TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 64
5
4
~ 646
0
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.480
3
6454
Re
cei
v
ed O
c
t
ober 1
6
, 201
3; Revi
se
d Ju
ne 2, 2014; A
c
cepted
Jun
e
16, 2014
Resear
ch on Attitude Measur
e
ment for Ballistic
Correction Rocket
Liang Zhi-jia
n*, Ma Tie-h
u
a
Ke
y
Lab
orator
y of Instrumentati
on Scie
nce &
D
y
namic Me
as
ureme
n
t, North Universit
y
of C
h
in
a,
T
a
iyua
n 03
005
1, Shan
xi, Ch
in
a, 1503
51
74
37
8
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zhijia
nl
ian
g
@
163.com
A
b
st
r
a
ct
Ballistic c
o
rrect
ion rock
et is a
kind of s
m
art a
m
mu
ni
tio
n
w
h
i
c
h can attac
h
ai
ms exactly. B
a
sed
on
do
mestic
an
d forei
gn l
i
teratur
e
, the tech
nol
o
g
y of f
lig
ht attitude
meas
ure
m
ent tech
nol
ogy
w
a
s summari
zed
.
T
he proc
ess o
f
the rese
arch
incl
udes
in
de
pen
de
ntly
in
ertial measur
e
m
e
n
t
unit and
in
ertial navi
gati
o
n
system
. The pr
evious stage
is
the
meas
urement technol
ogy
only depend on a na
vigation equipm
e
nt,
suc
h
as acc
e
ler
o
meter, Gyro or
electr
omag
ne
tic sens
or
s et
c, the l
a
tter
me
ans
co
mb
i
natio
ns of s
e
veral
me
asur
e
m
ent
units, on th
e
basis of co
mpl
e
mentary
adva
n
tages in
p
e
rformanc
e to i
m
prove c
o
mputi
n
g
accuracy e
a
ch
other. Based
on the
me
asur
ement tech
nol
ogy w
a
s ana
ly
z
e
d
an
d co
mp
ared, confi
gur
a
t
ion,
mer
i
t an
d d
e
m
er
its of multi
accel
e
ro
mete
r w
e
re di
scus
s
ed i
n
d
e
tail.
T
he pa
per
pro
s
pected t
he fu
tur
e
deve
l
op
ment o
f
this technol
og
y finally.
Ke
y
w
ords
:
ball
i
stic corre
ction rocket,
inertia
l
nav
i
gatio
n syste
m
, attitude
me
asur
e
m
ent,
inertia
l
me
asur
e
m
ent unit
Copy
right
©
2014 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
The pa
ram
e
ter of air ta
rg
e
t
flight attitude em
b
r
a
c
ed v
a
riation
of roll
velocity, pitch angle,
yaw a
ngula
r
etc, which pl
ayed a
n
imp
o
rtant
role
in
traje
c
tory
correctio
n
a
n
d
co
ntrollin
g t
he
attitude. Do
mestic a
nd foreig
n re
se
a
r
ch o
n
ai
r t
a
rget attitud
e
testing technolo
g
y is very
extensive, d
e
veloping
fro
m
the ea
rlie
st use
of G
y
ro or
accel
e
rom
e
ter m
e
asu
r
ing
ang
u
l
ar
accele
ration
to now re
se
arch te
chni
q
ue on
va
rio
u
s
ine
r
tial n
a
v
igation sy
stems. T
he a
r
ticle
pre
s
ente
d
a configuration a
nd the compu
t
ation al
go
rith
m analysi
s
o
n
the pro
c
e
ss of technol
og
y,
indep
ende
ntly inertial
mea
s
ureme
n
t unit
and
ine
r
tial n
a
vigation
syst
em. The
p
r
ob
lem ne
ed to
b
e
resolved of the future devel
opment was
pre
s
ente
d
finally.
2. Independe
ntly
Inertial Measur
e
men
t
Unit
In the ine
r
tial
navigation
system, Gyro
wa
s u
s
ed
init
ially to mea
s
ure th
e flight
attitude
angle, it ca
n
also m
e
a
s
ure
the flight attitude di
spla
ce
ment of pitch
angle, yaw
angul
ar a
nd roll
angle. When
air targ
ets
were MM
W-RCT
CM a
n
d
its perfo
rma
n
ce
su
ch a
s
volume, sp
eed,
accele
ration
and imp
a
ct
resi
stan
ce et
c had a
high
requireme
nt, it req
u
ire
d
that
Gyro h
ad th
ese
cha
r
a
c
teri
stics
su
ch
as sm
all volume, li
g
h
t wei
gh
t, st
rong im
pa
ct re
sista
n
ce a
nd
wide
ra
nge
et
c.
With the
developme
n
t of the technol
og
y of Gyro,
it had d
e
velop
e
d
from th
e 18
th centu
r
y Ri
gid
Rotor Gyro t
o
Liq
u
id
Flo
a
ted Gy
ro,
Gas Lu
bri
c
at
ed Gy
ro,
DT
G (Dynami
c
a
lly Tuned
Gy
ro),
c
u
rrently Elec
tros
tatic
Gyro, Las
er
Gyro, Fiber
Opti
c Gyro and
Hemi
sph
e
ri
ca
l Re
son
a
tor
Gyro
[1-3]
were
wi
dely u
s
ed. A
m
ong
them, t
he Fi
ber
Opti
c Gy
ro
devel
opment
is the
mo
st qui
ckly, and
from the future develo
p
m
ent pro
s
pe
ct
s, it is
the
main dire
ctio
n of the future develo
p
m
ent.
Although the
developm
ent
of the gyro
scope is
more than on
e hu
n
d
red ye
ars of
history, to m
eet
the nee
ds of
developm
ent
of future milit
ary, we
n
eed
to contin
ue t
o
red
u
ce the
volume, quali
t
y
and cost, to continue to im
prove the reli
ability, stability and dura
b
ili
ty.
Due to the
traditional m
e
ch
ani
cal gy
ro was m
a
d
e
based o
n
angula
r
mo
mentum
con
s
e
r
vation
prin
ciple,
which
ha
s co
mplex struct
ure
s
a
nd la
rger vol
u
me,
new
gyro
su
ch a
s
Laser Gyro, Fiber O
p
tic G
y
ro and mi
cromechani
ca
l
gyrosco
pe ha
ve highe
r co
st, poorer im
p
a
ct
resi
stan
ce, i
n
here
n
t zero
-d
rift and th
e e
r
ror is
accu
mu
lated g
r
ad
uall
y
with chan
g
e
of time, the
n
affecting the
preci
s
io
n of resolvin
g of syst
em attitude angl
e. So engine
ers and tech
nici
a
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Attitude Measurem
ent for Ballistic
Corre
c
tion Ro
cket (Liang Zhi
-
jian
)
6455
resea
r
ched
a
nd u
s
e
d
a
ccelero
meter in
stead
of Gy
ro, and
solve
d
the
ang
ular velocity of fli
ght
carrie
r from
spe
c
ific force
measu
r
ed b
y
accele
rom
e
ter. The re
se
arch sh
owed
that Non-gy
ro
Strap-d
o
wn Inertial
Navig
a
tion System
was
suit
abl
e for inertial
guida
nce wit
h
larg
e dyna
mic
rang
e a
n
d
sh
ort n
a
vigation
time, an
d h
a
d
adva
n
tage
s of lo
w
co
st, l
o
w
po
wer
co
nsum
ption, lo
ng
life, high reliability, anti-high over
load. With the emergence of hi
gh precisi
on ac
celerometer and
filter techniq
u
e
developm
e
n
t, accel
e
ro
m
e
ter
ca
n achi
eve better na
vigation pre
c
i
s
ion.
The te
chn
o
lo
gy of usi
ng t
he a
c
celero
meter
in
stea
d of Gyro
to
mea
s
ure flight body
attitude deve
l
oped for al
most 50 yea
r
s. As ea
rly
as in 196
2, Victor B.Co
rey discussed
the
prin
ciple
of th
e u
s
e of li
ne
ar a
c
cele
rom
e
ters me
asuri
ng the
ang
ul
ar a
c
cele
ratio
n
, put forwa
r
d a
s
i
mple presentation of an acc
e
lerometer [4]. In
the
year of
196
5, V.Krishn
a
n
discu
s
sed
the
mathemati
c
al
prin
ciple
s
of
measuri
ng a
n
gular
vel
o
city
and lin
ear a
c
celeration of
body by line
a
r
accele
rom
e
te
r installe
d in the evenn
ess
rotati
ng di
sk [
5
]. Alfred R.Schul
er then in
1967 came u
p
with the
idea
of a lin
ea
r
accele
rom
e
te
r me
asurin
g
the rotatio
nal
motion
of th
e obj
ect, an
d
a
variety of accele
rom
e
ter
config
uratio
n
[6]. A.
J.Padgaon
ka
r in 1
975 presente
d
the metho
d
o
f
cal
c
ulatin
g a
ngula
r
a
c
cel
e
ration
and
linear acceleratio
n
of
body by
usin
g me
ch
anics
cho
r
eo
graphy
of ni
ne-accelero
meter [7
]. In 198
2,
S
h
muel
J.Merh
av furthe
r
st
udied
no
n-gy
ro
inertial mea
s
urem
ent unit con
s
i
s
ted of rotating or
vibrating accele
rometer tripl
e
s, and discussed
the method
of isolatin
g
angul
ar velo
city and lin
e
a
r a
c
cele
rati
on from
accelero
meter
o
u
tpu
t
s
i
gnal[8].In the year of 1991, Al
grain elaborated that
at leas
t
6
acc
e
lerometers c
o
uld measure
angul
ar a
c
ce
leration
and
linear
accele
ration of the
object. Che
n
in 1994
di
scusse
d a n
o
vel
desi
gn of u
s
i
ng 6
accele
ro
meters to me
asu
r
e
atti
tude
. In 1999, L
e
e
gave an
alg
o
r
ithm of u
s
in
g
6
accele
rom
e
te
rs to m
e
a
s
ure
rotation mov
e
ment of
an
o
b
ject.And the
same ye
ar, Xi
e Ch
un-si a
n
d
others offere
d an idea, th
at was
usin
g
multiple la
se
r tracke
r to d
e
termin
e the missil
e
po
sition,
postu
re an
d
rolling
rate,Wang Gu
ang
-l
ong an
d othe
rs
in BIT (Be
ijing Institute of Tech
nolog
y)
also p
r
op
ose
d
that to use Earth Magn
etic Field
Sen
s
or
to mea
s
ure p
r
oje
c
tile attitu
de. In 20
00,
Thoma
s
Harkins an
d othe
rs propo
se
d the metho
d
of determini
ng
attitude by ph
ase info
rmati
on
of Magn
etic
Senso
r
s out
put wh
en ze
ro crossing. In
2001, Chi
n
-Woo pro
p
o
s
ed
a suffici
ent
c
o
nd
itio
n
to
de
te
r
m
ine
w
e
ath
e
r
th
e ac
ce
le
r
o
me
te
r
alloc
a
tion sc
heme was
feas
ible. In 2002, Lee
improve
d
filtering
algo
rith
m. In the year of
20
03,
Gui Yan
-
ning
and othe
rs
put forward
and
reali
z
ed
Sola
r Aspe
ct An
gle telem
e
tering sy
stem. I
n
200
4, Zh
a
ng
Wei-hua
and oth
e
rs p
u
t
forwa
r
d
the d
e
tection
of ro
cket rotatio
n
angle
by
Utili
zing
Ge
omag
netic In
du
ctio
n Coil. In 20
0
9
,
Li
Di
ng and
others put
fo
rwa
r
d
a met
hod of
me
as
uring
attitude
by the
co
m
b
ination
of t
w
o
Magneti
c
Sen
s
ors.
Usi
ng la
ser
to measu
r
e
missil
e
po
sition and attitude was
sui
t
able for mi
dco
u
rse
guida
nce an
d terminal
co
rre
ction, a
s
a
result
of gro
und-ba
sed l
a
ser
dev
ice, thus limitin
g the
missil
e
'
s
fligh
t
distance; the
method
of determi
ning attitude
by
phase inform
a
t
ion of Magn
etic
Senso
r
s outp
u
t when zero
cro
ssi
ng co
u
l
d only figure
out one information of pitch angl
e whe
n
proje
c
tile b
o
d
y
span for
a roun
d, and t
he re
sult wa
s bina
ry, whi
c
h ne
ed to e
s
timate the p
i
tch
angle
with th
e help of on
e
of the Magn
etic Sen
s
or
s.
The metho
d
of using Ea
rt
h Magn
etic Fi
eld
Senso
r
to m
easure
proje
c
tile attitude
had b
een
applie
d for
some type of
missile attitude
measurement
, the result
s o
f
measu
r
em
e
n
t met the
re
quire
ment
s, the testing
system ha
d sim
p
le
stru
cture, st
rong i
m
pa
ct re
sista
n
ce
, si
gn
al dete
c
tion
circuit
with
hig
h
sen
s
itivity,
stable
work, t
he
main de
sign i
dea
s of whi
c
h
was th
at thre
e coo
r
di
nate
axes of Earth
Magneti
c
Fie
l
d Sensor
were
fixedly con
n
e
c
ted i
n
p
r
oj
ectile co
ordi
nat
e, wh
i
c
h
was used to
me
a
s
ure th
e axial
ea
rth ma
gne
tic
field compo
n
ent, and
then
mea
s
u
r
e
on
e of pit
c
h
an
gle, yaw an
g
u
lar
and
roll
angle
thro
ug
h the
auxiliary met
hod to dete
r
mine attitude
angle of the
flight body co
o
r
dinate
sy
ste
m
in the geod
etic
coordinate
system, but the met
hod need auxiliary
m
eans, essentially still
could not complet
e
ly
rely on e
a
rth
magneti
c
re
alize
d
the in
depe
ndent
g
e
sture recog
n
ition. The di
gital sol
a
r a
s
pect
angle
telemet
e
ring
system
de
sign
ed
by the m
e
a
s
u
r
e
m
ent fun
dam
entals of
sol
a
r a
s
p
e
ct
angl
e
did a ran
ge dynamic te
st, which
coul
d withsta
nd ma
ximum 18000
g launching l
oad, and whi
c
h
wa
s the dom
estic first one
that su
ccessf
ully applied the prin
ciple of
sola
r aspe
ct angle to finish a
the proje
c
tile
attitude mea
s
urem
ent te
st unde
r th
e
co
ndition of th
e
high valu
e g,
the test
sho
w
ed
that the meth
od co
uld b
e
u
s
ed to me
asu
r
e spin-stab
ili
zed p
r
oj
ectile
attitude in flight, but only the
ca
se
of suffi
cient
su
nlight
duri
ng th
e
day and
with
a la
rge
r
a
p
p
lied limitatio
ns. Th
e id
ea
of
putting the magneti
c
indu
ction coils into
the
rockets
prop
osed by Zhang
Wei
-
h
ua and othe
rs,
whi
c
h u
s
e
d
the rocket rotation to ma
ke indu
ction
coils to in
ci
se
the mag
netic line an
d p
r
o
duce
electromotive
,
and the idea that
the change of indu
ction coils el
ectro
m
otive could refle
c
t the
situation of ro
cket rotation,
easily
a
c
hiev
e the test system of simple
combin
ation,
low co
st, hig
h
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 64
54 – 646
0
6456
reliability an
d
good
real
-time. But duri
ng the me
as
uring
proce
s
s, blind
zo
ne
appe
are
d
e
a
sily.
Becau
s
e of t
he sp
eed of chang
e of ro
ckets rotatio
n
a
ngle in flight wa
s fast, once the blind zo
ne
appe
are
d
, m
easure
m
ent
accuracy
wo
uld b
e
affe
cte
d
, furthe
rmo
r
e, indu
ction
coils
ele
c
trom
otive
wa
s con
c
e
r
n
ed with rotati
onal freq
uen
cy, so the method did not
applied to the low frequ
e
n
cy
rotation p
r
oje
c
tile. The me
thod of usin
g
comp
utatio
n
algorithm of
ratio of extre
m
e value of two
magneti
c
se
nso
r
s could
achieve th
e hig
h
-spe
e
d
proje
c
tile
body attitud
e
mea
s
u
r
em
ent,
simulatio
n
re
sult sho
w
e
d
high preci
s
io
n,
and
cha
r
a
c
teristics of all
-
we
athe
r, day
and
ni
ght
sui
ng.
Wheth
e
r it co
uld be ap
plie
d in pra
c
tice,
it needed mo
re comp
re
hen
sive validatio
n.
I
n
re
ce
nt
y
e
a
r
s,
re
sea
r
ch
of
mult
i-a
c
cel
e
ro
m
e
ter co
mbination
de
sign
is very
e
x
tensive,
desi
gn of si
x-accele
rom
e
ter, nine-a
ccelero
mete
r, ten-a
c
c
e
le
ro
meter,
sev
e
n-a
c
c
e
le
rome
ter
singl
e gyro
scope, eight-accele
r
om
eter a
nd twelve
-accelero
meter et
c co
me out, the followi
ng a
r
e
descri
be in d
e
tail for different combi
nati
ons
of config
uration
s
an
d comp
utation
algorith
m
.
(a)
(b)
(c
)
(d)
Figure 1. Con
f
iguration of
Six Accelero
meter
Figure 1
pro
p
o
se
d fou
r
in
stallation
ways,
the p
r
inci
ple
s
of
(a) an
d (b)
were
same
, which
wa
s suitabl
e for sle
nde
r cyl
i
nder
carrie
r. Becau
s
e of
the different o
f
two lever arm effects, to the
same
si
ze
accele
rom
e
ter e
rro
r, the
cal
c
u
l
ated va
lue
s
of
angul
ar accele
ration we
re
different.
T
h
e
collo
catio
n
m
e
thod
of (c) also wa
s suit
able
fo
r
slen
der cylind
e
r carrie
r.
The
sen
s
in
g
axis
of
accele
rom
e
te
r alon
g ea
ch f
a
ce of di
ago
n
a
l line
directi
on, whe
n
ea
ch edge
of parallelepip
ed
was
same,
thi
s
all
o
cation scheme
was
suitable for carrier such
as sate
llites et
c, simi
lar to
a
sphere
or cube.
T
he config
uratio
n of
(d) wa
s sui
t
able
for
tri
a
n
gular pri
s
m shape ca
rri
er, comp
ared with
the accel
e
ro
meter all
o
cation sch
e
me
o
f
non-gyro
strap
-
do
wn i
n
e
r
tial navigatio
n, whi
c
h
cou
l
d
adju
s
t len
g
th
of tria
ngul
ar pri
s
m
ba
se
d on
cha
r
a
c
teristi
c
s
of different ca
rri
ers,
an
d had
the
cha
r
a
c
teri
stic of the flexible installatio
n
. Shi
Zhen, Ma Shu-tian, Y
i
De-jin a
nd
others propo
sed
comp
utation
algorith
m
of
angul
ar velo
city at the
sam
e
time, sp
ecif
ic force
by the accel
e
ro
me
ter
output could
get the an
gul
ar a
c
cele
rati
on of ca
rrie
r, and inte
grat
e co
uld g
e
t angul
ar velo
city.
Becau
s
e
of th
e error of an
g
u
lar velo
city is a
c
cumu
late
d gra
dually
wi
th cha
nge
of time, it affecte
d
the navigatio
n accu
ra
cy
greatly.
But if effective filtering
algo
rith
m wa
s u
s
e
d
,
the re
solvi
n
g
accuracy
cou
l
d be imp
r
ov
ed to a
certa
i
n extent.
The pre
c
i
s
ion
o
f
resolvin
g all
o
catio
n
sch
e
m
e
wa
s lo
w, whil
e the
pri
c
e
was l
o
w,
suita
b
le for s
hort t
i
me navig
atio
n ap
plicatio
n
s
su
ch
as
sh
ort-
rang
e anti-ta
ctical balli
stic
missil
e
etc.
The in
stallati
on site
of a
c
celeromete
r in nine
-a
ccelero
meter al
locatio
n
sch
e
m
e was
s
h
ow
n
in
F
i
gu
r
e
2
.
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TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Attitude Measurem
ent for Ballistic
Corre
c
tion Ro
cket (Liang Zhi
-
jian
)
6457
Figure 2 pro
posed three
installatio
n
ways,
unde
r the influen
ce
of the accele
romete
r
measurement
erro
r, the allocatio
n
sche
me of (a) wo
uld pro
d
u
c
e highe
r ang
ul
ar velocity error,
mean
while, a
s
the
com
put
ation metho
d
simila
r with
si
x-accele
rom
e
ter, the an
gul
ar velo
city error
wa
s accum
u
l
a
ting fast with chan
ge of time. T
he allo
cation
sch
em
e of (b) wo
ul
d not appea
r the
phen
omen
on
of unlimited accumulatio
n
of erro
r simila
r with (a
), its error was bo
unde
d, so it wa
s
better than th
e way of (a
). The allo
catio
n
schem
e of (c) propo
se
d by W
ang Jin
-
son
g
and oth
e
rs
made full use of the redu
ndant inform
ation of acce
l
e
rom
e
ter out
put to compl
e
te the resol
v
ing,
effectively in
hibit the ite
r
ative error.
Angula
r
velo
city com
puta
t
ion algo
rith
ms of
allo
ca
tion
scheme of (a
) and (b
) we
re different fro
m
(a).
Specifi
c
force of acce
le
rom
e
ter
output co
uld be
use
d
to a
c
hi
eve ang
ular
accele
ration
of ca
rrie
r
a
n
d
its ab
sol
u
te value, the
n
integ
r
ated
the
angul
ar a
c
celeration a
nd g
o
t angula
r
velocity, the si
gn could b
e
look as the
sig
n
of the absol
ute
value to
achi
eve an
gula
r
v
e
locity of
bod
y, erro
r
of whi
c
h
wa
s
bou
n
ded. So
it effectively inhi
bited
the navigatio
n erro
r. The
co
st
of nine-accele
rom
e
te
r config
urat
io
n was hi
ghe
r than that of
six-
accele
rom
e
te
r, but ni
ne-accele
rom
e
ter i
m
prove
th
e
system a
c
cura
cy of the
use
of re
dun
dant
information.
(a)
(b)
(c
)
Figure 2. Con
f
iguration of
Nine Accel
e
rometers
The in
stallati
on site of a
c
celeromete
r in ten-a
c
cel
e
rom
e
ter all
o
catio
n
sche
me wa
s
sho
w
n i
n
Fig
u
re 3,
whi
c
h
solved
CCF (Cou
rse Corre
c
ting Fu
ze
) t
o
a certain
e
x
tent. It had the
cha
r
a
c
teri
stics of
po
sition of
cente
r
of ma
ss o
f
body
chan
ged
over ti
me an
d in
e
r
tial
measurement
unit was n
o
t installe
d in the carrie
r nea
r the cente
r
of mass.
Figure 4 sh
owe
d
the all
o
catio
n
sche
me of seve
n-a
c
cele
rome
ter and
sing
le-Gyro,
althoug
h the
comp
utation
method of a
n
gular vel
o
ci
ty
wa
s simil
a
r
with six-accel
e
rom
e
ter, Gy
ro
wa
s configu
r
ed, therefo
r
e,
cal
c
ulatio
n o
f
angula
r
vel
o
city on o
ne
dire
ction
wa
s more
accu
ra
cy,
accordingly, t
he p
r
obl
em o
f
calculate
re
sults
diverge
n
ce
over tim
e
wa
s
overco
me, and
syst
em
accuracy was improved, while the
syste
m
overloa
d
-p
roof dropp
ed.
Figure 3. Con
f
iguration of Ten Accele
ro
meters
Figure 4. Con
f
iguration of Gyro and M
u
l
t
i
A
ccel
e
r
o
met
e
rs
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 64
54 – 646
0
6458
Figure 5. Con
f
iguration of
Eight
A
ccel
e
r
o
met
e
rs
Figure 6. Con
f
iguration of Twelve
A
ccel
e
r
o
met
e
rs
Literatu
re [9]
expoun
ded d
e
sig
n
of eight
-accel
er
omet
er ine
r
tial nav
igation
syste
m
in the
trajecto
ry pla
ne; the alloca
tion scheme
wa
s sh
own in
the Figure 5.
In the figure, X is bomb axi
s
, eight accel
e
ro
m
e
ters we
re install
ed in
the YOZ plane, the
distan
ce bet
wee
n
each accele
rom
e
te
r and axle
cente
r
is a.
It got angular velo
city by
comp
utation,
and the
st
atic an
d dyn
a
mic
calib
rat
i
on. Beca
use
of the sch
e
me u
s
ing
2-D
installatio
n
of
accel
e
romet
e
r, la
cking
of
the
ac
cele
ro
meter
on
bo
mb axi
s
di
re
ction, the
e
r
ror
woul
d in
crea
se
qui
ckly
wi
th the
ch
ang
e of time,
an
d affecte
d
preci
s
ion
of
re
solving
g
r
eatl
y
,
whi
c
h ha
d to be revised.
Literatu
re [10
]
expound
ed
desi
gn of twe
l
ve-acc
el
ero
m
eter in
ertial
navigation
system of
high spinnin
g
proje
c
tile; the allocation schem
e wa
s shown in the Figure
6
.
The
autho
r d
edu
ced
form
ula of
ang
ula
r
velo
city, an
d too
k
a
si
m
u
lation. Th
e
simulatio
n
result (Fig
ure
7) sh
owed t
hat unde
r the
case of
azi
m
uth error, t
he erro
r wo
ul
d expand
rap
i
dly,
and affecte
d
pre
c
isi
on of resolvin
g gr
e
a
t
ly, which also had to be revised.
(a) Pitch Angl
e of Error
Cu
rve
(b)
Roll Angle
of Error C
u
rv
e
(c
) Yaw Angl
e of Error
Cu
r
v
e
Figure 7. Each Attitude Parameter of Error Cu
rve
3. Inertial Na
v
i
gation Sy
s
t
em
Inertial n
a
vig
a
tion
system
(follo
wing
I
N
S for sho
r
t) refers to
two
or mo
re
kind
s
of
navigation e
quipme
n
t get together in
an app
rop
r
ia
te way, on the ba
sis of compl
e
me
nta
r
y
advantag
es
in pe
rform
a
n
c
e to
get h
i
gher nav
iga
t
ion pe
rform
ance than
anyone i
nert
i
al
measurement
unit. Dome
stic
and
fore
ign resea
r
ch
tech
niqu
e f
o
r in
ertial
na
vigation
syst
em
inclu
d
e
s
com
b
ination of INS and Doppl
er navigat
io
n rada
r, GPS/INS System, INS/Star Sensor,
INS/OD, GP
S/SST/SINS,
Magnetometer/MEMS Gy
roscop
e/Accelero
meter, Combi
nation
of
Geoma
gneti
s
m and Gyro, combi
nation
of Magnet
om
eters
and M
E
MS Gyro [11], MEMS Gyro/
Accel
e
rometer/Micro Magnetometer [12]
, combi
natio
n
of Geomagn
etism And Solar Di
re
ction
,
GPS/ Geoma
gnetism, Pola
rize
d-li
ght As
sistin
g with G
eomag
netism
and GPS etc.
Inertial navig
ation system
prop
osed
fi
rst
wa
s m
ade
up of I
N
S a
n
d
Doppl
er na
vigation
rada
r, used l
ong-te
rm hi
g
h
pre
c
i
s
ion
chara
c
te
rist
i
c
s of Doppl
er radar to
revise sho
r
t-te
rm
high
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Attitude Measurem
ent for Ballistic
Corre
c
tion Ro
cket (Liang Zhi
-
jian
)
6459
pre
c
isi
on
of I
N
S, imp
r
ove
d
p
r
e
c
isio
n
o
f
navigat
ion.
The te
ch
niqu
e of
com
b
ina
t
ion of I
N
S a
nd
GPS wa
s
re
search
hotspot
in re
ce
nt yea
r
s, two of the
m
we
re
a
ll na
vigation eq
ui
pment of
glob
al,
all-weathe
r a
nd
all
-
time, and also
aff
o
rde
d
ve
ry complete
navi
gation data. The com
b
ina
t
ion
use
d
lon
g
-te
r
m stability an
d mod
e
rate
p
r
eci
s
io
n of G
PS to make
up the
disa
d
v
antage of
error
accumul
a
ted
with time i
n
INS, used
sho
r
t-te
rm
high p
r
e
c
isi
o
n of INS to
make up
the
disa
dvantag
e
of GPS re
cei
v
er’s e
r
ror i
n
crea
sed
wh
en
disturbed
and
lost of si
gnal
whe
n
in blo
ck,
gave full pl
ay to their
respe
c
tive st
rength
s
, lea
r
ned fro
m
e
a
ch
other.
The sy
stem
had
characteri
stics such
as sim
p
le st
ructure, high
reliability,
small
si
ze, li
ght weight, low
cost etc. F
o
r
the rea
s
on of
GPS require
s extern
al me
asu
r
ing d
e
vices, it was limi
t
ed on the ap
plicatio
n. CCD
optical se
nso
r
could also obtain
the
inf
o
rmatio
n
of a
i
r targ
et attitude, mad
e
a
data fusi
on
with
INS, could
a
l
so revise th
e po
sition, veloci
ty an
d
attitude angl
e of INS, an
d improved t
he
accuracy
of a
ttitude determ
i
nation to
so
me extent.
In
the year of
2
006, the
com
b
ination
of G
P
S,
SST and SINS propo
se
d
by Kang G
u
o-hu
a an
d ot
hers u
s
ed
m
odified a
ggre
gated filterin
g to
make
a d
a
ta
fusion
with
multi-sen
s
or
informatio
n a
nd u
s
ed
the
most
estima
tion metho
d
of
navigation m
ode, balli
stic
missil
e
for th
e appli
c
ation
obje
c
t, simul
a
tion re
sult
showed that t
he
combi
nation
coul
d
imp
r
ov
e
navigatio
n pre
c
isi
on of
missil
e
, filteri
ng alg
o
rithm
wa
s sta
b
le
a
n
d
reliabl
e, whet
her it wa
s fea
s
ible for the li
ve ammunitio
n
need
ed to b
e
verified.
Introdu
cing
o
f
magnetom
e
t
er in INS
co
uld ma
ke
up
the disadvant
age of
Gyro’
s
zero-
drift error a
c
cumul
a
tion.
The combin
a
t
ion atti
tude determi
nation
of three axi
a
l magn
etom
eter
and tri-axial rata Gyro pro
posed by Ba
o Ya-qi an
d o
t
hers
also
sol
v
ed the pro
b
l
e
m of blind zone
of explo
r
ation
exist i
n
m
a
g
netomete
r
, in
additi
o
n
, Xu
e Lia
ng
and
others
also p
r
opo
se
d
attitude
determi
nation
system ba
sed on MEMS Gyro, ac
cel
e
rom
e
ter an
d
micro ma
gn
etometer, wh
ich
had
advanta
ges of
small
volume, l
o
w co
st
and
rel
i
able
perfo
rm
ance et
c. Th
e two
schem
e
s
successfully verified only
throug
h the single-axis
turntable, ac
curacy and
stability of more
comp
re
hen
si
ve and detail
ed verificatio
n
system
ne
e
ded with the
high-preci
s
io
n three
-
axis
non-
magneti
c
turn
table to comp
lete.
Geoma
gneti
c
se
nsor a
s
a
se
nsitive
de
vice
to
mea
s
ure
the
geo
magneti
c
sig
nal, ha
d
been
widely
use
d
in the flight attitude meas
urement
s, Cao
Ho
ng
-so
ng a
nd ot
hers propo
se
d
attitude dete
c
t techniq
ue b
y
combin
atio
n of geom
agn
etism an
d Gy
ro, whi
c
h
stra
p do
wn in
stall
e
d
the
3-D geo
magneti
c
se
n
s
or and solid
-state
MEMS
Gyro on the
missil
e
body
,
sen
s
itive axis of
the geoma
g
n
e
tic se
nsor
were at the three axial di
re
ction of the body coo
r
dinate
s
, sen
s
itive a
x
is
of Gyro corre
s
po
nd to vertical axis of p
r
oj
e
c
tile body
, and used
si
ngle axis Gyro to measu
r
e
proje
c
tile
bod
y’s on
e attitu
de a
ngul
ar v
e
locity,
an
d reused th
ree
-
axis g
eoma
g
netic
se
nsor
to
detect
project
i
on o
n
the
bo
dy co
ordi
nate
s
of
th
e geom
agneti
c
ve
cto
r
,
an
d simulta
neou
sly solve
d
3-D attitude
of missile b
o
d
y by usi
ng
singl
e-p
o
in
t a
l
gorithm. T
h
e
techni
que
was e
a
sy to
m
eet
real
-time req
u
irem
ents
an
d error
wa
s n
o
t cumul
a
ti
ve, solid-state
chara
c
te
risti
c
s of the pro
g
ram
wa
s suita
b
le
for the use o
f
convention
a
l
ammuni
tion,
while sili
co
n
micro
-
gyroscope ha
d initial
temperature
-
drift characte
ristics,
which
must
be
com
pen
sated
wh
en in
servi
c
e,
in a
ddition,
b
lind
z
o
ne
e
x
is
te
d in
ge
o
m
ag
ne
tic
de
te
c
t
ion, in
a
p
p
licati
on it
could
e
n
su
re
co
ntin
uou
s, reli
abl
e of
measurement
data by th
e
method
of a
dding
re
du
n
d
ant sen
s
ors.
In the yea
r
o
f
2001,
Hua
n
g
Zheng
and
ot
hers p
r
op
ose
d
geo
magn
etism a
nd
sola
r
dire
ction attit
ude m
easure
m
ent sy
stem, it
con
s
i
s
ted of three axi
s
geo
magneti
c
po
sition sen
s
o
r
solid united o
n
the barycent
er of proj
ectil
e
and
sol
a
r attitude a
ngle
sensor solid
u
n
ited o
n
th
e missil
e
, syste
m
erro
r wa
s not
cumul
a
tive,
pre
c
isi
on of
measurement
wa
s hig
her,
impact
re
sistance
wa
s b
e
tter, but wh
en solving pi
tch
angle, ya
w a
ngle a
nd roll
angle by u
s
ing solar
attitude an
gle, the sele
ction
of the gro
u
n
d
coo
r
din
a
tes
wa
s certai
n
con
s
traints.
Whe
n
b
r
in
ging tog
e
the
r
ge
omag
ne
tism an
d G
PS
techn
o
logy to
achieve
proj
ectile po
sitio
n
and attitud
e
angle m
e
a
s
ureme
n
t, problem
s rel
a
te
d to
be corre
c
tion
of trajecto
ry
corre
c
tion
wa
s solved,
but be
cau
s
e
of the ultimate goal fo
r
the
attitude angl
e of trajecto
ry correctio
n
measur
ement
was the full
-attitude re
al-time detectio
n
,
geoma
gneti
c
detection at
titude determ
i
nation tech
n
o
l
ogy is not
very accu
ra
te, therefore,
it
sho
u
ld
be co
mbined with other
attitude
determin
a
ti
o
n
techn
o
logy
to achieve fu
sion of a va
ri
ety
of attitude a
ngle
dete
c
tio
n
technol
ogy
, so
as
to
m
o
re preci
s
e
guida
nce.
O
n
the ba
sis and
combi
ned
with the techn
o
l
ogy of polari
z
ation
-
se
n
s
itive neural
structures from
the sand a
n
t
’s
comp
oun
d ey
e, in the ye
ar of 20
09, Fa
n
Zhi-guo
and
others d
e
si
gn
ed a
kin
d
of
air p
o
lari
zatio
n
informatio
n detectio
n
an
d navigation
sen
s
or
, wh
ich a
c
hieve
d
the organi
c integration
of
polari
z
e
d
-lig
h
t, geomagneti
s
m and
GPS by self-de
s
ig
ned test platf
o
rm.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 64
54 – 646
0
6460
4. Conclusio
n
People d
u
rin
g
the co
urse
of st
udy on fli
ght attitude testing te
chnol
ogy, simple
u
s
e of the
inertial navig
ation syste
m
, inevitably bring abo
ut
the error a
c
cumu
lation over time. Although
the
INS mea
s
u
r
e
m
ent technol
ogy with
GPS, the
geom
a
gnetic se
nsor
and ot
her m
easure
m
ent
unit
to a certai
n e
x
tent, eliminate the erro
r a
c
cumulatio
n
, it also brin
gs
the probl
em
s su
ch a
s
difficult
comp
utation
algorith
m
, lo
w p
r
e
c
isi
on
of com
put
ati
on result, the mea
s
u
r
em
ent unit in
he
rent
adverse
cha
r
acteri
stics et
c. In the futu
re
p
r
o
c
e
ss
o
f
study and
developm
ent, if the followi
ng
probl
em
s can
be solved, th
e impa
cts to t
he practi
ca
l a
pplication of f
light attitude test technol
og
y
in the military may be far-reaching.
Accu
rate
me
asu
r
em
ent of
the me
asure
m
ent unit
i
n
stallation e
rro
r: installation
error i
n
the system is inevitable, small er
ror or "
z
ero" error is
the pursuit
of the goal of rese
arche
r
s, non
error is un
re
alistic, th
e p
r
oblem
of me
asu
r
ing
e
rro
r accu
rately
a
nd thu
s
elimi
nating th
e e
r
ror
waits
to solved.
The p
r
e
c
isi
o
n
of the test
system: som
e
desi
g
n
s
of I
N
S are fea
s
i
b
le in the
o
ry,
but the
result is not
satisfactory in
practi
cal a
pplication
s
, may be fo
r t
he rea
s
on
of the ma
nufa
c
ture
techn
o
logy of
system. Believe that with the dev
elopm
ent of high-te
ch ele
c
tronic
techn
o
logy, the
probl
em
s such as the
cost, difficulty and preci
s
i
on of circuit
production
w
ill be solved
in
the near
future.
Measurement
unit inhe
ren
t
characte
ri
stics:
In the I
N
S, whe
n
th
e mea
s
u
r
em
ent units
su
ch a
s
GPS and m
agn
etometer
se
nsor a
r
e
used,
althoug
h the
error
accum
u
lation of INS
is
sup
p
re
ssed,
at the same
time inh
e
re
nt
new erro
r
i
s
brou
ght in, m
e
thod to
elimi
nate all
kin
d
s of
errors co
ntain
ed in the syst
em need
s to be furthe
r sol
v
ed.
The de
sign o
f
verification platform: bef
ore any ki
n
d
of flight attitude test syste
m
is use
d
practically, it shall be
stri
ctly ve
rified on the correc
tness, accuracy, reliability,
a te
st platform that
simulate
the
actual
flight state of air target
should
b
e
set up
as soon
as
po
ssi
ble, at the
sa
m
e
time, how to
ensure
and
el
iminate the p
r
eci
s
ion
and e
rro
r of test pl
atform is
also
a task ne
ed
to
be solve
d
.
Referen
ces
[1]
Jian
g H
a
ita
o
,
Shan
g
Xiao
xin
g
. Mod
i
fie
d
M
V
RCORDI
C Al
gorithm
an
d it’s
Ap
plic
atio
n in
Attitud
e
Measur
ement.
T
E
LKOMNIKA Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2013; 1
1
(3): 1
148-
115
6.
[2]
Haid
on
g GUO. Neura
l
Net
w
o
r
k Aided K
a
lm
an F
ilt
eri
ng F
o
r Integrated G
PS/INS Naviga
tion S
y
stem.
T
E
LKOMNIKA Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2013; 1
1
(3): 1
221-
122
6.
[3]
MA Bao-Gu
o, Z
H
OU Shi-Qi
n. Res
earch
of Inertia
l
EF
PI F
i
ber-o
ptic
G
y
ro.
A
e
rody
nam
i
c M
i
ssile
Journ
a
l
. 19
99; 2(4): 39-4
1
.
[4]
Core
y Victor B
.
Measurin
g Angu
lar Accel
e
r
a
tion
w
i
t
h
Lin
e
a
r Acceler
a
tion
.
Control Eng
i
n
eeri
n
g
. 196
2;
3(3): 79-8
0
.
[5]
Krishn
an V. Measur
ement of
Angul
ar Ve
loc
i
t
y
a
nd L
i
n
ear
Acceler
a
tion
U
s
ing L
i
n
ear Ac
celer
o
meters.
Journ
a
l of the
F
r
anklin Institut
e
. 1965; 4(
4): 307-3
15.
[6]
Schul
er Alfred
R. Measurin
g Rotatio
nal Moti
on
w
i
th Li
ne
ar Acceler
o
meter
s
.
IEEE Trans on
AES
. 1
9
67;
3(5): 465-
47
2.
[7]
Padg
ao
nkar A
J
, Krieger KW
, King AI. Mea
s
ureme
n
t of Angu
lar Acce
ler
a
tion of a R
i
g
i
d Bod
y
Us
ing
Lin
ear Accel
e
r
o
meters.
Journ
a
l of Appl
ie
d Mecha
n
ics
. 19
75
; 9(42): 552-5
5
6
.
[8]
Merhav
Shmu
el J. A
N
on-g
y
roscop
i
c Inerti
al M
easur
eme
n
t Ui
nt.
Jour
n
a
l
of Gui
danc
e
an
d C
ontro
l
.
198
2; 3(5): 227
-235.
[9]
CUI Min, MA
T
e
i-Hua, Z
H
ANG Meng. R
e
search
on
Cal
i
b
ratio
n
An
d Er
ror Com
pens
ation for Gfsi
n
s.
Journ
a
l of Elec
tronic Meas
ure
m
e
n
t And Instrument
. 200
9; 9
(
9): 23-26.
[10]
ZHANG Hui,
CAO Yon
g
-Ho
ng, MA T
e
i-Hu
a, FAN
Ji
n-Bia
o
. Res
earch
o
n
Op
timization Al
gorithm of
Gfsi
n
s C
o
mpen
sa
ti
ng
Fix
e
d
Erro
rs.
Journ
a
l
of Projecti
les
Rockets Missi
l
e
s an
d Gui
dan
ce
. 200
9; 2(2):
13-1
7
.
[11]
BAO Ya-Qi, CHEN G
uo-Gu
a
ng, W
U
Kun, W
A
NG Xia
o
-R
ong.
R
e
searc
h
on Attitude D
e
termin
a
tio
n
Using M
agn
eto
m
eters and ME
MS Inertial Se
nsors.
Acta Arma
mentar
ii
. 20
08; 10(1
0
): 122
7-12
31.
[12]
XUE
L
i
an
g, LI
T
i
an-Z
h
i, LI
Xi
ao-Y
i
ng, CH
ANG
Ho
ng-L
o
ng.
Stud
y
of Micro
Attitude
Determination
S
y
stem Bas
ed
on MEMS Sen
s
ors.
Chin
ese
Journ
a
l of Sen
s
ors and Actu
a
t
ors
. 2008; 3(3)
: 457-46
0.
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