Reĩerences [1] Mcnsur Omcrbashich, Integrated INS/GPS Navigation from a Popular Pcrspcctive, Journal o f Air Transportation, Vol.. Salychcv, Applied Inertial Navigation: Problems and Sol
Trang 1V N U Joum al o f S cien ce, M ath em a tics - Physics 23 (2 0 0 7 ) 243-251
Land-vehicle mems INS/GPS positioning during GPS signal blockage periods
T D T a n 3,* L M H a \ N T L o n g 3, N D D u c \ N p T h u y a
aD e p a rtm e n t o f E lec tro n ics a n d T elecom m unications, C oỉỉege o f Technology, VNU, H a n o i
144 X u a n Thuy, C au Giay, H anoi, Vietnam
hS c ie n c e & T echnology D epartm ent, VNU, H anoi, Ị 44 X u a n Thuy, C au Giay, tìa n o i, V ietnam
R eceived 5 N o v e m b c r 2007; received in rev ised form 27 D e cem b er 2 0 0 7
A b s tra c t T h e dem and o f v eh icle navig atio n and guid an ce has b ee n urg en t for m a n y years T h e
idea o f in teg ratin g m u ltise n so r navig atio n system s w as im plem ented T h e m o st e íĩic ie n t
m u ltisen so r co n íig u ra tio n is th c systcm in tegrating an inertial n av ig atio n sy ste m (IN S ) c o n sistin g
O ÍM E M S b a se d m icro sen so rs and a global p ositioning sy stem (G P S ) In such sy ste m , th e G P S is
used for p ro v id in g p o sitio n a n d vclo city w hereas the IN S for p ro v id in g o rien ta tio n T h e estim atio n
o f the sy ste m erro rs is p erfo rm ed by a K alm an filter (K F ) A serio u s p ro b le m o cc u rs in the
IN S /G P S sy stc m ap p lica tio n th at is caused b y the accid en tal G P S signal b lo ck ag e s In th is p aper,
thc m ain o b je c tiv e is to im p ro v e the accu ra cy o f the o b tain ed n av ig atio n p a ram eters d u rin g p erio d s
o f G PS sig n al outages usin g đ iíĩe re n t m ethods T he overall p c ríb rm a n ce o f the sy ste m h ave b een
analyzcd b y ex p c rim en tatio n data; and resu lts show that thcse m cthods in d ced im p ro v e the quality
o f the n a v ig a tio n and g u id an ce system s
1 In t r o d u c tio n
In the la st decade, the dem and fo r accurate la n d -v e h ic le n a v ig a tio n in se ve ra l a p p lic a tio n s has gro \vn r a p id ly [1 ] W ith the stro n g g ro w th o f M ic ro -E le c tro -M e c h a n ic a l-S y s te m ( M E M S ) te c h n o lo g y , there appears a n e w trenđ in n a v ig a tio n and guidance d o m a in : it consists o f the in te g ra tio n o f IN S and GPS a lto g c th e r [2] In te g ra tin g these tw o n a v ig a tio n m ethods can im p ro v e the p e río rm a n c e o f the system and reduce c o n c u rre n tly the disadvantages o f b o th ENS and G PS T h e K a lm a n í ì lt c r (K F ) is
u tiliz e d to e stim ate the System e rro rs in o rd e r to im p ro v e the a ccu ra cy o f the o v e ra ll system [ 3] In the case o f the GPS sig n a l b lo c k a g e , p o s itio n in g is p ro v id e d b y the IN S u n til G PS s ig n a ls are re a cq u ire d
D u rin g such p e rio d s , n a v ig a tio n e rro rs increase ra p id ly w ith tim e due to the tim e -d e p e n d e n t IN S e ư o r
b e h a vio r F o r accurate p o s itio n in g in these cases, some s o lu tio n s sh o u ld be used to im p ro v e n a v ig a tio n
in íb rm a tio n In th is paper, a ĩle x ib le c o n íìg u ra tio n o f K F w il l be used ío r the IN S /G P S in te g ra tio n
T h e la n d -v e h ic le k in e m a tic s data set is also used w ith in d uce d G PS outages B y u s in g these m ethods, the results sh ow ed re m a rka b le im p ro v e m e n t o f p o s itio n errors
2 Integration o f INS and GPS usỉng Linearized Kalman Filter
T h e IN S system has tw o m a in advantages w h e n c o m p a rin g w ith o th e r n a v ig a tio n system : s e lf- contained a b ility a nd h ig h a ccu ra cy fo r sh o rt te rm n a v ig a tio n T h e serious p ro b le m o f the IN S caused
* Corresponding author E-mail: tantd@vnu.edu.vn
243
Trang 2244 T D Tan ei al / VNU Journal o f Science, Mathematics - Physics 23 (2007) 243-251
b y a c c u m u la tio n o f g yro s c o p e and a ccelerom eter e rro rs T h e re fo re , in lo n g -te rm n a v ig a tio n
a p p lica tio n s, the IN S w o rk s w ith the a id o f o th e r system s such as ra d io n a v ig a tio n system s (L o ra n ,
T acan), sa te llite n a v ig a tio n system s (G P S , G L O N A S S ) T h e im p o rta n t advantage o f these system s is stable períb rm an ce C o n se q u e n tly, there is a great need fo r in te g ra tio n o f IN S w ith One o f these systems T he in te g ra tio n o f IN S and GPS is considered an o p tim a l c o m b in a tio n T he heart o f
in tegrated system is K a lm a n a lg o rith m
T h e K a lm a n íìlte r is a m u ltip le in p u t, m u ltip le o u tp u t d ig ita l íìlte r that can o p tim a lly estim ate in real tim e the states o f the system based on its n o is y outputs Som e o f the m ost successíul a p p lic a tio n s
o f K a lm a n íìlte r in g is that it can deal w ith n o n -lin e a r m easurem ent re la tio n s h ip s T he p rin c ip le approach in such cases is to lin e a riz e the n o n -lin e a r m o d e l íĩrs t and then a p p ly the S ta n d a rd K a lm a n íilt e r to o b ta in the State o f the system T here are e ig h t such states vvhich c o n s is t o f v e lo c ity e ư o rs (e V N, e V E, e V D), d r ift term s (G x , G y , G z ) and a ttitu d e e rro rs (T n , T e ) T h e GPS o u tp u t is used as a
to o l to estim ate the e ư o r in the IN S and to co rre ct the e rro r as m u c h as possible I t is c a lle d the G PS- aided IN S system c o n fig u ra tio n [4 ] L o o k in g at the S tate space m o d e l:
w h e re F is the d yn a m ic m a trix (o b ta in e d b y p a rtia l d e riv a tiv e s ), X is the State v e c to r, G is the design
m a trix and u is the íiorcing ĩu n c tio n
Because o u r n a v ig a tio n system w o rk s in real tim e m ode, w e c o n v e rt e q u a tio n 1 to its discrete tim e fo rm :
w here <I>k is the State tran sitio n m atrix, w k is the driven resp o n se at tk+i due to th e p resence o f input
w h ite noise d u rin g tim c in te rv a l ( t k, tk+i)
Because th is tim c in te rv a l is sh ort ( it means that the upd a tc rate o f thc IN S is h ig h ), w e can approxim ate <ĩ)k as:
a n d th c c o v a r ia n c c m a trix a s s o c ia te d w ith w k is
Q k = E [ w kw ; ] * * kG Q G T* Ĩ A t
(4)
w h e r e Q = d i a g Ị o ^ a ị a l G *x ơ ^ x Ơ^XỊ
L /)o k in g a t th e o b s e rv a tio n e q u a tio n :
w here R k = E [ v kv ‘ j = d ia g Ị is the co va ria n ce m a trix fo r v k
In th is system, w e assum e th a t the process noise w k and the m easurem ent noise v k are
u ncorrelated
Fig 1 F eed fo rw ard (o p en -lo o p ) co n ĩig u ra tio n
Trang 3T D Tan et al / VNU Journaỉ o f Science, Mathematics - Physics 23 (2007) 243-251 245
F ig 1 illu s tra te s an open lo o p (o r fe e d fo rw a rd ) c o n íig u ra tio n Its advantage is that p ro v id e s a
ra p id íìlte r response A lte m a tiv e ly , the c o n íìg u ra tio n in F ig 2 is a closed lo o p One T h is c o n fig u ra tio n
is m o re c o m p le x than the open lo o p one b u t it can p ro v id e b e tte r p eríb rm a n c e in the existance o f
n o n lin e a r e ffe c ts
Fig 2 F eed b ack (clo sed -lo o p ) co nfiguration
3 Vehicle Motion Constraints
It is o b v io u s that the p erfo rm a n c e o f the IN S w i l l degradc in the absence o f GPS signal The reason is that the lo w co st M E M S IM U s consists o f lo w q u a lity sensors w h ic h p ro v id e large e ư o rs and noises In these cases, w e s o m c tim c u tiliz e d la n d v e h ic le m o tio n a ttrib u te s to p re ve n t IN S e ư o r
a c c u m u la tio n T h e e qu a tion d e riv e d fro m b e h a v io r o f a lanđ v e h ic le w i l l com pensate the G P S ’ s
m casurem ent In th is paper, w e m e n tio n to v e lo c ity and h e ig h t constraints
3.1 Velocity Constraỉnts
W e have to m ake sure th a t the v e h ic le does not s lip on the road and n o t ju m p o f the ground
T h e n , the v e lo c ity o f the v e h ic le in the d ire c tio n p e rp e n d ic u la r to the m o ve m e n t o f the v e h ic le w o u ld
be zero as sh o w n in F ig 3
z
Fig 3 Land vehicle v elo city constraints
T he c o n s tra in ts are:
v xb 0 ) = 0
v}(t) = 0
Eq 6 can be tra n s íb rm e d to the n a v ig a tio n fram e:
(6)
Trang 4246 T D Tan ei ai. / VNU Jo u m a ỉ o f Science, Mathematics - Physics 23 (2007) 243-251
VE = CỈ v ; VD
v *k
T h is e q u a tio n can p ro v id e the Virtual v e lo c ity m easurem ents to a id the EMU W h e n a GPS sig n a l is lo s t, a c o m p le m e n ta ry K a lm a n íilt e r is used to c o m b in e the IN S and Virtual v e lo c ity
m easurem ents in o rd e r to reduce the p o s itio n and v e lo c ity e rro rs (see F ig 4)
Fig 4 V elocity co n sttain ed n av ig atio n b lo ck
3.2 Height Constraỉnts
T h is c o n s tra in t is d e riv e d fro m the fa c t that the h e ig h t does n o t change m u ch in land v e h ic u la r
s itu a tio n , e s p e c ia lly in sh o rt tim e p eriods It n o t o n ly im p ro ve s the h e ig h t s o lư tio n , b u t also the o v e ra ll
h o riz o n ta l s o lu tio n a ccuracy d u rin g G PS outage H o w e v e r, a re a lis tic m easurem ent u n c e rta in ty value
m u st be chosen fo r these m easurem ents, because any e ư o rs in the h e ig h t s o lu tio n w il l u ltim a te ly skew the h o riz o n ta l s o lu tio n
4 E x t e r n a l H e a d in g A id in g
T o take the in -m o tio n a lig n m e n t o f the n a v ig a tio n system , w e use the h e a d in g fro m GPS o r the
e x te m a l h e a d in g m easurem ents such as m a g ne tom ete r in to the a ttitu d e c o m p u ta tio n s T h e heading
e rro r is an im p o rta n c e param eter because o f its re la tio n to the system e rro r statcs T h e heading e rro r is
d e riv e d based on the fo llo w in g h ea d in g c o m p u ta tio n e qu a tion w h ic h can be tra n s íb rm e d to the
n a v ig a tio n íram e:
(1,2)
5 E x p e r im e n ta tio n R e s u lts
In th is stud y, as fo r the ĨN S system w e have used the I M U B P 3 0 1 0 (see F ig 4 ) w h ic h consists
o f three A D X R S 3 0 0 g y ro s and three heat com pensated A D X L 2 1 0 E accelerom eters T h e
m easurem ents are re a liz e d b y I M Ư ’ s m ic ro -c o n tro lle rs and tra n s m itte d o u t v ia R S 2 32 interfa ce T he
u n it tra n s m its o u tp u t data as a n g u la r in c re m e n ta l and v e lo c ity in c re m e n ta l data in s e ria l fram es o f 16
b ytes at the íre q u e n c y o f 64 H z
Trang 5T D Tan et al / VNU Journaỉ o f Science, Maíhematics - Physics 23 (2007) 243-251 247
Fig 5 T h e IM Ư B P 3 0 1 0 - A M E M S unit used in o u r IN S /G P S system
T h e in tegrated n a v ig a tio n system im p le m e n ts b o th open lo o p and closed lo o p c o n íĩg u ra tio n s
T h e e ư o r co m p en sa tion m o d u le u tiliz e s the v e h ic le m o tio n c o n stra in ts and the m a g n e to m e te r
m easurem ent d u n n g GPS outages T h e lo g ic svvitches in the V C + + soítvvare allovvs the f ilt e r to s w itc h betw een v a rio u s íìlte r designs, d e p c n d in g on GPS a v a ila b ility
A íte r c h a ra c te riz in g the I M U e rro rs [ 5] , the in fo rm a tio n o f these noises is a p p lie d to the K F based M E M S -IN S /G P S in te g ra tio n m o d u le in o rd e r to estim ate thc v e lo c itie s , p o s itio n s and a ttitu d e o f the object
T o see the uscíulness o f the K F , lo o k at the F ig 6 and F ig 7 th a t illu s tra te the h e a d in g o f IN S vvhile standing s till in the case vvithout K F and w ith K F , re s p c c tiv e ly
tưne(s)
F ig 6 T h e d riít o f h ea d in g (w ith o u t K F)
tữne (s)
Fig 7 T h e head in g w ith the p re sen t o f K F N o te th at ứie
d iíĩe re n c e in scaỉe o f the g raphs in F ig 6 and Fig 7
Trang 6248 T D Tan et al / VNU Journal o f Science, Mathematics - Physics 23 (2007) 243-251
F o r the e x p c rim e n t o f the IM Ư on ro a d [6], GPS and the đata a c q u is itio n system w ere in sta lle d
in a ve h icle T he v e h ic le w as d riv e n fo r 12 m in u te s in a 5 k m trạ je c to ry I n itia lly th c ve h ic le was at rest, w ith the engine on, fo r abo u t 60 seconds in o rd e r to estim ate the d e te rm in e d errors
T he update fro m the IN S w as taken every 0.015625S, the GPS update w as taken e very ls and the
K F was ru n every 0.5s to achieve b etter accuracy T he fíe ld test 2 -D trạ je c to ry is presented in Fig 8
Fig 8 T ra je cto ry o f the experim en tal v ehicle
In the case that the G PS loses its signal as in an e x p e rim c n t in F ig 9, thc IN S co n tin u e s to com pute the p o s itio n d u rin g the p c rio d o f lo s t G PS signal ( fro m the 4 0 0 th to th c 4 7 0 lh scconds, in the
ừ a je c to ry in F ig 9) It can be seen that the IN S /G P S tra je c to ry (s o lid c u rv c ) su pp o rtc d b y K F fo llo w s the GPS one (d o t cu rve ) w ith s m a ll e rro r fo r q u ite a lo n g trip In th is c o m b in e d stru ctu re , the closed
lo o p K F is u tiliz e d w hen the G PS sig n al is a v a ila b le and the open lo o p K F is a p p lie d w h e n GPS is outage W e note that th is íĩg u re show s the p o s itio n o f the v e h ic le a lo n g N o rth and East d ire c tio n on the E arth instead o f the la titu d e and the lo n g ú u d e T h e reason is that w e can p rc v e n t n u m c ric a l
in s ta b ilitie s in c a lc u la tin g the K a lm a n gain
Fig 9 T rajecto ry o f the land v eh icle in the case o f G P S outage T h e insert sh o w s th e tim e tim c interval w herc
the G PS signal is blockageđ
Trang 7T D Tan et al / VNU Journal o f Science, Mathematics - Physics 23 (2007) 243-251 249
F ig lO a a n d lO b s h o w th e E a s t a n d N o r th v e lo c itie s o f th e in te g ra te d system It c a n b e s e e n
th a t the IN S /G P S v e lo c itie s su pported b y K F (s o lid c u rv e ) fo llo w s the G PS one (d o t cu rv e ) vvith sm all
e rro r fo r q u ite a lo n g trip In case o f the GPS sig n al outtage, the a ccuracy is a ffe cte d as w e can see fro m th e graphs B u t once the n e w G PS values are read b y the p ro g ra m , the K F takes v e ry less tim e to settle dovvn to w a rd s the actual values
(a)
LU
time (s)
(b)
F ig u re 10 V e lo cities in the n av ig atio n fram e: in th e N o rth (a) an d in the E ast (b)
F ig 11 a and 11 b s h o w the r o ll and p itc h o f the n a v ig a tio n system T hese re su lts seem to be quúe reasonable fo r a system w as on to a la n d ve h ic le
Trang 8250 T D Tan et ai / VNU Journal o f Science, Maíhemaíics - Physics 23 (2007) 243-25 ì
10
5
1 0 1
è -5
Jữ
ọ
o -10
-15
-20
tìm e (s) (b) Figure 11 R oll (a) and pitclì (b) angles o f the in teg rated n av ig atio n system
6 C o n c lu s io n s
In th is paper, an e ig h t State K a lm a n íĩlt e r was proposed to be used in o rd e r to enhance the
q u a lity o f a co m b in e d GPS and IN S system T h e v e h ic le m o tio n c o n s tra in ts and m a g ne tom ete r
m easurem ents are u tiliz e d to reduce the IN S e rro r d e g ra d a tio n d u r in g the p e rio d s o f GPS
u n a v a ila b ility T h e e xp e rim e n ta l results have shovvn that the in itia l c a lib ra tio n and a lig n m e n t is accurate e n o u g h to allovv n a v ig a tio n w ith I M U sensors fo r e x te n de d p e rio d o f tim e w ith lo w dcad
re c k o n in g e rro rs In fact, the K a lm a n íìlte r tre m e n d o u s ly im p ro v e s accuracies co m p a re d to the GPS and IN S w h e n o pe ra tin g alone as in d iv id u a l n a v ig a tio n system s T h e a ccuracy o f estim a te d param eters
Trang 9T D Tan et al ỉ VNU Journaỉ o f Science, Mathematics - Physics 23 (2007) 243-251 251
is im p ro v e d b y in c re a s in g the d im e n s io n o f the system s’ states space O b v io u s ly , b y its s im p lic ity , th is
m o d e l can be em bedded e a s ily in to a real tim e system F u tu re w o rk w i l l in ve s tig a te in - f lig h t
c a lib ra tio n and a lig n m e n t a lg o rith m s e x te n d in g the e rro r m o d e ls o f the IN S system
A c k n o \v le d g m e n ts T h is w o rk is supported b y the V N U p ro g ra m Q G T D 0 5 0 9
Reĩerences
[1] Mcnsur Omcrbashich, Integrated INS/GPS Navigation from a Popular Pcrspcctive, Journal o f Air Transportation, Vol
7 No 1 (2002) 103
[2] Olcg s Salychcv, Applied Inertial Navigation: Problems and Solutions, BMSTU Press, Moscow Russia, 2004.
[3] Pcter s Maybcck, Stochastic Models, Estimation, and Control, Academic Press, Vo] 1 (1994) 1.
[4] Robert Wolf, Giintcr w Hein, Bemd Eifcller, A Kalman Filter for the Integration o f a Low Cost INS and an attitude
GPS, hxstiíute o f Geodesy and Navigation, Munich, Germany, 1997, 1.
[5] Haiying Hou, Modeling Inertial Sensors Eưors Using Allan Variance, UCEGE reports number 20201, Mastcr's thesis,
University o f Calgary» Scptember 2004
[6] s Panzicriy, F Pascucciz, G Uliviy, An Outđoor Navigation System Usỉng GPS And Inertial Platíorm, IEEE ASM E Transactions on Mechatronics Vol 7 No 2 (2002) 134.
Trang 10V N U Joum al o f S cien ce, M ath em a tics - Physics 23 (2 0 0 7 ) 243-251
Land-vehicle mems INS/GPS positioning during GPS signal blockage periods
T D T a n 3,* L M H a \ N T L o n g 3, N D D u c \ N p T h u y a
aD e p a rtm e n t o f E lec tro n ics a n d T elecom m unications, C oỉỉege o f Technology, VNU, H a n o i
144 X u a n Thuy, C au Giay, H anoi, Vietnam
hS c ie n c e & T echnology D epartm ent, VNU, H anoi, Ị 44 X u a n Thuy, C au Giay, tìa n o i, V ietnam
R eceived 5 N o v e m b c r 2007; received in rev ised form 27 D e cem b er 2 0 0 7
A b s tra c t T h e dem and o f v eh icle navig atio n and guid an ce has b ee n urg en t for m a n y years T h e
idea o f in teg ratin g m u ltise n so r navig atio n system s w as im plem ented T h e m o st e íĩic ie n t
m u ltisen so r co n íig u ra tio n is th c systcm in tegrating an inertial n av ig atio n sy ste m (IN S ) c o n sistin g
O ÍM E M S b a se d m icro sen so rs and a global p ositioning sy stem (G P S ) In such sy ste m , th e G P S is
used for p ro v id in g p o sitio n a n d vclo city w hereas the IN S for p ro v id in g o rien ta tio n T h e estim atio n
o f the sy ste m erro rs is p erfo rm ed by a K alm an filter (K F ) A serio u s p ro b le m o cc u rs in the
IN S /G P S sy stc m ap p lica tio n th at is caused b y the accid en tal G P S signal b lo ck ag e s In th is p aper,
thc m ain o b je c tiv e is to im p ro v e the accu ra cy o f the o b tain ed n av ig atio n p a ram eters d u rin g p erio d s
o f G PS sig n al outages usin g đ iíĩe re n t m ethods T he overall p c ríb rm a n ce o f the sy ste m h ave b een
analyzcd b y ex p c rim en tatio n data; and resu lts show that thcse m cthods in d ced im p ro v e the quality
o f the n a v ig a tio n and g u id an ce system s
1 In t r o d u c tio n
In the la st decade, the dem and fo r accurate la n d -v e h ic le n a v ig a tio n in se ve ra l a p p lic a tio n s has gro \vn r a p id ly [1 ] W ith the stro n g g ro w th o f M ic ro -E le c tro -M e c h a n ic a l-S y s te m ( M E M S ) te c h n o lo g y , there appears a n e w trenđ in n a v ig a tio n and guidance d o m a in : it consists o f the in te g ra tio n o f IN S and GPS a lto g c th e r [2] In te g ra tin g these tw o n a v ig a tio n m ethods can im p ro v e the p e río rm a n c e o f the system and reduce c o n c u rre n tly the disadvantages o f b o th ENS and G PS T h e K a lm a n í ì lt c r (K F ) is
u tiliz e d to e stim ate the System e rro rs in o rd e r to im p ro v e the a ccu ra cy o f the o v e ra ll system [ 3] In the case o f the GPS sig n a l b lo c k a g e , p o s itio n in g is p ro v id e d b y the IN S u n til G PS s ig n a ls are re a cq u ire d
D u rin g such p e rio d s , n a v ig a tio n e rro rs increase ra p id ly w ith tim e due to the tim e -d e p e n d e n t IN S e ư o r
b e h a vio r F o r accurate p o s itio n in g in these cases, some s o lu tio n s sh o u ld be used to im p ro v e n a v ig a tio n
in íb rm a tio n In th is paper, a ĩle x ib le c o n íìg u ra tio n o f K F w il l be used ío r the IN S /G P S in te g ra tio n
T h e la n d -v e h ic le k in e m a tic s data set is also used w ith in d uce d G PS outages B y u s in g these m ethods, the results sh ow ed re m a rka b le im p ro v e m e n t o f p o s itio n errors
2 Integration o f INS and GPS usỉng Linearized Kalman Filter
T h e IN S system has tw o m a in advantages w h e n c o m p a rin g w ith o th e r n a v ig a tio n system : s e lf- contained a b ility a nd h ig h a ccu ra cy fo r sh o rt te rm n a v ig a tio n T h e serious p ro b le m o f the IN S caused
* Corresponding author E-mail: tantd@vnu.edu.vn
243