TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 11, Novembe
r
2014, pp. 78
1
6
~ 782
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i11.49
07
7816
Re
cei
v
ed O
c
t
ober 2
5
, 201
3; Revi
se
d Augu
st
18, 201
4; Acce
pted
Septem
ber 3, 2014
Design of Adaptive Filter for Laser Gyro
Jinming Li
1,2
, Zeming Li*
1,
2
, Xiaojun Y
a
n
1,2
，
Yanjiao Yang
1,2
, Chengrui Zhai
1,2
1
Nation
al Ke
y
Lab
orator
y for Electron
ic Mea
s
urem
e
n
t T
e
ch
nol
og
y, North
Univers
i
t
y
of Chin
a,
T
a
iyua
n 03
005
1, P. R. China, Ph./F
ax:+
86-0
351-
355
92
58
2
Ke
y
L
abor
ator
y of Instrument
ation Sci
enc
e & D
y
n
a
mic Me
asurem
ent of Ministr
y
of Edu
c
ation,
North Un
iversit
y
of Ch
ina, T
a
iyu
an 0
3
0
051,
P. R. China, Ph./F
ax:+
86-0
3
5
1
-35
592
58
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: lizemin
g5
65
@16
3
.com
A
b
st
r
a
ct
Accordi
ng to t
he filter
in
g of
laser
gyro
out
put si
g
n
a
l
of l
o
w
precisi
on,
slow
spe
ed
of dyna
mi
c
re
sp
on
se
, th
e
re
se
a
r
ch
an
d
im
pl
em
en
ta
ti
on o
f
a
n
e
w
m
e
t
hod
of l
a
ser
g
y
ro filter
i
ng
pro
c
ess, the sc
he
me
usin
g LMS
ad
a
p
tive filt
erin
g a
l
gorith
m
, th
e d
i
ther fe
edb
a
ck si
gna
l as
the
iter
ative filt
er d
a
ta
inp
u
t, the
dith
er
sign
al, rand
o
m
noise, w
h
ite n
o
ise as the ref
e
renc
e sign
al
filter, digit
a
l filte
r
and
the exter
nal co
ntrol usi
n
g
F
P
GA, give the filter alg
o
rith
m an
d har
dw
are block di
agr
a
m
. Experi
m
ent
al results
sh
o
w
that
the filtering
mo
du
le w
i
th fi
l
t
er w
i
th hi
gh
p
r
ecisio
n
and
w
i
de
dyn
a
m
ic r
e
spons
e ra
ng
e, can
meet t
h
e
req
u
ire
m
ents
of
spee
d an
d pre
c
ision
of laser
gyro de
mod
u
la
tion aer
osp
a
ce
fields.
Ke
y
w
ords
:
las
e
r gyro, ada
pti
v
e filter, F
P
GA
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. Introducti
on
Ring
la
ser gy
ro
(rin
g
la
se
r
gyro, gyrosco
pe)
wi
th high
sen
s
itivity
an
d
preci
s
io
n, whi
c
h
i
s
made of Sag
nac
effect ba
sed
on opti
c
al ring
ro
a
d
. At present it has
been
wi
dely use
d
in
the
strap
do
wn in
ertial navigati
on syste
m
[1]. Becau
s
e th
e lase
r gyro l
o
ck-in th
re
sh
old exists,
wh
en
the extern
al i
nput spee
d l
e
ss than
lock-in thres
hold,
lase
r gyro i
s
unabl
e to
se
nse th
e external
angul
ar rate, will pro
d
u
c
e the lock-i
n effect, whi
c
h
g
r
eatly limits its applicati
on scop
e. In orde
r to
make th
e gy
ro ha
s b
een
workin
g in t
he lo
ck
regi
o
n
, people
usually use
me
cha
n
ical Dith
er.
Comm
only used app
ro
ach is the introdu
ction of perio
di
c si
nu
soidal v
i
bration [2]. T
he me
cha
n
ical
dither i
s
provided by re
so
n
ance
of pie
z
o
e
lectri
c
cera
mics.In p
r
a
c
tical ap
plicatio
ns, due to
small
cha
nge
s i
n
t
he
cha
r
a
c
teri
stics of
pie
z
oele
c
tr
ic ceramic insta
b
ili
ty and gy
ro
its m
e
chani
cal
stru
cture, will
cau
s
e the g
y
ro vibration
perio
d and a
m
plitude is n
o
t a con
s
tant
value. Then the
gyro output d
a
ta jitter strip
p
ing ha
s cert
ain difficu
lty, usin
g co
nven
tional cycl
e offset conve
n
tional
and not
ch m
e
thod can n
o
t accurately strippi
ng, wh
ich affe
ct the accu
ra
cy
of the gyrosco
pe.
Based on t
he an
alysi
s
o
n
the p
r
in
cipl
e of ad
apt
ive
filtering al
go
rithm, the a
r
ticle p
r
o
p
o
s
e
s
to
achi
eve the l
a
se
r gyro o
u
tput
sig
nal of
high spe
ed, high
p
r
e
c
i
s
io
n
dem
odul
ation
sch
e
me u
s
ing
LMS adaptiv
e filtering.Th
e method ca
n satisfy t
he high preci
s
io
n demod
ulati
on, but also
has
good p
r
a
c
tica
bility and engi
neeri
ng p
r
a
c
tical value.
2. Analy
s
is
of LMS Au
to
- Adap
ted Fi
lter Algorith
m
LMS adaptive filtering alg
o
rithm ma
ke
s the
small
e
st mean squ
a
re deviatio
n
of error
betwe
en the filter output an
d the ex
pecte
d output of the minimum, so it is called t
he lea
s
t mea
n
squ
a
re
(LMS) auto - adapt
ed filter algo
ri
thm
[3]. Its basic
stru
cture is as follo
ws:
Figure 1. The
Basic Mo
del
of LMS Auto-Adapted Filte
r
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TELKOM
NIKA
ISSN:
2302-4
046
De
sign of Ad
aptive Filte
r
for La
se
r Gyro
(Jinm
i
ng Li)
7817
Among them
,
()
()
()
en
d
n
y
n
,d(n) is
the referenc
e input,
X(n) is the filter input.In
pra
c
tical
ap
pl
ication
s
, d
u
e
to the mi
ni
mum me
an
squ
a
re
a
r
e h
a
rd to
calcul
ate, we
u
s
e
the
squ
a
re
of th
e
erro
r
sign
al,
estimated
a
s
the me
an
sq
uare
e
rro
r val
ue [4]. In
ord
e
r to
re
alize t
he
attenuation o
f
certain freq
uen
cy refere
nce si
gnal
,
D ( n ), X ( n ) shall ha
ve the following
mathemati
c
al
relation
ship:
()
1
(
)
2
()
()
1
(
)
dn
d
n
d
n
Xn
x
n
(
1
)
The d1
(n) a
n
d
d2(n
)
ha
s no co
rrelatio
n; x1(n
) and
d1(n
)
are mo
st correl
ation,
but the
y
and d
2
(n
) h
a
s
no
co
rrelati
on. Wh
en the
filter is
stabl
e, the co
mpo
nents
of
d1
(n
) output i
n
e(n)
can b
e
gre
a
tly attenuated, thereby reali
z
ing filtering.
The
co
re of
L
M
S adaptive
filtering al
gori
t
hm is
to
upd
ate form
ula
weight coeffici
ent, and
what
we a
r
e
usin
g is
Wi
dro
w
an
d Ho
ff LMS algori
t
hm. The alg
o
rithm u
s
e
s
the most
rap
i
d
desce
nt method in the optimizati
on met
hod
s and its
final weight c
oefficient upd
ating formula
is
as
follows
:
(
)
(
1
)
2
()
()
Wk
Wk
e
k
x
k
(
2
)
Among th
em,
the
w(k) rep
r
esents the
filter
weight
co
efficient ve
ctor , x
(
k)
rep
r
ese
n
ts th
e filter
input data ve
ctor,
is the converg
e
n
c
e factor. O
n
ly when
satisfie
s
a ce
rtain ra
n
ge, the filter
will tend to
be
stable
after m
u
ltiple it
erations.
T
o
make
the weight
coe
fficient vector of
the
mathemati
c
al
expectatio
n
can
co
nv
erg
e
to the
Wie
ner
sol
u
tion,
ran
g
e
s
shou
ld sati
sfy the
following formula:
ma
x
1
0
(
3
)
m
rep
r
e
s
ent
s the maximum
eigenvalu
e
of
the input d
a
ta matrix. The
size of the
is
dire
ctly relat
ed to the ite
r
ati
on time
s
that the filter rea
c
h a
sta
b
le time. Th
e small
e
r th
e T,
iteration n
u
m
ber i
s
la
rge
r
, but the exp
e
cted
output
is cl
ose to th
e true valu
e, and the e
r
ro
r is
smalle
r. So the value of
is often the m
o
st impo
rtant
factor
s affe
cting the p
e
rfo
r
mance of the
filter. In practi
cal
appli
c
atio
n, we
u
s
e th
e
MATLAB
sof
t
ware
to
cal
c
ulate the
ap
propriate
value
as
the optimal converg
e
n
c
e factor [5].
3. The Design of Adaptive Filter
3.1. The Selection of the
Referen
ce Signal for th
e Auto - Ad
apted Filter
Acco
rdi
ng to
the pri
n
ci
ple
of LMS filter,
we
mu
st first sele
ct the
a
ppro
p
ri
ate referen
c
e
input, filter input, and bet
wee
n
them
must me
et ce
rtain math
e
m
atical
correl
ation. In ord
e
r to
make the la
ser gyro work
as mu
ch a
s
possibl
e
to avoid lock
regi
on, we intro
d
u
ce the pe
rio
d
ic
sinu
soi
dal vibration m
o
re
over white
noise
with a
certain lev
e
l is sup
e
ri
mposed on
the
mech
ani
cal d
i
ther [6]. Then the output data of la
se
r gyro com
p
o
nent of three
parts,in
c
ludi
ng
mech
ani
cal vibration, noi
se
, the external inpu
t. They are related by the followi
ng e
quation:
si
n
(
)
(
)
(
)
NA
w
t
B
t
C
t
(
4
)
The
sin
(
t+) repre
s
e
n
ts th
e me
cha
n
ical
ditheri
ng
rat
e
,
Ω
(t) re
presents th
e inp
u
t
angula
r
rate,
ε
(t) rep
r
ese
n
ts
the
ra
ndom noise sign
al.We sa
mp
led th
e ou
tput values o
f
lase
r gyro
with
uniform time
sampli
ng, an
d get down
：
1
sin
(
)
s
in(
)
()
(
)
ii
i
NA
w
t
A
w
t
Bt
t
C
t
t
(
5
)
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TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 78
16 – 782
3
7818
We
gen
erally
use10K
HZ
a
s
the
sampli
n
g
fre
quen
cy,
assumin
g
tha
t
the
sampli
n
g
pe
riod
to
t
,,we can g
e
t the followin
g
formula u
s
i
ng the differe
ntial prin
ciple:
1
si
n
(
)
s
i
n
(
)
c
o
s(
)
ii
i
Aw
t
A
w
t
A
w
w
t
t
(
6
)
So the Type 1.4 can b
e
re
written a
s
:
co
s
(
)
(
)
(
)
ii
i
i
NK
w
t
B
t
C
t
t
KA
w
t
(7)
A general ra
ndom noi
se i
s
more than
1KHz, th
e ex
ternal inp
u
t si
gnal is bel
ow 100Hz,
the gyro dith
er freq
uen
cy
is abo
ut 300
Hz, do
not
h
a
ve the co
rre
l
ation betwee
n
the three,
and
the magnitud
e
relation
shi
p
is
KC
B
.To obtain
the input an
gular
rate, the first, the three in
the type must
be stripp
ed [7]. So we will refer
to Ni a
s
the input sig
n
a
l of adaptive
filter.
3.2. The Selection of the
Filter Input S
i
gnal
To stri
ppin
g
part of the
si
gnal fro
m
the
referen
c
e
si
gnal
without i
n
trodu
c
in
g e
r
rors from
the refe
ren
c
e sig
nal, the
input si
gnal
and the
dither
sign
al, random
noi
s
e
sign
al mu
st
be
relevant, an
d
external in
p
u
t angul
ar ve
locity is
n
o
t relevant. Whil
e the dithe
r
f
eedb
ack
sign
al
reflect
s
th
e vi
bration
of
pie
z
oel
ectri
c
ce
ramics,
whi
c
h
co
ntain
s
o
n
l
y
the dithe
r
a
n
d n
o
ise of t
w
o
comp
one
nts, its value and
the external i
nput
ang
ular
rate, whi
c
h can be expressed a
s
:
()
s
i
n
(
)
(
)
Xt
D
w
t
F
t
(
8
)
The dith
er fe
edba
ck
signa
l is a
n
a
nalo
g
voltage
sign
al, so
we
ne
e
d
to sampl
e
t
he dithe
r
feedba
ck sig
nal usin
g hi
gh pre
c
i
s
ion
A/D .Sam
pling value multiplied by
an appropriate
coeffici
ent, then the re
sult can b
e
used
as
the inp
u
t to the filter iteration.
Based
on
the
above
analy
s
is,
we
will
re
fer to type
2.4 a
s
a
refe
re
nce
si
gnal, type 2.5
a
s
the iterative filter input si
g
n
a
l, expresse
d
as follows:
cos(
)
(
)
(
)
si
n(
)
(
)
ii
i
i
ii
NK
w
t
B
t
C
t
t
Xi
D
w
t
F
t
(
9
)
3.3. The Selection of the
Filter Param
e
ter
s
Normali
z
ation
algo
rithm i
s
ad
opted i
n
the LMS
algo
rithm
and im
plem
ented in
MATLAB.The
sele
ction of
and the refe
ren
c
e in
put value
s
are not
linked,
so we simplify th
e
input model,
LMS filter input are a
s
follows:
0
:
199
9
200
c
o
s
(
2
*
*
/
33
2
)
50
s
i
n(2
*
*
/
33
0.
5
)
i
ii
i
t
Np
i
t
Xi
p
i
t
(
1
0
)
Figure 2. Filter Input Wavef
o
rm in MATL
AB
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
De
sign of Ad
aptive Filte
r
for La
se
r Gyro
(Jinm
i
ng Li)
7819
Iterative filter
orde
r i
s
set t
o
7 b
and
s, at
different
μ
v
a
lues
, the
s
i
mulation
res
u
lts
are as
follows
:
μ
=0.00
006
μ
=0.00
003
μ
=
0
.0
00
0
06
Figure 3. The
Iteration Re
sult Value with
Different
μ
As can b
e
seen from the
figure, the value of
μ
affect the iterati
v
e step and
iteration
accuracy wh
en the filter to stabilize re
ach
steady.After analysi
s
, we can sel
e
ct
μ
=0.0000
06,
this
filter has hig
h
e
r accu
ra
cy, and at the sa
me time,
stab
le time is with
in the accept
able ra
nge.
3.4. Filter Simulation an
d Optimiza
tion
Utilization of the
μ
, we mod
i
fy the parameters of the in
put model to simulate the
pro
c
e
ss
of laser gy
ro
sign
al. In MATLAB, the filter input mo
de
l is as follo
ws:
0
:
19
99
20
0
c
o
s
(
2
*
*
/
3
3
2
)
+
13.
2s
i
n
(
(
2
*
p
i
/
500)
*
t
)
50
s
i
n(
2
*
*
/
33
0.
5
)
i
ii
i
t
Np
i
t
Xi
p
i
t
(
1
1
)
N rep
r
e
s
ent
s the
external d
y
nam
ic input
freque
ncy
of
gyro,
typically 20
Hz. Filte
r
output
sign
als i
s
as f
o
llows:
Figure 4. The
Simulation Result
s of Basi
c LMS Filt
er
Model of Sign
al Processin
g
of Lase
r Gyro
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TELKOM
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KA
Vol. 12, No. 11, Novem
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14: 78
16 – 782
3
7820
What can be seen clearly in the figure is that
fil
t
ering result
s has great volatility.
We take
the second
in
refe
ren
c
e
si
gnal
(o
utside
input
ang
ula
r
velo
city)
an
d 80
0
- 1
000
sa
mplin
g p
o
i
n
ts
of the filtering result
s, to ob
tain the varia
n
ce:
Table 1. Co
m
pari
s
on of Th
eoreti
c
al Valu
e and Filteri
n
g Value
Signal Variance
Sum
values
Angular velocity
i
nput
13.13
-1911.711
The filtering resul
t
19.43
-1952.031
As can
be
se
en fro
m
the t
able th
e filteri
ng re
sult vari
ance i
s
si
gnif
i
cantly la
rge
r
, hen
ce
the filtering
re
sults have
greater vol
a
tility, and i
n
tr
od
uce a l
a
rg
e e
r
ro
r. Acco
rding
to the th
eory
of
adaptive filter. The final result of
filter iteration filter out
put e (k
) th
e
minimum m
e
an squa
re e
r
ror,
and e (k)
= d (k) - y (k), so
the fi
nal purp
o
se filter itera
t
ion is t
he ref
e
ren
c
e
sign
al
d(k) and o
u
tput
y(k) p
o
rtio
n o
f
the amplitude and p
h
a
s
e con
s
i
s
ten
c
y betwee
n
rel
e
vance [8]. So that this ou
tput
value e
(
k) i
n
cluded
ju
st a
part,whi
ch
is
not a
s
soci
at
e
d
with
iterative filter i
nput
sign
al.Whil
e
t
he
basi
c
LMS iterative formul
a (1.2) a
r
e di
rectly to
the E (k) into account, so we
need to opti
m
ize
the filter in the feedba
ck link.
Here the
ref
e
ren
c
e
sig
nal
of lase
r gyro i
nput LMS
adaptive filter, it
erative filter inp
u
t
sign
al is sim
p
lified as type:
'
1
1
in
dn
d
d
Xn
d
(
1
2
)
The d1
、
di
n resp
ectively repre
s
e
n
t the ditherin
g
and
external inpu
t compon
ent of count
sign
al, A/D
sampling
dith
er
com
pone
n
t
values
of
d1’ feed
ba
ck sign
al. Freq
uen
cy ra
nge
of
d1
、、
din
d1’ is as
sho
w
n in
the following
table:
Table 2. Dith
er Signal F
r
e
quen
cy Com
pone
nts
Signal F(Hz)
d1 250-450
din 0-20
d1’ 250-450
The expressi
on of e(k) can
be expre
s
se
d as follo
ws:
'
()
1
1
2
1
ek
k
d
k
d
d
i
n
(
1
3
)
The two f
r
eq
uen
cy has
ob
vious
segm
e
n
tation,
in the ran
ge of 0
-
20Hz, 250
-4
5
0
Hz. We
can divide
d d
i
fference filter for removal
of e(k) in
the din sig
nal, filtering itself ha
s ce
rtain e
rro
r,
while the
r
e is relatio
n
ship
between e
r
ror and ratio L of the signal freque
ncy to the sampli
ng
freque
ncy. L
is small, the filtering
effect
is bet
ter, the hig
her the a
c
cura
cy. Beca
use
fdin/fs
ample
≈
10/100
00, so
in the sam
p
ling pe
riod
S the value
of din is see
n
as rem
a
ini
ng
unchan
ged, and
'
1
(
)(
)
(
)1
1
2
1
nn
s
en
e
k
e
k
k
d
k
d
. So ju
st
sel
e
ct th
e a
ppro
p
ri
ate S
value, reli
abl
e
differential filtering
can b
e
achi
eved. LM
S adaptive
filter fram
e after optimization
are a
s
follows:
Figure 5. Optimized L
M
S Adaptive Filter
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De
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aptive Filte
r
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se
r Gyro
(Jinm
i
ng Li)
7821
By choo
sing
different S fo
r testin
g , we sel
e
ct S
=
4
as a
differe
ntial differen
c
e value
betwe
en t
w
o
adja
c
ent filter differe
nc
e in
the p
e
ri
od. T
hen th
e filter
output simula
tion
results are
s
h
ow
n
in
F
i
gu
r
e
6
:
Figure 6. Optimized Filte
r
Simulation Results
Thus, th
e op
timization m
o
del of LMS a
daptive filter, and two inp
u
t sele
ction
analysi
s
ende
d, compl
e
tes the theo
ry analysis a
n
d
mode
lin
g of LMS adaptive filter of lase
r gyro.
4. Circuit Im
plem
enta
tio
n
of the
Ada
p
tiv
e
Filter
4.1. Hard
w
a
r
e
Design
Acco
rdi
ng to
the above
pri
n
cipl
e
，
we re
alize th
e ad
a
p
tive filtering
algorith
m
an
d
system
control by usi
ng FPGA as t
he pro
c
e
s
sin
g
core
，
Stru
ct
ure dia
g
ram as follo
ws:
P
o
w
e
r s
u
p
p
l
y
c
i
rc
u
i
t
P
l
a
s
tic
is
o
l
a
t
io
n
ci
r
c
u
i
t
FP
GA
Co
mm
u
n
i
cat
i
o
n
s
in
te
r
f
a
c
e
c
i
r
c
u
its
A
m
p
l
if
ic
a
tio
n
an
d
c
o
n
d
itio
n
i
n
g
AD
±1
5
V
5V
Sq
u
a
r
e
wa
v
e
d
i
t
h
ered
f
e
e
dba
c
k
PC
Figure 7. Adaptive Filtering
Module Ci
rcuit Diagram
Five parts a
r
e
includ
ed in this
circuit:
T
he
p
o
we
r
su
pply ci
rcuit, Plastic i
s
ol
ation
circuit,
The A/D
co
n
v
ersio
n
circui
t, The FPGA
modul
e
，
co
mmuni
cation interface circuit.squa
re wa
ve
enter th
e ad
a
p
tive filtering
module
，
co
m
p
lete the
sign
al sh
apin
g
an
d photo
ele
c
tri
c
isolation fi
rst,
and the
n
the
sign
al into t
he FPGA, a
s
the in
put referen
c
e
sig
n
al for the
a
daptive filter in
cou
n
ting sam
p
ling.
Dither fee
dba
ck
sign
al through the hi
g
h
pr
e
c
isi
on A
/
D conve
r
si
o
n
, and then
enter the
FPGA, within
the FPGA, we put the filte
r
sa
mp
lin
g freque
n
cy a
s
t
he samplin
g
perio
d to sa
mple
the an
alog to
digital
conve
r
sio
n
valu
e, finally, mu
ltipli
ed by a
certa
i
n coefficient
as th
e inp
u
t
of
iterative filter LMS adaptive
filter.
4.2. Soft
w
a
r
e
design of a
d
aptiv
e
filter
Filter mod
u
le
of the FPGA prog
ram in
cl
ude:
Pha
s
e d
e
modul
ation
module, An a
d
aptive
filter mod
u
le,
FIR filter mo
dule, Th
e A/
D a
c
q
u
isition
modul
e
, Co
mmuni
cation
interface m
o
dule.
The organi
zat
i
on of softwa
r
e system i
s
illustrate
d on Fi
gure 8.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 78
16 – 782
3
7822
Figure 8. Adaptive Filter
Module
FPGA Block Diag
ra
m
Phase
discri
m
ination a
nd
reversibl
e
co
unting mo
dul
e
：
Sine an
d
square wave
signal into
the ph
ase d
e
m
odulatio
n m
odule, th
e
sq
uare
wave
si
gnal and
the main clo
c
k synchroni
zatio
n
,
and
output
s
with di
re
ction
informatio
n al
ternating
si
gn
al CW,
CCW
，
then CW, CCW
re
sp
ectiv
e
ly
into the reversible
cou
n
ting
module, and
filter sampl
e
the reve
rsi
b
le
cou
n
t and cl
e
a
r with 10K
HZ.
ADC control
module:
We
use
FPGA to
control th
e ex
ternal
ADS1
2
58, an
d
15M
HZ A
DC
maste
r
cl
ock
and 7.5M
HZ
SPI clock an
d
cont
rol si
gna
ls is
provid
ed
usin
g the
con
t
rol bu
s, finall
y
,
we u
s
e data
bus to read a
nd write A
D
S1258 inte
rnal
regi
ster throu
gh the SPI port;
The mo
dule
of Fixed to floating: Th
e
modul
e
co
nversi
on
reversi
b
le count a
s
32 si
ngl
e
pre
c
isi
on floa
ting point format, so that the LMS ad
ap
tive filter and
FIR filter to do floating p
o
int
arithmeti
c
.
Adaptive filter: Its main j
o
b
is to
de
sign
the
iterative fi
lter de
sig
n
a
nd
weight
co
efficient
update m
odul
e. Iterative filter is
a FIR fil
t
er of
order
7
.
The co
mple
x floating poi
nt addition a
nd
multiplicatio
n
is d
e
sig
ned
b
y
Weig
ht co
efficient
u
pdate
modul
e. Wh
en the
po
we
r filter, after 3
00
iteration
s
of t
he iterative fil
t
er, and filter
will
tend to
b
e
stabl
e [9]. FPGA ada
ptive filter pro
g
ram
block dia
g
ra
m in Figure 9.
Figure 9. FPGA Block
Dia
g
ra
m of the A
daptive Filter
5. Results a
nd Analy
s
is
The la
se
r gyro is pl
aced i
n
the sta
nda
rd turn
tabl
e, turntabl
e in th
e testing
pro
c
e
ss, in
each rotation
3600 outp
u
t fixed angle in
a pulse, the
p
u
lse wi
dth is
about 2u
s, so
we modify th
e
FPGA pro
g
ra
m, let the filtering
re
sult
s
in
a con
s
tant
angle
pul
se
doe
s not
co
me have b
een
accumul
a
ted,
when a fixe
d angle p
u
lse arrive
s to
sen
d
out a data, at the same time, the
accumul
a
tor reset, the follo
wing te
st results table:
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TELKOM
NIKA
ISSN:
2302-4
046
De
sign of Ad
aptive Filte
r
for La
se
r Gyro
(Jinm
i
ng Li)
7823
Table 3. The
Test Data wit
h
Different An
gular
Speeds (removal of
Earth's
rotation effec
t
s)
Angular rate
Positive va
lue
Negative values
±5 220753.5
-220753.5
±10 220753.3
-220753.3
±20 220753.2
-220753.2
±50 220753.4
-220753.4
±100
220753.6
-220753.6
±200
220753
-220753
±300
220754.6
-220754.6
Seen from th
e table in te
st data, in different an
gula
r
rate ca
se,turntable rotation
of 360
0
lase
r
gyro
o
u
tput value
s
are e
qual,
so th
e
adapt
ive filtering
module
al
so
ha
s
a very
high
precisi
on and wide dynam
ic range, and will comp
l
e
te the output data of
gyroscope accurat
e
demod
ulation
.
Fluctuation
behin
d
the d
e
cimal
point
test data i
s
d
ue to the pro
c
e
ss of m
a
n
ual
cal
c
ulatio
n of roun
ded o
u
t by roundi
ng.
The a
daptive
filter alg
o
rith
m is supe
rim
posed
with
a
20
ord
e
r FI
R filter,
so
the filter
delay block is approximatel
y equal to
the delay of low orde
r FIR filt
er. Its expression is
(Fs*2
0
)
/2=1m
s
, wh
ere Fs i
s
the
sa
mpling frequ
e
n
cy.Com
pa
re
d with the
ori
g
inal
High O
r
der L
o
w
- p
a
ss
FIR filter, its
pro
c
e
ssi
ng
speed i
s
im
proved g
r
eatly, so the
filter
can
meet the
req
u
irem
ent
s of
lase
r gyro d
e
m
odulatio
n speed in the fi
el
ds of ae
ro
space, wea
p
o
n
s, etc.
6. Summar
y
The p
r
e
s
ente
d
desi
gn of t
he ada
ptive filter
ha
s bee
n rep
eatedly
applie
d to la
ser
gyro
sign
al p
r
o
c
e
ssi
ng, filterin
g pr
ocessin
g
delay
of th
e ci
rcuit is
1.1ms, m
u
ch
lower th
an
the
conve
n
tional
delay time
of
10ms,
an
d h
a
s
a hi
gh
filte
r
ing
a
ccu
ra
cy
and
wi
de
dynamic rang
e, to
meet the
accura
cy an
d re
spo
n
se spee
d of the
st
ri
ct requi
rem
ent
s of a
ppli
c
ati
ons. th
ere
is a
stron
g
engi
ne
ering u
s
e val
ue.
Referen
ces
[1]
Fritze KR, Killp
atrick JE, Betndt DF. Ring las
e
r g
y
r
o
dith
er stripper: US, 52
490
31. 19
93-0
9
-28.
[2]
Josep
h
E K
ill
patrick, Min
n
e
apo
lis. Dit
her
Stripp
er W
i
th No
n-li
ne
arit
y
Correcti
o
n
，
Unite
d
State
s
Patent
，，
US 20
04/02
01
851 A
1
2004.1
0
[3]
David
A
Do
hen
y, J
ohn
L
Ko
lli
g. Dith
e
r stri
pp
er h
a
vin
g
least
-mean-s
quar
es
ad
aptiv
e u
p
d
a
t
ing
of d
i
the
r
stripper g
a
ins:
US, 4740
10
9 B1. 2008-
12-
21.
[4]
Doheny
D A
．
Adaptiv
e filters
for corrected
nois
e
red
u
ctio
n in ri
ng
laser
g
y
r
o
i
nertia
l
s
ystems. F
l
orida,
US: Universit
y
of South F
l
orid
a, 2004.
[5]
W
u
Mei, P
e
i
F
u
jun. Impr
ov
ed
distrib
u
ted
particl
e filter
for simu
ltan
eo
u
s
loc
a
liz
ation
and
map
p
i
n
g
.
TEL
K
OMNIKA
. 2013; (11): 7
6
17-7
626.
[6]
Without ada
pta
t
ion de
la
y
.
IEEE
T
r
ansom
Sig
nal Proc
essin
g
.
1998; 46(
3): 775~77
9.
[7]
GEST
ON D R, HROVAT
A C
.
Dither sig
n
a
l
remover for
a dith
ered r
i
ng
laser a
n
g
u
lar
rate sens
or
utilizi
ng a
n
ad
a
p
tive di
gital filt
er. United Stat
es: 5331
40
2, 1994-
07-1
9
.
[8]
IEEE Standard
for Binar
y
Fl
oa
ting-Po
int Arith
m
etic
：
Ne
w
Yo
rk, NY 10017,
USA. 1985.
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