
in
at
io
n
u
s
e
s
r
elativ
e
ca
r
r
ier
-
p
h
ase
p
o
s
itio
n
i
n
g
b
et
w
ee
n
m
u
ltip
le
an
te
n
n
as
m
o
u
n
ted
o
n
th
e
s
a
m
e
v
eh
ic
le.
GNSS
at
titu
d
e
i
s
v
er
y
n
o
is
y
,
b
u
t
d
o
es
n
o
t
d
r
if
t,
m
a
k
in
g
it
h
i
g
h
l
y
co
m
p
le
m
e
n
tar
y
to
I
NS
attitu
d
e
an
d
a
s
o
lu
tio
n
to
th
e
h
ea
d
i
n
g
ca
lib
r
atio
n
p
r
o
b
lem
t
h
at
o
cc
u
r
s
f
o
r
s
o
m
e
I
NS/
GNS
S
ap
p
licatio
n
s
[
4
]
.
B
y
co
m
b
in
in
g
a
lo
w
er
p
r
ec
is
io
n
ME
MS
I
N
S
w
it
h
m
u
ltip
le
an
te
n
n
a
GN
SS
,
a
p
r
ec
is
e
an
d
s
tab
le
at
tit
u
d
e
s
o
l
u
tio
n
m
a
y
b
e
o
b
tain
ed
.
T
h
e
in
er
tial
at
tit
u
d
e
s
o
lu
t
io
n
ca
n
al
s
o
aid
t
h
e
GN
SS
a
m
b
ig
u
it
y
r
eso
l
u
tio
n
p
r
o
ce
s
s
b
y
s
i
g
n
i
f
ican
tl
y
r
ed
u
cin
g
th
e
s
ea
r
c
h
s
p
ac
e.
W
ith
a
s
h
o
r
t b
aseli
n
e,
th
e
i
n
er
tial
attitu
d
e
m
a
y
co
m
p
le
tel
y
r
eso
l
v
e
th
e
a
m
b
ig
u
it
y
.
A
f
u
ll
G
NSS
att
itu
d
e
s
o
l
u
tio
n
r
eq
u
ir
es
th
r
ee
o
r
m
o
r
e
an
te
n
n
as.
Ho
w
e
v
er
,
t
w
o
an
ten
n
as
i
s
s
u
f
f
icie
n
t
f
o
r
I
NS/GN
SS
w
h
er
e
co
n
v
e
n
tio
n
al
I
NS/G
NSS
m
ee
ts
th
e
r
o
ll
an
d
p
itc
h
ac
c
u
r
ac
y
r
eq
u
ir
e
m
e
n
t
s
[
5
]
.
T
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
4
,
Dec
em
b
er
2
0
1
5
:
2
43
–
2
53
244
ac
cu
r
ac
y
o
f
I
N
S/GN
SS
atti
tu
d
e
d
eter
m
i
n
atio
n
d
ep
en
d
s
o
n
th
e
q
u
ali
t
y
o
f
th
e
in
er
tial
s
en
s
o
r
s
an
d
th
e
a
n
ten
n
a
s
ep
ar
atio
n
.
L
o
n
g
er
lev
er
ar
m
s
p
r
o
d
u
ce
m
o
r
e
p
r
ec
is
e
GNSS
attitu
d
e
m
ea
s
u
r
e
m
e
n
ts
b
u
t
ca
n
b
e
s
u
b
j
ec
t
to
f
le
x
u
r
e
[
6
,
]
.
Gen
er
ally
,
i
n
th
e
in
teg
r
atio
n
o
f
I
NS/GNS
S,
th
e
s
m
all
an
g
le
ap
p
r
o
x
i
m
atio
n
is
ap
p
lied
to
th
e
attitu
d
e
er
r
o
r
s
.
T
h
is
is
u
s
u
al
l
y
v
alid
f
o
r
t
h
e
r
o
ll
a
n
d
p
itc
h
att
itu
d
e,
w
h
ic
h
m
a
y
b
e
o
b
s
er
v
ed
th
r
o
u
g
h
le
v
elli
n
g
.
Ho
w
e
v
er
,
th
e
h
ea
d
i
n
g
(
o
r
az
im
u
th
)
an
g
le
is
m
o
r
e
d
if
f
icu
lt
to
f
in
d
f
o
r
in
it
ializatio
n
o
f
th
e
in
teg
r
ated
s
y
s
te
m
.
Hig
h
er
g
r
ad
es
a
n
d
e
x
p
en
s
iv
e
I
NS
ar
e
o
n
l
y
ca
p
ab
le
o
f
g
y
r
o
co
m
p
a
s
s
i
n
g
.
Si
m
i
lar
l
y
p
r
ec
is
e
v
e
lo
cit
y
a
n
d
p
o
s
itio
n
ca
n
a
ls
o
b
e
o
b
tain
ed
f
r
o
m
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
en
ts
.
A
cc
u
r
ate
v
e
lo
cit
y
m
e
asu
r
e
m
en
t
p
la
y
s
a
n
i
m
p
o
r
tan
t r
o
le
i
n
m
a
n
y
n
a
v
i
g
a
tio
n
ap
p
licatio
n
s
s
u
ch
a
s
au
to
m
atic
g
u
id
an
ce
a
n
d
co
n
tr
o
l o
f
an
u
n
m
a
n
n
ed
ae
r
ial
v
eh
ic
le
(
U
A
V)
an
d
ca
lib
r
atio
n
o
f
in
er
tial
n
av
i
g
atio
n
s
y
s
te
m
s
[
7
]
.
C
o
n
v
e
n
tio
n
all
y
a
G
NSS
r
ec
ei
v
er
esti
m
ate
s
v
elo
cit
y
b
y
d
if
f
e
r
en
cin
g
t
w
o
co
n
s
ec
u
ti
v
e
p
o
s
iti
o
n
s
o
r
b
y
u
s
i
n
g
Do
p
p
ler
m
ea
s
u
r
e
m
e
n
t
s
r
elativ
e
to
r
ec
eiv
er
–
s
ate
llit
e
m
o
tio
n
[
8
]
.
Do
p
p
ler
b
ased
v
elo
cit
y
is
th
e
m
o
s
t
w
id
el
y
u
s
ed
tec
h
n
iq
u
e
an
d
u
s
u
all
y
h
as
m
/s
ec
ac
cu
r
ac
y
,
w
h
i
le
th
e
v
elo
cit
y
o
b
tain
ed
d
if
f
er
en
cin
g
co
n
s
ec
u
ti
v
e
p
o
s
itio
n
s
f
r
o
m
s
i
n
g
le
p
o
in
t
p
o
s
itio
n
in
g
h
as
a
n
ac
cu
r
ac
y
o
n
e
o
r
d
er
o
f
m
a
g
n
i
tu
d
e
lar
g
er
.
W
h
en
a
g
r
ea
ter
ac
cu
r
ac
y
i
s
r
eq
u
ir
ed
,
v
elo
cit
y
ca
n
b
e
est
i
m
a
ted
b
y
p
r
o
ce
s
s
i
n
g
d
if
f
er
en
ce
s
o
f
co
n
s
ec
u
ti
v
e
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
t
s
,
w
h
ic
h
e
n
ab
les
ac
cu
r
ac
ies
at
th
e
m
m
/
s
lev
el.
T
h
e
ca
r
r
ier
p
h
ase
a
m
b
ig
u
it
y
is
s
u
e
u
s
u
al
l
y
li
m
i
ts
th
e
u
s
e
o
f
th
i
s
o
b
s
er
v
ab
le,
b
u
t
t
h
e
ti
m
e
-
d
if
f
er
e
n
ce
d
ca
r
r
ier
p
h
ase
tec
h
n
iq
u
e
o
v
er
co
m
es
th
is
p
r
o
b
le
m
.
Dif
f
er
e
n
ci
n
g
t
w
o
co
n
s
ec
u
tiv
e
ca
r
r
ier
p
h
ases
g
r
ea
tl
y
r
ed
u
c
es
th
e
e
f
f
ec
t
s
o
f
v
ar
io
u
s
co
m
m
o
n
m
o
d
e
er
r
o
r
s
b
et
w
ee
n
t
h
e
m
ea
s
u
r
e
m
e
n
t
s
allo
w
i
n
g
v
er
y
ac
c
u
r
ate
v
elo
cit
y
e
s
ti
m
atio
n
.
A
li
m
ita
tio
n
o
f
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
t
s
is
t
h
e
r
ed
u
ce
d
s
o
lu
tio
n
in
h
ar
s
h
s
it
u
atio
n
s
s
u
ch
a
s
u
r
b
an
ca
n
y
o
n
s
b
ec
au
s
e
o
f
th
e
4
s
atellite
s
av
ailab
ilit
y
r
eq
u
ir
e
m
en
t
s
[
7
]
.
T
h
e
ai
m
o
f
th
is
p
ap
er
is
t
h
e
m
at
h
e
m
atica
l
m
o
d
elli
n
g
f
o
r
th
e
es
ti
m
atio
n
o
f
att
itu
d
e,
v
e
lo
cit
y
a
n
d
p
o
s
itio
n
f
r
o
m
GNSS
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
ts
an
d
th
eir
p
er
f
o
r
m
a
n
ce
a
n
al
y
s
is
w
it
h
I
N
S t
h
r
o
u
g
h
s
i
m
u
latio
n
r
esu
lt
s
.
T
h
e
d
ata
o
f
th
e
t
w
o
s
y
s
te
m
s
is
f
u
s
ed
t
h
r
o
u
g
h
li
n
ea
r
ized
Kal
m
a
n
f
ilter
u
s
i
n
g
a
lo
o
s
el
y
co
u
p
led
ap
p
r
o
ac
h
.
Sim
u
latio
n
r
esu
l
ts
f
o
r
a
lo
w
er
g
r
ad
e
ME
MS
I
MU
(
STI
M3
0
0
)
au
g
m
e
n
ted
w
ith
GNSS
ar
e
p
r
o
d
u
ce
d
to
s
h
o
w
th
e
e
n
h
a
n
ce
d
i
m
p
r
o
v
e
m
en
t
in
t
h
e
n
a
v
i
g
ati
n
g
p
ar
a
m
e
ter
s
.
2.
I
NS
E
RRO
R
M
O
DE
L
T
o
tr
an
s
f
o
r
m
t
h
e
I
MU
an
d
G
NSS
d
ata
to
th
e
u
s
er
r
eq
u
ir
ed
n
av
ig
at
io
n
p
ar
a
m
eter
s
,
t
h
e
r
e
latio
n
s
h
ip
b
et
w
ee
n
d
if
f
er
en
t
co
o
r
d
in
ate
f
r
a
m
es
m
u
s
t
b
e
p
r
o
p
er
ly
m
o
d
elled
.
E
ac
h
f
r
a
m
e
is
co
n
s
id
er
e
d
as
an
o
r
th
o
g
o
n
al,
r
ig
ht
-
h
an
d
ed
co
-
o
r
d
in
ate
f
r
a
m
e.
Def
i
n
itio
n
o
f
t
h
e
f
r
a
m
e
s
u
s
ed
in
th
is
p
ap
er
f
o
r
th
e
I
N
S
m
ec
h
an
iza
tio
n
,
er
r
o
r
an
al
y
s
is
a
n
d
in
te
g
r
atio
n
o
f
I
N
S/GP
S a
r
e
g
iv
e
n
b
elo
w
[4
],
[
9
-
1
0
]
.
a)
I
n
er
tial f
r
a
m
e
(
i
-
f
r
a
m
e)
b)
E
C
E
F (
e
-
f
r
a
m
e)
c)
B
o
d
y
f
r
a
m
e
(
b
-
f
r
a
m
e)
d)
Nav
i
g
atio
n
f
r
a
m
e
(n
-
f
r
a
m
e)
I
n
er
tial
f
r
a
m
e
(
i
-
f
r
a
m
e)
h
a
s
its
o
r
ig
in
at
t
h
e
ce
n
tr
e
o
f
t
h
e
ea
r
th
an
d
i
s
n
o
n
-
r
o
tati
n
g
w
it
h
r
es
p
ec
t
to
t
h
e
f
i
x
ed
s
tar
s
,
a
s
s
h
o
w
n
i
n
F
ig
u
r
e
1
.
E
ar
th
C
e
n
tr
ed
E
ar
th
Fi
x
e
d
(
E
C
E
F)
f
r
a
m
e
(e
-
f
r
a
m
e)
i
s
a
co
o
r
d
in
ate
f
r
a
m
e
w
h
ic
h
h
as
its
o
r
i
g
i
n
at
t
h
e
ea
r
t
h
’
s
ce
n
tr
e
o
f
m
ass
an
d
h
as
ax
es
w
h
ich
ar
e
f
ix
ed
i
n
th
e
ea
r
th
.
Nav
i
g
atio
n
f
r
a
m
e
(
n
-
f
r
a
m
e)
is
a
lo
ca
l
lev
el
g
eo
d
etic
f
r
a
m
e
h
a
v
in
g
o
r
ig
i
n
at
th
e
m
as
s
ce
n
tr
e
o
f
n
a
v
i
g
atio
n
s
y
s
te
m
.
E
ast
-
No
r
t
h
-
Up
(
E
NU)
f
r
a
m
e
is
ch
o
s
en
a
s
a
lo
ca
l
le
v
el
n
a
v
i
g
atio
n
f
r
a
m
e
i
n
t
h
i
s
p
ap
er
.
T
h
e
b
o
d
y
f
r
a
m
e
(
b
-
f
r
a
m
e)
h
a
s
o
r
ig
in
co
i
n
cid
en
t
w
it
h
t
h
e
n
av
ig
atio
n
f
r
a
m
e
a
n
d
h
as
t
h
r
ee
f
i
x
ed
ax
i
s
d
ef
in
ed
a
s
x
-
(
r
i
g
h
t)
,
y
-
(
f
o
r
w
ar
d
)
an
d
z
-
(
u
p
)
.
Fo
r
an
g
u
lar
m
o
tio
n
,
x
is
th
e
p
itch
ax
i
s
,
y
is
th
e
r
o
ll
ax
i
s
an
d
z
-
ax
is
is
t
h
e
y
a
w
ax
is
.
A
lin
ea
r
er
r
o
r
m
o
d
el
o
f
I
NS
d
ev
elo
p
ed
in
n
-
f
r
a
m
e
i
s
u
s
ed
to
in
v
est
ig
ate
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
I
NS/G
NSS
i
n
te
g
r
ated
s
y
s
te
m
u
s
i
n
g
th
e
ca
r
r
ier
p
h
a
s
e
m
ea
s
u
r
e
m
e
n
ts
o
f
attit
u
d
e,
v
e
lo
cit
y
an
d
p
o
s
itio
n
s
.
L
i
n
ea
r
ized
er
r
o
r
eq
u
atio
n
s
o
f
atti
tu
d
e,
v
elo
cit
y
a
n
d
p
o
s
itio
n
ar
e
g
i
v
e
n
b
e
lo
w
[
1
1
]
.
Fig
ur
e
1
.
I
n
er
tial f
r
a
m
e
(
i
-
f
r
a
m
e)
C
oor
di
nat
e f
r
am
es
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
I
n
teg
r
a
tio
n
a
n
d
S
imu
la
tio
n
o
f
I
N
S
/GN
S
S
S
ystem
Usi
n
g
th
e
A
p
p
r
o
a
ch
o
f Ca
r
r
ier P
h
a
s
e
...
(
K
h
a
n
B
a
d
s
h
a
h
l)
245
2
2
2
1
(
sin
ta
n
)
(
c
o
s
)
(
sin
ta
n
)
sin
ta
n
ta
n
(
c
o
s
)
(
c
o
s
se
c
)
N
EE
E
ie
N
ie
U
N
E
Nh
Nh
M
h
M
h
N
E
E
E
N
ie
E
U
ie
N
Nh
M
h
Nh
Nh
N
N
E
E
E
U
ie
E
N
ie
E
Nh
M
h
Nh
Nh
v
vv
L
L
L
v
h
R
R
R
R
v
v
v
v
L
L
L
L
h
R
R
R
R
v
v
v
v
L
L
L
L
L
L
v
h
R
R
R
R
R
2
U
Nh
N
(
1
)
2
2
t
a
n
[
]
[
2
si
n
t
a
n
]
[
2
c
os
]
t
a
n
2
[
(
si
n
c
os
)
se
c
]
[
]
[
2
si
n
t
a
n
]
[
2
NU
EE
E
U
N
N
U
E
ie
N
ie
U
Nh
Nh
Nh
E
N
E
U
E
N
ie
U
N
E
Nh
Nh
UN
E
N
U
E
E
U
ie
E
N
U
E
Nh
M
h
M
h
v
L
v
vV
v
f
f
v
L
L
v
L
v
R
R
R
v
v
v
v
v
v
L
v
L
v
L
L
L
h
RR
vv
v
v
f
f
L
L
v
v
v
v
R
R
R
2
2
2
22
2
2
22
c
os
se
c
]
t
a
n
[]
2
2
[
2
c
os
]
2
si
n
[
]
E
ie
Nh
NU
E
N
M
h
Nh
NN
EE
U
N
E
E
N
ie
E
N
E
ie
U
Nh
M
h
M
h
Nh
v
L
L
L
R
vv
vL
h
RR
vv
vv
v
f
f
L
v
v
v
L
L
h
R
R
R
R
(
2
)
2
2
1
se
c
1
se
c
ta
n
se
c
Mh
N
N
Mh
EE
E
Nh
Nh
Nh
U
v
L
v
h
RR
v
v
L
L
v
L
L
L
h
R
R
R
hv
(
3
)
W
h
er
e
T
E
N
U
is
t
h
e
attit
u
d
e
er
r
o
r
;
T
n
E
N
U
v
v
v
v
an
d
T
p
L
h
ar
e
v
elo
cit
y
a
n
d
p
o
s
itio
n
er
r
o
r
v
ec
to
r
s
;
an
d
ar
e
g
y
r
o
d
r
i
f
t
a
n
d
ac
ce
ler
o
m
ete
r
b
ias er
r
o
r
s
w
h
ic
h
ar
e
ass
u
m
ed
to
b
e
co
n
s
tan
t
0
0
T
b
x
y
z
T
b
x
y
z
(
4
)
GNSS
atti
tu
d
e,
p
o
s
itio
n
a
n
d
v
elo
cit
y
p
ar
a
m
eter
s
a
n
d
th
eir
co
r
r
esp
o
n
d
in
g
m
ea
s
u
r
e
m
e
n
t
m
o
d
el
s
ar
e
d
er
iv
ed
in
t
h
e
f
o
llo
w
i
n
g
s
ec
ti
o
n
.
A
cc
u
r
ate
a
ttit
u
d
e
d
eter
m
i
n
atio
n
o
f
a
b
o
d
y
h
as
b
ee
n
a
c
h
alle
n
g
e
f
o
r
p
r
ec
is
e
n
av
i
g
atio
n
.
T
h
r
ee
n
o
n
-
co
lli
n
e
ar
an
te
n
n
ae
ar
e
in
s
talled
o
n
t
h
e
v
eh
ic
le
w
it
h
k
n
o
w
n
b
ase
l
in
e
v
ec
to
r
s
i
n
b
o
d
y
f
r
a
m
e,
as
s
h
o
w
n
i
n
Fi
g
-
2
.
T
h
e
r
elativ
e
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
en
ts
p
r
o
d
u
ce
th
e
b
ase
li
n
e
v
ec
to
r
s
b
et
w
ee
n
t
h
e
an
ten
n
a
s
i
n
E
C
E
F
f
r
a
m
e
[
4
]
.
T
h
e
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
ts
o
f
t
h
e
b
ase
li
n
e
s
v
ec
to
r
s
a
n
d
th
e
k
n
o
w
n
b
a
s
e
lin
es i
n
b
o
d
y
f
r
a
m
es a
r
e
p
r
o
ce
s
s
ed
to
o
b
tain
ed
th
e
attit
u
d
e
m
atr
ix
n
b
C
as
n
n
b
b
r
C
r
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
4
,
Dec
em
b
er
2
0
1
5
:
2
43
–
2
53
246
W
h
er
e
b
r
an
d
n
r
ar
e
co
n
s
tr
u
cted
f
r
o
m
v
ec
to
r
s
b
asis
a
s
1
2
2
3
1
2
2
3
T
b
b
b
b
b
r
r
r
r
r
(
6
)
1
2
2
3
1
2
2
3
T
n
n
n
n
n
r
r
r
r
r
(
7
)
C
ar
r
ier
–
p
h
ase
m
ea
s
u
r
e
m
en
ts
g
iv
e
t
h
e
v
ec
to
r
s
in
E
C
E
F f
r
a
m
e
w
h
ich
ca
n
b
e
tr
an
s
f
o
r
m
ed
i
n
to
th
e
n
-
f
r
a
m
e
as
n
n
e
e
r
C
r
(
8
)
W
h
er
e
n
e
C
tr
an
s
f
o
r
m
s
t
h
e
v
ec
to
r
f
r
o
m
E
C
E
F f
r
a
m
e
i
n
to
n
a
v
ig
a
ti
o
n
f
r
a
m
e
w
h
ic
h
ca
n
b
e
ca
lc
u
la
ted
f
r
o
m
p
r
ec
is
e
GP
S p
o
s
itio
n
as
s
in
c
o
s
0
s
in
c
o
s
s
in
s
in
c
o
s
c
o
s
c
o
s
c
o
s
s
in
s
in
n
e
C
L
L
L
L
L
L
(
9
)
T
h
e
attitu
d
e
m
atr
i
x
n
b
C
is
th
en
co
m
p
u
ted
as
Fig
u
r
e
3
.
GP
S C
ar
r
ier
P
h
ase
1
(
)
[
(
)
]
n
n
b
T
b
b
T
b
C
r
r
r
r
(
1
0
)
A
n
ten
n
a
2
A
n
ten
n
a
1
A
n
ten
n
a
3
Fig
u
r
e
2
.
An
ten
n
ae
Sc
h
e
m
e
R
ang
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
I
n
teg
r
a
tio
n
a
n
d
S
imu
la
tio
n
o
f
I
N
S
/GN
S
S
S
ystem
Usi
n
g
th
e
A
p
p
r
o
a
ch
o
f Ca
r
r
ier P
h
a
s
e
...
(
K
h
a
n
B
a
d
s
h
a
h
l)
247
T
h
u
s
p
itch
,
r
o
ll a
n
d
y
a
w
a
n
g
le
s
o
f
th
e
v
e
h
icle
ar
e
1
sin
[
(
3
,
2
)
]
a
r
c
ta
n
2
[
(
3
,
1
)
,
(
3
,
3
)
]
a
r
c
ta
n
2
[
(
1
,
2
)
,
(
2
,
2
)
]
n
b
nn
bb
nn
bb
C
CC
CC
(
1
1
)
Gen
er
all
y
,
t
h
e
d
er
iv
ate
o
f
r
ec
eiv
er
p
o
s
itio
n
is
u
s
ed
to
esti
m
ate
t
h
e
v
elo
cit
y
o
f
th
e
v
eh
ic
le
w
h
ic
h
is
v
er
y
i
n
ac
c
u
r
ate
m
et
h
o
d
.
T
im
e
-
d
if
f
er
en
ce
d
ca
r
r
ier
p
h
a
s
e
m
ea
s
u
r
e
m
en
t
s
at
t
w
o
s
u
cc
es
s
i
v
e
ep
o
ch
s
e
n
ab
les
to
esti
m
ate
th
e
v
elo
cit
y
a
t th
e
m
m
/s
ec
le
v
el
ac
c
u
r
ac
y
[
7
]
.
T
h
e
p
s
eu
d
o
-
r
an
g
e
m
ea
s
u
r
e
m
e
n
t (
)
ca
n
b
e
w
r
itte
n
as
()
u
s
i
o
n
e
p
h
t
r
o
p
d
c
t
t
O
E
T
(
1
2
)
W
h
er
e
d
is
t
h
e
ac
t
u
al
g
eo
m
etr
ic
r
ec
eiv
er
-
s
atellite
r
an
g
e
as
s
h
o
w
n
i
n
Fi
g
-
3;
c
is
th
e
v
elo
c
it
y
o
f
lig
h
t
a
n
d
,
us
tt
ar
e
u
s
er
a
n
d
s
atel
lit
e
clo
ck
er
r
o
r
s
;
,,
i
o
n
e
p
h
t
r
o
p
O
E
T
ar
e
co
m
m
o
n
m
o
d
e
er
r
o
r
s
as
in
d
icate
d
;
is
th
e
r
ec
eiv
er
w
h
ite
n
o
is
e
.
T
h
e
p
s
eu
d
o
r
an
g
e
an
d
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
t
s
(
)
ar
e
r
elat
ed
as
()
N
(
1
3
)
Her
e
N
is
th
e
to
tal
n
u
m
b
er
o
f
c
y
cles
as
s
h
o
w
n
in
F
ig
-
3
w
h
ic
h
is
ca
lled
th
e
in
te
g
er
a
m
b
ig
u
it
y
(
I
A
)
;
is
th
e
w
av
e
le
n
g
th
o
f
th
e
ca
r
r
ier
p
h
ase.
Su
b
s
tit
u
ti
n
g
E
q
-
1
2
in
1
1
a
n
d
d
o
in
g
s
o
m
e
r
ea
r
r
an
g
e
m
e
n
t
[
1
2
]
,
w
e
g
et
()
u
s
i
o
n
e
p
h
t
r
o
p
d
c
t
t
N
I
E
T
(
1
4
)
T
h
e
d
if
f
er
en
ce
b
et
w
ee
n
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
en
t
s
at
t
w
o
s
u
cc
e
s
s
i
v
e
ep
o
ch
s
1
j
t
an
d
j
t
as
s
h
o
w
n
in
Fi
g
-
3
,
n
eg
lec
tin
g
t
h
e
s
m
all
co
m
m
o
n
m
o
d
e
er
r
o
r
s
an
d
I
A
[
7
]
()
t
u
s
d
c
t
t
(
1
5
)
T
h
e
s
atellite
clo
ck
er
r
o
r
is
also
co
r
r
ec
te
d
f
r
o
m
ep
h
e
m
er
i
s
d
ata
ts
d
c
t
(
1
6
)
A
ll
v
ec
to
r
s
s
h
o
w
n
i
n
Fi
g
-
3
ar
e
ex
p
r
ess
ed
in
E
C
E
F f
r
a
m
e.
T
h
e
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
r
ec
eiv
er
–
s
atellite
r
an
g
e
at
t
w
o
s
u
cc
es
s
i
v
e
ep
o
ch
s
is
e
x
p
r
ess
ed
as
1
1
1
1
(
)
(
)
[
(
)
(
)
]
.
(
)
[
(
)
(
)
]
.
(
)
jj
j
j
j
j
j
j
d
d
t
d
t
r
t
b
t
e
t
r
t
b
t
e
t
(
1
7
)
W
ith
(
)
(
)
()
(
)
(
)
jj
j
jj
r
t
b
t
et
r
t
b
t
,
11
1
11
(
)
(
)
()
(
)
(
)
jj
j
jj
r
t
b
t
et
r
t
b
t
(
1
8
)
W
h
er
e
d
is
r
elate
d
to
th
e
ch
an
g
e
in
r
ec
eiv
er
p
o
s
itio
n
b
as [
b
o
o
k
]
.
(
)
.
j
d
e
t
b
(
1
9
)
Su
b
s
ti
tu
t
in
g
E
q
-
1
9
in
1
6
to
o
b
tain
t
h
e
ad
j
u
s
ted
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
4
,
Dec
em
b
er
2
0
1
5
:
2
43
–
2
53
248
(
)
.
t
j
u
e
t
b
c
t
(
2
0
)
T
h
er
e
ar
e
f
o
u
r
u
n
k
n
o
w
n
s
;
T
x
y
z
b
b
b
b
an
d
u
ct
in
2
4
,
th
er
ef
o
r
e
4
s
atellites,
at
least
ar
e
r
eq
u
ir
ed
to
b
e
v
is
ib
le
at
t
w
o
co
n
s
ec
u
ti
v
e
ep
o
ch
s
f
o
r
ac
cu
r
ate
v
elo
cit
y
esti
m
atio
n
.
T
h
is
is
th
e
m
ai
n
d
r
a
w
b
ac
k
o
f
t
h
e
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
t
s
.
I
f
t
h
er
e
ar
e
m
n
u
m
b
er
o
f
v
is
ib
le
s
atel
lites
(
m
≥
4
)
th
en
th
e
f
o
u
r
un
k
n
o
w
n
p
ar
a
m
eter
s
ca
n
b
e
es
ti
m
ated
u
s
i
n
g
lea
s
t sq
u
ar
e
m
et
h
o
d
.
1
()
TT
x
H
H
H
z
(
2
1
)
W
h
er
e
T
x
y
z
r
x
b
b
b
c
t
,
12
T
m
z
(
2
2
)
1
1
1
2
2
2
(
)
(
)
(
)
1
(
)
(
)
(
)
1
(
)
(
)
(
)
1
x
y
z
j
j
j
x
y
z
j
j
j
x
y
z
m
j
m
j
m
j
e
t
e
t
e
t
e
t
e
t
e
t
H
e
t
e
t
e
t
(
2
3
)
Fig
u
r
e
4
.
Satellite
-
r
ec
eiv
er
T
h
e
av
er
ag
e
v
elo
cit
y
o
f
t
h
e
v
e
h
icle
is
o
b
tai
n
ed
as
e
b
v
t
(
2
4
)
T
h
is
is
th
e
v
elo
cit
y
in
E
C
E
F f
r
a
m
e
w
h
ich
ca
n
b
e
tr
an
s
f
o
r
m
ed
in
to
th
e
n
-
f
r
a
m
e
as
nn
ee
v
C
v
(
2
5
)
P
o
s
itio
n
in
g
f
r
o
m
ca
r
r
ier
p
h
as
e
m
ea
s
u
r
e
m
e
n
ts
i
s
m
o
r
e
p
r
ec
is
e
th
a
n
f
r
o
m
co
d
e
p
h
ase.
A
c
cu
r
ac
y
o
f
ce
n
ti
m
etr
e
lev
el
i
n
p
o
s
itio
n
is
attain
ab
le
u
s
i
n
g
t
h
e
p
r
o
ce
d
u
r
e
o
f
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
e
n
ts
.
Ho
w
ev
er
,
t
h
e
in
te
g
er
a
m
b
i
g
u
it
y
is
a
cr
itical
is
s
u
e
to
b
e
r
eso
l
v
ed
f
o
r
p
r
ec
is
e
p
o
s
itio
n
in
g
[
4
]
.
Ma
n
y
tec
h
n
iq
u
es
h
a
v
e
b
ee
n
r
esear
ch
e
d
an
d
p
r
o
p
o
s
ed
to
r
e
m
o
v
e
t
h
i
s
a
m
b
i
g
u
it
y
.
As
g
i
v
en
i
n
E
q
-
1
2
,
th
e
ca
r
r
ier
p
h
a
s
e
m
ea
s
u
r
e
m
e
n
t
is
m
o
d
elled
as
()
r
s
i
o
n
e
p
h
t
r
o
p
d
c
t
t
I
E
T
N
(
2
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
I
n
teg
r
a
tio
n
a
n
d
S
imu
la
tio
n
o
f
I
N
S
/GN
S
S
S
ystem
Usi
n
g
th
e
A
p
p
r
o
a
ch
o
f Ca
r
r
ier P
h
a
s
e
...
(
K
h
a
n
B
a
d
s
h
a
h
l)
249
W
h
er
e
d
is
th
e
tr
u
e
g
eo
m
e
tr
ic
r
an
g
e
b
et
w
ee
n
th
e
r
ec
ei
v
er
an
d
s
atellite
as
s
h
o
w
n
in
Fig
-
3
.
T
h
e
v
ar
iab
les ca
p
ed
w
it
h
“
~”
an
d
“
^”
r
ep
r
esen
t r
esp
ec
ti
v
el
y
th
e
m
ea
s
u
r
ed
an
d
esti
m
ated
q
u
a
n
t
ities
.
2
2
2
(
)
(
)
(
)
s
r
s
r
s
r
d
x
x
y
y
z
z
(
2
7
)
W
h
er
e
T
r
r
r
x
y
z
is
th
e
r
ec
ei
v
er
’
s
tr
u
e
p
o
s
itio
n
a
n
d
T
s
s
s
x
y
z
is
th
e
s
atelli
te
p
o
s
itio
n
in
E
C
E
F
f
r
a
m
e.
E
q
u
atio
n
-
2
6
is
a
n
o
n
li
n
ea
r
f
u
n
ctio
n
w
h
ic
h
ca
n
b
e
li
n
ea
r
ized
ar
o
u
n
d
a
b
est e
s
ti
m
ated
p
o
s
itio
n
o
f
th
e
r
ec
eiv
er
.
P
er
tu
r
b
in
g
t
h
e
r
e
ce
iv
er
’
s
p
o
s
itio
n
ab
o
u
t t
h
e
esti
m
ated
p
o
s
itio
n
ˆˆ
ˆ
T
r
r
r
x
y
z
ˆ
r
r
r
x
x
x
,
ˆ
r
r
r
y
y
y
,
ˆ
r
r
r
z
z
z
(
2
8
)
Su
b
s
ti
tu
t
in
g
E
q
-
2
8
in
2
7
an
d
s
i
m
p
li
f
y
in
g
(
)
(
)
(
)
ˆ
ˆ
r
s
r
r
s
r
r
s
r
x
x
x
y
y
y
z
z
z
dd
d
(
2
9
)
Her
e
ˆ
d
is
th
e
esti
m
ated
r
an
g
e.
Usi
n
g
t
h
e
v
al
u
e
o
f
d
in
2
6
an
d
n
eg
lec
tin
g
t
h
e
co
m
m
o
n
m
o
d
e
er
r
o
r
s
(
)
(
)
(
)
ˆ
ˆ
r
s
r
r
s
r
r
s
r
r
x
x
x
y
y
y
z
z
z
d
c
t
N
d
(
3
0
)
E
q
u
atio
n
-
3
0
is
f
u
r
th
er
s
i
m
p
li
f
i
ed
as
z
A
x
(
3
1
)
W
h
er
e
ˆ
zd
,
T
r
r
r
r
x
x
y
z
N
c
t
(
3
2
)
2
2
2
ˆˆ
ˆ
1
ˆˆ
ˆ
(
)
(
)
(
)
1
r
s
r
s
r
s
r
s
r
s
r
s
x
y
z
x
x
y
y
z
z
A
x
x
y
y
z
z
A
A
A
(
3
3
)
I
t
m
u
s
t b
e
n
o
ted
h
er
e
th
at
n
u
m
b
er
o
f
u
n
k
n
o
w
n
s
h
as i
n
cr
ea
s
e
d
b
y
i
n
teg
er
a
m
b
ig
u
it
y
.
Fo
r
f
o
u
r
v
i
s
ib
le
s
atellite
s
(
m
=
4
)
at
ep
o
ch
t
,
eq
u
atio
n
s
3
2
an
d
3
3
w
ill
m
o
d
i
f
y
a
s
[
1
2
]
.
1
2
3
4
T
r
r
r
r
x
x
y
z
N
N
N
N
c
t
(
3
4
)
11
22
33
44
ˆ
ˆ
ˆ
ˆ
d
d
z
d
d
,
1
1
1
222
333
444
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
x
y
z
x
y
z
x
y
z
x
y
z
A
A
A
AAA
A
AAA
AAA
(
3
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
4
,
Dec
em
b
er
2
0
1
5
:
2
43
–
2
53
250
3.
SI
NS/
G
N
SS
I
NT
E
G
RA
T
I
O
N
AL
G
O
RI
T
H
M
I
n
th
i
s
in
teg
r
atio
n
alg
o
r
it
h
m
t
h
e
GP
S
d
er
iv
ed
attitu
d
e,
p
o
s
it
io
n
an
d
v
elo
cit
y
p
ar
a
m
eter
s
ar
e
u
s
ed
as
a
m
ea
s
u
r
e
m
e
n
t
to
t
h
e
ce
n
tr
ali
ze
d
Kal
m
an
Fil
ter
.
T
h
e
Kalm
an
f
il
ter
(
KF)
is
th
e
o
p
ti
m
al
est
i
m
a
to
r
th
at
m
i
n
i
m
izes
t
h
e
m
ea
n
s
q
u
ar
e
er
r
o
r
w
h
e
n
th
e
s
tate
a
n
d
m
ea
s
u
r
e
m
en
t
d
y
n
a
m
ics
ar
e
lin
ea
r
i
n
n
atu
r
e,
p
r
o
v
id
ed
th
e
p
r
o
ce
s
s
an
d
m
ea
s
u
r
e
m
en
t
n
o
is
es
ar
e
m
o
d
elled
as
w
h
ite
Ga
u
s
s
ian
.
T
h
e
SIN
S
er
r
o
r
s
d
y
n
a
m
ic
is
a
co
n
ti
n
u
o
u
s
ti
m
e
p
r
o
ce
s
s
g
o
v
er
n
ed
b
y
a
li
n
ea
r
s
to
ch
asti
c
eq
u
a
tio
n
s
.
x
F
x
w
(
3
6
)
k
k
k
k
z
H
x
(
3
7
)
W
h
er
e
x
is
t
h
e
s
tate
v
ec
to
r
an
d
F
is
t
h
e
d
y
n
a
m
ic
m
atr
i
x
;
w
an
d
k
ar
e
p
r
o
ce
s
s
an
d
m
ea
s
u
r
e
m
en
t
w
h
ite
n
o
is
es.
F
m
atr
ix
i
s
o
b
tain
ed
b
y
co
m
b
in
in
g
an
d
r
ea
r
r
an
g
in
g
t
h
e
ter
m
s
in
E
q
s
-
1
,
2
,
3
an
d
4
.
T
h
e
s
tate
v
ec
to
r
is
d
esig
n
ed
as
.
(
)
(
)
(
)
(
)
(
)
T
T
n
T
T
b
T
b
T
b
T
x
v
p
l
(
3
8
)
W
h
er
e
b
l
is
t
h
e
le
v
er
ar
m
v
ec
to
r
f
r
o
m
I
NS
to
th
e
GNS
S
an
te
n
n
a
ce
n
tr
e,
e
x
p
r
ess
ed
i
n
b
o
d
y
f
r
a
m
e.
T
h
e
GNSS
d
er
i
v
ed
attit
u
d
e,
v
elo
cit
y
a
n
d
p
o
s
itio
n
ar
e
s
u
b
tr
a
cted
f
r
o
m
I
NS
d
ata
a
n
d
u
s
ed
as
a
m
ea
s
u
r
e
m
en
t
s
to
th
e
ce
n
eter
lized
L
KF.
T
h
e
d
esig
n
m
atr
i
x
f
o
r
attit
u
d
e
m
ea
s
u
r
e
m
en
t
s
is
co
n
s
tr
u
c
ted
h
er
e
f
o
r
f
u
s
i
n
g
t
h
e
d
ata
o
f
th
e
t
w
o
s
y
s
te
m
s
.
Def
i
n
e
t
h
e
attitu
d
e
m
ea
s
u
r
e
m
e
n
ts
a
s
T
g
p
s
g
p
s
g
p
s
g
p
s
A
,
T
i
n
s
i
n
s
i
n
s
i
n
s
A
(
3
9
)
i
n
s
g
p
s
A
A
A
(
4
0
)
T
TT
i
n
s
i
n
s
i
n
s
g
p
s
g
p
s
g
p
s
(
4
1
)
T
h
e
attitu
d
e
d
if
f
er
en
ce
is
r
elat
ed
to
th
e
attitu
d
e
er
r
o
r
v
ec
to
r
as
E
na
N
b
w
U
CC
(
4
2
)
W
h
er
e
a
w
C
is
ca
lcu
lated
as
c
o
s
0
sin
c
o
s
0
1
sin
sin
0
c
o
s
c
o
s
a
w
C
(
4
3
)
1
(
)
(
)
E
a
n
T
w
b
N
U
CC
(
4
4
)
T
h
e
s
en
s
iti
v
e
m
ea
s
u
r
e
m
e
n
t
m
atr
ix
is
d
esi
g
n
ed
f
o
r
th
e
attit
u
d
e
m
ea
s
u
r
e
m
e
n
t
s
as
11
1
3
6
3
6
3
3
(
)
(
)
0
0
0
an
wb
H
C
C
(
4
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
I
n
teg
r
a
tio
n
a
n
d
S
imu
la
tio
n
o
f
I
N
S
/GN
S
S
S
ystem
Usi
n
g
th
e
A
p
p
r
o
a
ch
o
f Ca
r
r
ier P
h
a
s
e
...
(
K
h
a
n
B
a
d
s
h
a
h
l)
251
W
e
co
n
s
id
er
th
e
lev
er
ar
m
e
f
f
ec
t
to
i
m
p
r
o
v
e
th
e
p
o
s
itio
n
an
d
v
elo
cit
y
ac
c
u
r
ac
y
o
f
t
h
e
in
te
g
r
ated
s
y
s
te
m
.
I
f
b
l
is
a
le
v
er
ar
m
v
ec
t
o
r
f
r
o
m
I
NS c
alib
r
atio
n
ce
n
tr
e
to
th
e
GN
SS
a
n
ten
n
a
ce
n
tr
e
e
x
p
r
ess
ed
in
b
o
d
y
f
r
a
m
e,
t
h
en
G
NSS p
o
s
itio
n
an
d
v
elo
cit
y
v
ec
to
r
s
ca
n
b
e
ex
p
r
ess
ed
as
.
n
n
b
g
p
s
r
v
b
r
p
M
C
l
(
4
6
)
()
n
n
n
b
b
g
p
s
i
n
s
b
e
b
v
v
C
l
(
4
7
)
T
h
e
m
ea
s
u
r
e
m
e
n
t
m
o
d
el
f
o
r
v
elo
cit
y
an
d
p
o
s
itio
n
i
s
co
n
s
tr
u
cted
as
.
1
2
nn
g
p
s
g
p
s
n
n
n
n
n
i
n
s
g
p
s
i
n
s
g
p
s
z
p
r
p
p
r
z
v
v
v
v
v
(
4
8
)
Su
b
s
ti
tu
t
in
g
E
q
-
4
8
in
4
6
&
4
7
,
w
e
g
et
1
nb
r
v
b
z
p
M
C
l
(
4
9
)
2
()
n
n
b
b
b
e
b
z
v
C
l
(
5
0
)
T
h
e
s
en
s
iti
v
e
m
ea
s
u
r
e
m
e
n
t
m
atr
ix
f
o
r
p
o
s
itio
n
a
n
d
v
elo
cit
y
is
:
3
3
3
3
3
3
3
6
2
3
3
3
3
3
3
3
6
0
0
0
(
)
0
0
0
nb
b
e
b
n
r
v
b
IC
H
I
M
C
(
5
1
)
T
h
e
f
in
al
m
ea
s
u
r
e
m
e
n
t
m
o
d
el
f
o
r
attitu
d
e,
v
elo
cit
y
a
n
d
p
o
s
itio
n
m
ea
s
u
r
e
m
e
n
ts
i
s
o
b
tain
ed
b
y
co
m
b
i
n
g
E
q
-
4
5
an
d
5
1
as
1
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
6
3
3
3
3
3
3
3
6
(
)
(
)
0
0
0
0
0
0
0
(
)
0
0
0
a
n
T
wb
nb
b
e
b
n
r
v
b
CC
H
I
C
I
M
C
(
5
2
)
4.
SI
M
UL
AT
I
O
N
O
F
T
H
E
I
N
T
E
G
RA
T
E
D
SYS
T
E
M
T
h
e
attitu
d
e,
v
elo
cit
y
a
n
d
p
o
s
itio
n
m
ea
s
u
r
e
m
en
t
s
o
f
GP
S
s
y
s
te
m
ar
e
o
b
tain
ed
f
r
o
m
s
i
m
u
latio
n
o
f
tr
aj
ec
to
r
y
d
ata
u
s
in
g
Ma
tlab
en
v
ir
o
n
m
e
n
t.
A
lo
w
er
p
r
ec
is
io
n
ME
MS
b
ased
I
MU
(
S
T
I
M3
0
0
)
p
ar
am
eter
s
ar
e
u
s
ed
to
an
al
y
s
e
t
h
e
p
er
f
o
r
m
a
n
ce
an
d
v
alid
it
y
o
f
th
e
i
n
te
g
r
at
ed
s
y
s
te
m
t
h
r
o
u
g
h
s
i
m
u
latio
n
r
esu
lts
.
T
h
e
in
i
tial
m
is
a
lig
n
m
e
n
t
an
g
les,
w
it
h
lar
g
e
h
ea
d
in
g
an
g
le
ar
e
ass
u
m
ed
to
s
h
o
w
t
h
e
ef
f
ec
ti
v
en
e
s
s
o
f
th
e
GNS
S
attitu
d
e
m
ea
s
u
r
e
m
e
n
t
s
.
Si
m
u
latio
n
r
esu
lt
s
ar
e
p
r
o
d
u
ce
d
w
it
h
;
G
y
r
o
d
r
if
t:
4
d
eg
/h
o
u
r
,
G
y
r
o
r
an
d
o
m
w
al
k
:
1
.
7
d
eg
/√
h
o
u
r
,
A
cc
eler
o
m
eter
b
ia
s
:
1
.
5
×1
0
-
3
g
,
A
cc
eler
o
m
eter
r
an
d
o
m
w
al
k
:
0
.
2
×1
0
-
3
g
,
L
ev
e
r
ar
m
v
ec
to
r
:
[
1
2
3]
T
m
,
GNS
S a
ttit
u
d
e,
v
elo
cit
y
an
d
p
o
s
itio
n
ac
cu
r
ac
y
r
esp
ec
t
iv
el
y
ar
e:
0
.
3
d
eg
,
[
1
1
5
]
T
m
,
0
.
5
cm
/
s
ec
.
Fig
u
r
e
5
.
I
NS
A
tt
itu
d
e
E
r
r
o
r
Fig
u
r
e
6
.
I
NS
V
elo
cit
y
E
r
r
o
r
200
400
600
800
1000
-
4
0
-
2
0
0
(
'
)
200
400
600
800
1000
-
4
0
-
2
0
0
(
'
)
200
400
600
800
1000
-
6
0
-
4
0
-
2
0
(
'
)
T
i
m
e
(
s
)
200
400
600
800
1000
20
40
60
v
E
(
m
/
s
)
200
400
600
800
1000
-
6
0
-
4
0
-
2
0
0
v
N
(
m
/
s
)
200
400
600
800
1000
10
20
30
v
U
(
m
/
s
)
T
i
m
e
(
s
)
200
400
600
800
1000
-
4
0
-
2
0
0
(
'
)
200
400
600
800
1000
-
4
0
-
2
0
0
(
'
)
200
400
600
800
1000
-
6
0
-
4
0
-
2
0
(
'
)
T
i
m
e
(
s
)
200
400
600
800
1000
20
40
60
v
E
(
m
/
s
)
200
400
600
800
1000
-
6
0
-
4
0
-
2
0
0
v
N
(
m
/
s
)
200
400
600
800
1000
10
20
30
v
U
(
m
/
s
)
T
i
m
e
(
s
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
4
,
Dec
em
b
er
2
0
1
5
:
2
43
–
2
53
252
Fig
u
r
e
7
I
NS p
o
s
itio
n
er
r
o
r
Fig
u
r
e
8
I
NS/GNSS
at
tit
u
d
e
er
r
o
r
Fig
u
r
e
9
I
NS/GNSS
at
tit
u
d
e
er
r
o
r
Fig
u
r
e
1
0
I
NS/GNS v
elo
cit
y
e
r
r
o
r
Fig
u
r
e
1
1
I
NS/GNSS
p
o
s
itio
n
er
r
o
r
Fig
u
r
e
5
,
Fig
u
r
e
6
an
d
Fig
u
r
e
7
s
h
o
w
th
e
s
tan
d
alo
n
e
M
E
MS
I
NS
er
r
o
r
s
g
r
o
w
t
h
w
h
ile
Fig
u
r
e
8
s
h
o
w
s
th
e
attit
u
d
e
er
r
o
r
o
f
t
h
e
in
te
g
r
ated
s
y
s
te
m
w
it
h
o
u
t
u
s
in
g
t
h
e
at
tit
u
d
e
o
b
s
er
v
atio
n
.
Fig
u
r
e
9
ill
u
s
tr
ates
th
e
attit
u
d
e
er
r
o
r
o
f
th
e
in
te
g
r
ated
s
y
s
te
m
u
s
i
n
g
t
h
e
attit
u
d
e
m
ea
s
u
r
e
m
e
n
t
to
th
e
f
ilter
in
th
e
i
n
it
ial
s
ta
g
e
w
h
ic
h
s
h
o
w
ed
a
f
aster
d
ec
r
ea
s
e
in
th
e
att
it
u
d
e
er
r
o
r
s
.
T
h
e
h
ea
d
in
g
a
n
g
le
ac
c
u
r
ac
y
i
s
i
m
p
r
o
v
ed
w
h
ic
h
i
s
v
er
y
u
s
e
f
u
l
f
o
r
th
e
n
av
i
g
atio
n
s
y
s
te
m
d
u
r
i
n
g
n
o
n
ac
ce
ler
atin
g
p
er
i
o
d
s
.
Si
m
ilar
l
y
t
h
e
v
elo
cit
y
an
d
p
o
s
itio
n
er
r
o
r
s
o
f
th
e
in
teg
r
ated
s
y
s
te
m
s
h
o
w
n
i
n
Fi
g
u
r
e
1
0
an
d
Fig
u
r
e
1
1
ar
e
b
o
u
n
d
ed
to
th
e
c
m
le
v
el
ac
cu
r
ac
y
.
5.
CO
NCLU
SI
O
N
GNSS
at
titu
d
e,
v
elo
cit
y
an
d
p
o
s
itio
n
f
r
o
m
ca
r
r
ier
p
h
ase
m
ea
s
u
r
e
m
en
t
s
ar
e
m
at
h
e
m
a
tical
l
y
d
er
iv
ed
an
d
d
is
cu
s
s
ed
f
o
r
ac
cu
r
ate
in
t
eg
r
atio
n
.
L
o
o
s
el
y
co
u
p
led
ap
p
r
o
ac
h
is
u
s
ed
to
f
u
s
e
th
e
d
at
a
o
f
I
NS
an
d
GNSS
u
s
i
n
g
ce
n
tr
ali
s
ed
L
KF.
A
lo
w
ac
cu
r
ac
y
ME
MS
b
ased
I
MU
(
STI
M3
0
0
)
p
a
r
am
eter
s
ar
e
u
s
ed
to
g
en
er
ate
th
e
I
NS
an
d
GNSS
d
ata
f
o
r
s
i
m
u
latio
n
.
L
ar
g
e
at
tit
u
d
e
er
r
o
r
is
u
s
ed
to
s
h
o
w
th
e
e
f
f
ec
ti
v
e
n
es
s
o
f
th
e
G
NSS
attitu
d
e
m
ea
s
u
r
e
m
e
n
t
s
.
Si
m
u
l
atio
n
r
es
u
lts
s
h
o
w
ed
t
h
at
att
i
tu
d
e
er
r
o
r
s
d
ec
r
ea
s
e
m
u
c
h
f
a
s
ter
th
a
n
t
h
e
f
ilter
w
it
h
o
u
t
attit
u
d
e
m
ea
s
u
r
e
m
e
n
t
s
.
T
h
e
ac
cu
r
ac
y
o
f
h
ea
d
in
g
an
g
le
i
s
h
i
g
h
l
y
i
m
p
r
o
v
ed
w
h
ic
h
is
v
er
y
i
m
p
o
r
tan
t
f
o
r
in
it
ializatio
n
an
d
f
o
r
n
a
v
ig
a
tio
n
s
y
s
te
m
s
d
u
r
in
g
t
h
e
b
en
ig
n
o
r
n
o
n
ac
ce
ler
ati
n
g
p
er
io
d
.
T
h
er
e
is
a
200
400
600
800
1000
-
1
0
0
10
20
(
'
)
200
400
600
800
1000
-
1
0
0
10
20
(
'
)
200
400
600
800
1000
0
50
100
150
(
'
)
T
i
m
e
(
s
)
200
400
600
800
1000
-2
-1
0
x
1
0
4
L
(
m
)
200
400
600
800
1000
1
2
3
x
1
0
4
(
m
)
200
400
600
800
1000
2000
4000
6000
8000
10000
12000
h
(
m
)
T
i
m
e
(
s
)
200
400
600
800
1000
-
1
0
0
10
20
(
'
)
200
400
600
800
1000
-
1
0
0
10
20
(
'
)
200
400
600
800
1000
0
50
100
150
(
'
)
T
i
m
e
(
s
)
200
400
600
800
1000
-2
-1
0
x
1
0
4
L
(
m
)
200
400
600
800
1000
1
2
3
x
1
0
4
(
m
)
200
400
600
800
1000
2000
4000
6000
8000
10000
12000
h
(
m
)
T
i
m
e
(
s
)
200
400
600
800
1000
-5
0
5
(
'
)
200
400
600
800
1000
-
1
0
-5
0
(
'
)
200
400
600
800
1000
-
2
0
-
1
0
0
(
'
)
T
i
m
e
(
s
)
200
400
600
800
1000
-
0
.
0
5
0
0
.
0
5
v
E
(
m
/
s
)
200
400
600
800
1000
-
0
.
0
5
0
0
.
0
5
v
N
(
m
/
s
)
200
400
600
800
1000
-
0
.
0
4
-
0
.
0
2
0
0
.
0
2
0
.
0
4
v
U
(
m
/
s
)
T
i
m
e
(
s
)
200
400
600
800
1000
-5
0
5
(
'
)
200
400
600
800
1000
-
1
0
-5
0
(
'
)
200
400
600
800
1000
-
2
0
-
1
0
0
(
'
)
T
i
m
e
(
s
)
200
400
600
800
1000
-
0
.
0
5
0
0
.
0
5
v
E
(
m
/
s
)
200
400
600
800
1000
-
0
.
0
5
0
0
.
0
5
v
N
(
m
/
s
)
200
400
600
800
1000
-
0
.
0
4
-
0
.
0
2
0
0
.
0
2
0
.
0
4
v
U
(
m
/
s
)
T
i
m
e
(
s
)
200
400
600
800
1000
-2
-1
0
1
L
(
m
)
200
400
600
800
1000
-1
-
0
.
5
0
0
.
5
(
m
)
200
400
600
800
1000
-4
-2
0
h
(
m
)
T
i
m
e
(
s
)
Evaluation Warning : The document was created with Spire.PDF for Python.