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a G a B D
ADVISORY GROUP FOR AEROSPACE RESEARCH
&
DEVELOPMENT
7
RUE ANCELLE 92 NEUILLY-SUR-SEINE FRANCE
. .
.
Hybrid Navigation
Systems
N O R T H A T L A N T I C T R E A T Y O R G A N I Z A T I O N -
-
I
INITIA L DISTRIBUTION IS LIMITED
FOR ADDITIONAL COPIES SEE BACK COVER
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A G A R D Conference Proceedings No. 54
N O R T H
ATLANTIC TREATY ORGANIZATION
ADVISORY G R O U P F O R AEROSPACE RESEARCH A N D DEVELOPMENT
(ORGANISATION D U TRAITE D E L ATLANTIQUE N O R D )
HYBRID NAVIGATION SYSTEMS
Papers presented at the Guidance and Control Panel 9th Meeting held at Delft, Netherlands,
22-26 September 1969
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C H A I R M AN , G U I D A N C E A N D C O N T R O L P A N E L
P r o f e s s o r Walter Wrigley
D e p a r t m e n t o f A e r o n a u t i c s a n d A s t r o n a u t i c s
M a s s a c h u se t t s I n s t i t u t e o f T e c hn o lo g y
Cam br idge , Massachuse t t s 0 2 1 3 9
-
USA
D E P U T Y C H A I R M A N , G U I D A N C E A N D C O N T R O L P A N E L
M H:
G. R.
Robinson
Head, Av ion ics Department
R o y a l A i r c r a f t , E s t a b l i s h m e n t
Farnborough, Hampshire , England
C H A I R MA N , G U I D A N C E A N D C O N T R O L P A N E L
(as
of 2 2 September 1 9 6 9 )
Mr
H. G.
R. Robinson
Head, Av ion ics Department
R o y a l A i r c r a f t E s t a b l i s h m e n t
Farnborough, Hampshire , England
D E P U T Y C H A I R MA N , G U I D A N C E A N D C O N T R O L P A N E L
(as
o f 2 2 September 1 9 6 9 )
P r o f e s s o r , C. T. Leondes
Depar tm ent o f Enginee r ing
U n i v e r s i t y o f C a l i f o r n i a
Los
A n g e l e s , C a l i f o r n i a 9 0 0 2 4
C H A I R M A N
OF
P R O G R A M C O M M I T T E E
M
W.
J.Rhine
NASA,
E l e c t r o n i c s R e s ea r ch C e n t e r
Cam br idge , Massachuse t t s 0 2 1 3 9 , USA
HOST
N A T I O N
COORDINATOR
Mr A.
H.
Geudeker
N e d e r l a n d s e D e l e g a t i e
B i j
de
AGARD
c / o S t i c h t i n g N a t io n a a l L u c h t -e n
R uim t e v a a r t l a b o r at
o r
ium
Kluyverweg 1
D e l f t , N e t h e r l a n d s
E X E C U T I V E , G U I D A N C E A N D C O N T R O L P A N E L
Major C.D.Mount, USAF
AGARD
i i i
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FOREWORD
T he e v o l u t i o n o f g u id a n ce a nd c o n t r o l s y s t e m s o v e r t h e p a s t d e c a d e h a s i n c l u d e d
t h e d e ve lo pm e nt o f r a t h e r s o p h i s t i c a t e d h y b r i d s y st em s .
h y b r i d s y s t e m s as
s te l lar
m o n i t o r e d i n e r t i a l s y s t e m s , LORAN i n e r t i a l s ys t e m s , D o pp le r
i n e r t i a l LORAN o r DILS systems,
v a r i o u s c o m b i n at io n s o f sa te l l i t e m o n i t o r e d i n e r t i a l
sys t em s , and numerous o t h er combi na t i ons .
This
h a s i n c l u d e d s u c h
T h e f u t u r e w i l l u n d o u b te d l y b r i n g many f u r t h e r s i g n i f i c a n t a d v a nc e d d e v e l o pm e n t s
i n h y b r i d g u i d a n c e a n d c o n t r o l s y st e m s . N e v e r t h e l e s s t h e G u id a nc e a nd C o n t r o l P a n e l
o f
NATO-AGARD was
well a w a r e o f t h e a p p r o p r i a t e n e s s o f a r ev ie w o f 't he s t a t u s o f t h e
f i e l d at t h i s time and s o t h e s e c o n f e r e n c e p r o c e e d i n g s w h ic h e v o l v e d f r om a meet i ng
at
t h e D e l f t U n i v e r s i t y o f T ec h n ol og y , D e l f t , N e t h e r l a n d s , S e p te m b e r 2 2 - 2 6 , 1 9 6 9 .
are
d e v ot e d t o t h e g e n e r a l s u b j e c t o f c u r r e n t t e c hn o lo g y i n h yb r id g u id a n ce a nd c o n t r o l
systems.
T h e s u b j e c t w a s t r e a t e d
a t
t h e m e et in g i n f i v e b r oa d c a t e g o r i e s w it h f u l l s e s s i o n s
d e v ot e d t o e a c h c a t e go r y .
o f H y b r i d N a v i g a t i o n T e c h n i q u e s ,
A i r
T r a f f i c C o n t r o l a n d L a n di n g S ys te m s A p p l i c a t i o n s ,
t h e I n t e r a c t i o n o f A i r b o r n e a n d G ro un d E l e m e n t s , A i r c r a f t E x p e ri e n c e a nd A p p l i c a t i o n s ,
a n d A n a l y t i c a l
a nd T h e o r e t i c a l C o n s i d e r a t i o n s o f H y b r i d T e c hn iq u es . T he n e t r e s u l t i s
a r a t h e r t h o r o u g h
t reatment
o f t h e s u b j e c t , a nd t h e s e C o n f e re n c e P r o c e ed i n g s s h o u l d
t h e r e f o r e p r ov e t o b e q u i t e v a l u a b le t o p r a c t i c i n g g u id a nc e a nd c o n t r o l e n g i n e e r s .
T h es e s e s s i o n s i n c l u d e d s e s s i o n s o n S y st e m s A p p l i c a t i o n s
A g r e a t d e a l o f c r e d i t f o r t h e t e c h n i c a l s u c c e s s o f t h i s c o n fe re n ce m u st g o t o t h e
program commit tee of which
M W.
J .Rh i ne was Chairman.
C o n t ro l P a n e l made v a l u a b l e c o n t r i b u t i o n s a nd t h e i r h e l p is g r e a t l y a p p r e c ia t e d .
Major C.D.Mount was o u t s t a n d in g i n h i s p e rf or m an c e i n h a n d l in g h i s f i r s t c o n f e r en c e
i n h i s n ew c a p a c i t y as t h e E x e c u t i v e , G u id a nc e a n d C o n t r o l P a n e l . F i n a l l y , g r a t i t u d e
i s
a l s o e x p r e ss e d t o t h e N e t h e r l a n d s G ov ern me nt
f o r o f f e r i n g t o s e r v e
as
t h e h o s t
c o u n t r y f o r t h i s S ym po siu m.
c a n t l y t o t h e s u c c e s s o f t h e S ym posium .
as h o s t n a t i o n c o o r d i n a t o r .
A l l
members of the Guidance and
The facilities were e x c e l l e n t and c o n t r ib u t e d s i g n i f i -
M A.H.Geudeker was o u t st a n di n g i n h i s r o l e
C. T.
Leondes
E d i t o r
Gu i dance and Con t ro l Panel
A G M
i v
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CONTENTS
SESSI ON I . SYSTEMS APPLI CATI ONS OF HYBRI D NAVI GATI ON TECHNI QUES
HYBRI D GUI DANCE AND NAVI GATI ON SYSTEMS
by Dr G. R. Mar ner
CHARACTERI STI CS OF A SATELL I TE NAVI GATI ON SYSTEM OPERATED I N CONJ UNCTI ON W TH
A USER I NERTI AL SYSTEM
by
Dr B. P . Leonar d
GLOBAL NAVI GATI ON/ TRAFFI C SURVEILLANCE/COMMUNICATION SATELLI TE SYSTEM FOR
MI LI TARY AND CI VI L VEHI CLES
by M.
W Mi t c hel l
THE TMA ROLE OF HYBRI D SYSTEM RADI O SENSORS
by F. S . St r i nger
SESSI ON 11. AI R TRAFFI C CONTROL AND SYSTEMS APPL I CATI ONS
THE USE OF F I LTERI NG TECHNI QUES AND/ OR MI XED NAVI GATI ON SYSTEMS I N COMBI NATI ON
W TH BAROMETRI C ALTI METRY T O GENERATE GL I DE SLOPES FOR PRECI SI ON APPROACH
by
M.
G. Pear son
THE USE OF I NERTI AL I NFORMATI ON TO I MPROVE AUTOMATI C I L S APPROACH PERFORMANCE
by N. H. - Hughes
I MPROVEMENT OF THE ACCURACY OF AUTOMATI C L ANDI NG SYSTEMS BY USE OF KALMAN- F I LTERI NG
TECHNI QUES AND I NCORPORATI ON OF I NERTI AL DATA
by W Sc hm dt
COLLI SI ON AVOI DANCE AND THE AI R TRAFF I C CONTROL ENVI RONMENT
by A. Br owde
SESSI ON 111. THE I NTERACTI ON OF AI RBORNE AND GROUND EL EMENTS
I NTEGRATED HYBRI D- I NERTI AL AI RCRAFT NAVI GATI ON SYSTEMS
by
R. C. St ow and B. Dani k
MODERN AI RCRAFT NAVI GATI ON SENSORS FOR HYBRI D SYSTEMS
by W R. Fr i ed
LORAN SYSTEMS TECHNOLOGY
by R. E. Weaver , J r
SYSTEME DE NAVI GATI ON A I NERTI E HYBRI DE OPTI MI SE
par P . Fau r r e
TACTI CAL LORAN
by L. D. Hi ggi nbot ham
SESSI ON I V. AI RCRAFT EXPERI ENCE AND APPLI CATI ONS
THE C- . 5 NAVI GATI ON SYSTEM - AN APPLI CATI ON OF DI GI TAL SYNERGI STI C STOCHASTI C
HYBRI D NAVI GATI ON TECHNOLOGY
by Dr B. J . Mi l l er
THE HYBRI D NAVI GATI ON SYSTEM FOR THE NI MROD MARI TI ME PATROL AI RCRAFT
by
R. P. G. Col l i ns on
Ref er ence
1
2
9
1 0
11
1 2
13
1 4
1 s
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T H E U S E O F H Y B R ID T E C H N I Q U E S
I N
COMMERCIAL TRANSPORT AIRCRAFT
by S . B. P o r i t z k y
I N T E G R A T E D A V I O N I C S Y S T E M D E S I G N F O R H E L I C O P T E R S
A N D
VTOL
b y L A . K a u f m a n
S E S S I O N V . ANALYTICAL
A N D
T H E O R E T I C A L C O N S I D E R A T I O N S OF H Y B R I D T E C H N I Q U E S
INTEGRATED NAVI GATION BY L EAST SQUARE ADJUSTMENT
by
P r o f .
D r - I n g .
K .
R a m s a y e r
A
SIMPLE KALMAN FILTER FOR VOR/DME
b y M A . V . M a t t h e w s
O P T I M A L C O R R E C T I O N O F S T O C H A S T I C E R R O R S O F I N E R T I A L S Y S T E M S
by R . S w i c k
D E S I G N O F LOW S E N S I T I V I T Y KALMAN F I L T E R S F O R H Y B R I D N AV I G AT I O N S Y S T E M S
by
P r o f . C . E . H u t c h i n s o n
R e f e r e n c e
1 6
17
18
19
20
21
vi
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HYBRID SYSTEMS FOR GUIDANCE AND NAVIGATION
G.
R.Marner
D i r e c t o r o f Research,
Col l ins Radio Company,
Cedar Rapid s, Iowa
1
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1-1
H Y B R I D
SYSTEMS FOR
GUIDANCE
AND
N A V I G A T I O N
G.
R.
Marner
D i r ec t o r o f R es ea rc h
Col 1
i
s Radio Company
Cedar Rapids, Iowa
SUMMARY
Developments i n sensors, computers, d at a tran smis s ion te chnique s and systems theory have g re a t l y
acce le ra ted the t ren d tpward hy br id gu idance and na v ig a t ion sys tems. Opera t iona l needs fo r new types o f
d a ta , f o r a cc ur ac y and r e l i a b i l i t y , and f o r m u lt i- mo de o p e r a t i o n t o c o mp le te m i s s io n s d e s p i t e f a i l u r e o r
l ac k o f i np u t da ta hav e mo t i v a te d th i s t r end . Gene r al comments c onc e r n ing the c ha r ac t e r i s t i c s o f r edun -
dant , complementary and sy ne rg is t i c sys tems are made, and a l i s t o f imp or ta n t hy br id sys tem examples i s
g i v en. Ope r a t i ona l needs f o r some fu t u r e hy b r i d s ys tems a r e ou t l i ne d . These i nc l ude a r eas o f a i r c r a f t
l a n di n g , n a v i g a t i o n an d t r a f f i c c o n t r o l , m a r in e n a v i g a t i o n an d t r a f f i c c o n t r o l a nd sp ace n a v ig a t i o n .
SOMMAI RE
L 'G vo lu t ion des techn iques , en mat ie re de de tec teurs se ns ib les , de ca lcu la t eu rs , de t ransmiss ion de
donnCes e t de thC o r i e des s ys ts mes, a f o r d l a tendanc e en d i r ec t i on des s y s th es hy b r i des de guidage
e t d e n a v ig a t i o n .
1 'achPv emen t de tou te m is s ion , qu e l l e s que s o i en t l e s db fec tuo s i tbs ou pe r tes d ' i n f om a t i o ns . Pou r
r6pondre
3
ce c r i t s r e , de nouvel le s formes de donnCes e t des modes m ul t i p l es de fonct ionnem ent sont
n gc es sa ir es , a i n s i q u' un e a m C l i o r a ti o n de l a p r k c i s i o n e t d e l a f i a b i l i t 6 .
pr in c i pe s redondants, cc inplbmentaires e t "syn erget ique " appl iqu 6s aux systemes hybr i des majeurs donnCs
en exemple , de meme que l ' a pp l i ca t i o n fu tu re 3 l a n a v ig a t io n e t au c o n t r o l e a 6r ie n , m a r i ti m e e t s p a t i a l ,
de nouveaux sys thes hybr ides .
L 'u t i l i s a t i o n des sy stemes hy b r ides es t mo t i v be pa r l es bes o ins opb r a ti onne l s r equb r an t
S on t e ga le me nt t r a i t & l e s
I n t r o d u c t i o n
The use o f h yb r i d gu idance and nav ig a t io n sys tems has been grow ing r ap id ly i n rece nt years .
Th i s
g r ow th has been due t o bo th tec hno log i c a l c a pa b i l i t i e s and ope r a t i ona l r equ ir emen ts , On t h e t e c h n o l o g i c a l
s i de we have seen the development o f many pr ec is e and re l ia b l e components and sensors such as gyros, acce ler-
ometers, readout dev ices , t ime and f requency s tandards , ra d i o rece ive rs capab le o f t ime, f requency o r phase
c ompar is ons, e tc . So l i d s ta te and, r ec e n t l y , m ic r oe lec t r on i c tec hn iques have per m i t t ed us e o f mor e c omplex
e l e c t r o n ic c i r c u i t s w i t h g r e a te r s t a b i l i t y and r e l i a b i l i t y a nd s m a ll e r s i z e .
miss ions , p rocess ing and combina t ion have developed ra p i d l y and now g i ve th e sys tem des igner g re a t f l e x i -
b i l i t y f o r system c om b in at io n.
D ev elopment o f d i g i t a l t ec hniques has been v e ry impo r tan t i n th i s c onnec t i on.
Mos t r ec en t
dev elopmen ts i n d i g i t a l da ta t r ans mis s ion and p roc es sing have opened s o many p os s i b i l i t i e s f o r s y s tem in t e -
g r a t i o n t h a t o ne has t h e f e e l i n g t h a t s ys te m s y n th e s is c a p a b i l i t y e xp an si on wo ul d y i e l d c o n si d e ra b l e b e n e f i t .
O p e r at i o na l n eeds i n t h e p a s t
30
year s have encouraged, and t o a con sid era ble ext en t, sponsoreCl. system
and hybr id system developments.
and a i r ope r a t i ons , m i s s i l e guidanc e and nav iga t i o n , nuc lea r s ubmarine ope r a t i on ,
I C B M
l a un c h g ui da nc e, c i v i l
a i r c r a f t o p e ra t i on , s u pe r so n ic m i l i t a r y a i r c r a f t , h e l i c o p t e r de ve lo pm en t, sp ac e o p e ra t i on s , a nd s u pe r so n ic
c i v i 1 a i r c r a f t . Fu tu r e needs
w i
11 cont i nue t o encourage h yb r i d systems.
pl ex combinat ions o f sensors as a u n i f ie d system, ra th er than a hy br id system. There i s , however, some bene-
f i t i n sys tem syn thes is t o con s ider a com bina t ion o f sensors wh ich i nd iv id u a l ly make measurements o f gu idance
and nav iga t i on qua n t i t i e s as a hy b r i d sy stem. We inc lude c omb ina ti ons o f i d en t i c a l sy stems, and i n s ane
ins tances , sys tems i n wh ich the combina t ion p rocess i s ca r r i ed o u t by man.
i n t h e d e f i n i t i o n , t h e n h y b r i d sy ste ms h ave a n c ie n t o r i g i n .
Techn iques f o r da ta t r ans -
Development o f system anal ys i s theo ry has progressed as equipment technology has developed.
Some of the pr inc ipal needs came from the fo l lowing areas:
WW I 1 mar ine
The ana lys is techniques and data comb inat ion methods c ur re nt ly employed make i t poss ib le to cons ider com-
I f we in cl ud e the human elemen t
C l a s s i f i c a t i o n o f H y b r i d System s
There a r e severa l m ot iva t ion s f o r th e deve lopment and use o f hy br id sys tems.
W h i l e the r e a r e v a r i ous
ways t o c l a s s i f y s yste ms, c l a s s i f i c a t i o n a nd d i s c u s s i o n w i t h r e f e r en c e t o t h e o p e r a t i o n a l m o t i v a t i o n i s con -
ven ien t .
I t
may a l so be he lp fu l t o t he des ign o f new sys tems.
One i m p o r t a n t f u n c t i o n o f h y b r i d sy ste ms i s t o a t t a i n o u t p u t q u a n t i t i e s w h ic h a r e n o t a v a i l a b l e f ro m
i n d i v i d u a l s en so rs .
A
system wh ich syn thes izes new qu an t i t i es f rom a combina t ion o f measurab le qu an t i t i es
i s c a l l e d a s y n e r g i s t i c sy ste m.
p r obab l y th e o lde s t h y b r i d s ys tems .
s peed th rough the w a te r, and a method f o r de te r m in ing t ime i n te r v a l s pe r m i t s de te r m ina t i o n o f l a t i t ud e and
lo ng i tu de changes .
g i v e s l a t i t u d e and l o n g i t u d e .
However, c e l e s t i a l d a t a a v a i l a b i l i t y i s l i m i t e d b y l i g h t i n g and w ea th er c o n d i t i o n s , s o c o nt i nu o us o u tp u t s a r e
no t ob ta ined .
I t s s ho rt co m in gs a r e t h a t
i t
measu res on l y d i f f e r e nc e s i n po s i t i on , and th a t the e r r o r s ou rc es ( compass
head ing , water c ur re n t , speed measurement) cause inc reas ing e r ro r as the t ime i n t e r va l inc reases .
I f t h e o p e r a t o r i s i n c l u d e d as p a r t o f t h e s ys te m, s y n e r g i s t i c s ys te ms a r e
For example, th e magnetic compass, a method f o r measur ing th e ve sse l 's
L i k ew is e , op t i c a l measu rement o f a l t i t u de angles o f c e l es t i a l ob jec ts c ombined w i th GMT
The c e le s t i a l p os i t i o n de te r m ina t ions hav e been qu i t e ac c u r a te s i nc e p r e c i s e t imep iec es became av a i l a b le .
The dead reckon ing process , however, i s i n p r in c i p l e capab le o f p roduc ing con t inuous da ta .
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2
C omb inat ion o f thes e two s ys tems t o fo r m a hy b r i d sy stem r e s u l t s i n g r e a t l y impr oved po s i t i on da ta .
i l l u s t r a te s ano ther t y pe o f hy b r i d sy stem i n w h ic h tw o s ys tems w h ic h meas ure es s en t i a l l y the same quan t i t i e s
bu t w i th d i f f e r e n t da ta r a te s , and e r r o r s pec t r a a r e comb ined t o de te rm ine the same qu an t i t i e s w i th impr ov ed
d a t a a v a i l a b i l i t y a nd i m p ro ve d e r r o r s pe ct ru m.
rudime ntary example a ls o i l l u s t r a t e s th a t system for ma tio n can be compounded: we have combined two syne rgis-
t i c systems t o form a complementary system.
o f th e subsys tems invo lved , and the combina t ion method. I n mos t sys tems the des igner a t tempts t o f i n d sub-
sy st em s wh ic h a r e f r e e f r o m c m o n e r r o r s ou rc es a nd w hi ch i n d i v i d u a l l y h av e u s e f u l d a ta c h a r a c t e r i s t i c s .
I n many i n s t a nc e s s i g n i f i c a n t b e n e f i t s i n a cc ur ac y a nd r e l i a b i l i t y c an be o b t ai n e d t h ro u gh c o m bi n at i on
o f i d e n t i c a l sy ste ms.
c u ss io n o f su ch r ed un da nt s ys te ms i n t h i s c o n t e x t i s c o n ve n ie n t and f r u i t f u l . A g ai n a t t h e l e v e l o f ma nua l
c omb ina t i on, many common examp les o f c ombined i d en t i c a l o r s i m i l a r s ys tems ex i s t . The dual a i r c r a f t f l i g h t
and eng ine i ns t r umen t comb ina ti ons a r e fa m i l i a r ex amples . The u t i l i t y o f s uc h dua l c omb ina ti ons i s w ide l y
r ec ogn i zed . To ob t a in the f u l l po t en t i a l o f s uc h c ombina t ions i t s ess en t ia l t o min imize common modes o f
e r r o r a nd f a i l u r e , and
t o
p r o v i d e means o f d e t e c t i n g f a i l u r e s i n t h e i n d i v i d u a l sys te ms .
a c om p le te , b u t n o t m u t u a l l y e x c l u si v e , c l a s s i f i c a t i o n .
and mon i to r i ng techn iques have pe rm i t t ed the deve lopment o f systems wh ich change system con f i gu ra t i on i n re -
spon se t o d i f f e r e n t d a t a a v a i l a b i l i t y , t o s ub sys te m f a i l u r e s an d t o changes i n d e s ir e d o p e ra t i on .
tempted to l i s t such adaptab le mu l t i-mode sys tems as " f a i l ope ra t io na l " sys tems because o f t h e i r remarkab le
a b i l i t y t o c o mp le te m i ss i on s s u c c e s s f u l ly d e s p i t e f a i l u r e s a nd ch an gi ng c o n d i t i o n s .
Th i s
We may c a l l such arrangements complementary systems.
T h i s
Complementary sys tems have vary ing ch ar ac te r i s t ic s depending upon the e r ro r spec t ra and da ta av a i l a b i l i t y
W h i le t h es e may n o t c o n s t i t u t e h y b r i d sy st em s i n t h e s t r i c t e s t s en se o f t h e w ord , d i s -
Th is d es c r ip t i on o f combined sys tems
--
redundant, complementary, and sy ne rg is t i c
- -
p r o b a b l y c o n s t i t u t e
Recent advances i n system org an iza t io n techn iques
One i s
C ha r ac t e r i s t i c s o f H y b r i d Systems
Hy br i d systems ta ke so many forms t h a t i t s d i f f i c u l t t o d is cu ss g e ne ra l c h a r a c t e r is t i c s .
We c e r t a i n l y
c anno t a t temp t t o o u t l i ne the gene r al dev elopmen t o f c o n t r o l t heo r y w h ic h has now gr ow n to a v e r y s op h i s t i -
c a t ed s t a t e .
some ex am ple s, p a r t i c u l a r l y i l l u s t r a t i n g h y b r i d s ys te ms d ev el op ed i n t h e U n i t e d S t a t es .
l o c a l i z e r mode o f 1941, t h e g y r o s t a b a l i z e d m a g ne t ic compasses o f 1 942 a nd t h e f l i g h t d i r e c t o r s o f t h e l a t e
40 's a re good examples o f complementary sys tems (See Tab le 1 ) . Speak ing sp e c i f i c a l ly o f the gy ro -s ta b i l -
i z ed magne t ic compass and r e fe r r i n g t o F igu r e
1,
we cons ider a f l uc tu a t in g magnet ic head ing p l us no ise as
the ou tpu t o f Sy s tem
I.
f l u c t u a t i n g m ag ne ti c f i e l d s caused by e l e c t r i c a l c i r c u i t s i n t h e a i r c r a f t , e t c .
However, we
w i l l
make some comments o f pa r t i c u l a r ap p l i c ab i l i t y t o hy b r i d s ys tems , and l i s t
A
c onv en ien t and h i s to r i c a l l y impo r ta n t s t a r t i ng po in t w ould be c omplemen ta ry s ys tems.
T h e a u t o p i l o t
The compass i s s e n s i t i v e t o a i r c r a f t m o ti on s, f i n e s t r u c t u r e i n t h e ma gn e ti c f i e l d ,
I f an average over t ime and
F i g u r e
1 .
Complementary Hybrid System'.
lo ca t i on cou ld be de termined, however , a reasonab ly accura te magnet ic head ing co u ld be de termined.
f o r e p ass t h e compass o u t p u t t h r o ug h a l ow pa ss f i l t e r w i t h t r a n s f e r f u n c t i o n
Ksn/(s+Km).
Th is reduces the
no i s e bu t i n t r oduc es a l ag i n the head ing da ta .
an d h as v e ry l i t t l e h i g h f re qu en cy n o i se .
It
does have a slow d r i f t a nd no a b i l i t y t o seek m a gn et ic n o rt h .
We a c c or d i ng l y pass t h i s o u t p u t t hr ou g h a hi g h pass f i l t e r w i t h t r a n s f e r f u n c t i o n
s/(s+Km).
i s chosen as a compromise between the low frequency g yro er ro rs and the h ig h frequency compass er ro rs .
T h i s c h o ic e o f f i l t e r c o n st a nt s , w i t h w e i g h ti n g c o ns t an t s K1
=
K2
=
1/2, makes the overal l composi te trans-
f e r f u n c t i o n f o r t h e he ad in g, t h e p h y s i c a l
c ha r ac te r i s t i c w h i ch bo th s ys tems a r e measu ri ng, be un i t y . Tha t
i s , t h e o u t p u t
w i l l
f o l l ow any t ime head ing changes w i th f i d e l i t y and w i t hou t any t ime l ag .
th e compass has a sys temat ic e r r o r dur in g tu r ns wh ich can be cor rec ted by d isconnec t ing
i t
o r t u r n r a t es
We the r e -
The d i r e c t i o na l gy r o ou tpu t r es ponds c o r r ec t l y t o maneuv ers
The
Km
c ons tan t
I n p r a ct i c e
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i n ex ce ss o f a c hose n t h r e s h o l d o r b y i n t r o d u c i n g a c om p en sa ti on f ro m v e r t i c a l o r d i r e c t i o n a l g y r o d a ta
s i n c e t h e f u n c t i o n a l n a t u re o f t h e e r r o r i s known.
t i o n , t o g i v e u n eq ua l w e i g h t i n g i n t h e c om b i na t io n pr oc es s ( e s p e c i a l l y i f a f a i l u r e o r u n d e s i ra b l e c o nd i -
t i o n deve lops on one c hanne l ) , and mor e than two i npu t s may be u t i l i z ed . The f i l t e r i n g , w e igh t i ng , and
combina t ion p rocess may be ca r r ie d ou t i n a computer . The genera l ch ar ac te r i s t ic s , however , o f combin ing
d i f f e r e n t t y pes o f measu rement o f t he same pa rameter ,as sess ing the s pe c t r a l p r ec i s i on and da ta av a i l ab i l i t y ,
and c ombini ng ac c o r d ing t o th e des i r ed ou tpu t c ha r ac te r i s t i c s a r e th e f ea tu r e s o f c omplemen ta ry s y s tems.
Many systems have been des igned w i t h these ch ar ac te r i s t ic s as they f u rn is h impo r tan t ope ra t i ona l advantages .
I mp ro ve d s p e c t r a l f i d e l i t y a nd p r e c i s i o n ( im p ro ve d p r e c i s i o n w i t h o u t a v er a g in g d e l a y ) , r ed uc ed v u l n e r a b i l -
i t y
t o comnon modes o f e r r o r a nd f a i l u r e , v e r s a t i l i t y i n sw i t c h i n g modes o f o p e r a t i o n as d i f f e r e n t s e t s
o f d a t a a r e a v a i l a b l e an d /o r as d i f f e r e n t r e s u l t s a r e de s i re d , an d t h e n a t u r a l C o mb in at io n o f v a ri o u s
dat a i n a more conven ien t fo rm ar e t yp ic a l o f modern, complex, mu l t i-mode complementary sys tems.
m od els o f f l i g h t d i r e c t o r s a r e e x c e l l e n t exa mples o f t h i s c l a ss o f s ystem .
We s hou ld ex pec t c on t i nua l
g r ow th o f c om p lex i t y and sc ope o f ap p l i c a t i o n o f s uch s y stems.
A second c lass o f sys tems are th e redundant sys tems. These are s i m i l a r t o the complementary systems
ex c ep t th a t the e r r o r s pec tr um o f eac h c hanne l i s the s ame. I t
i s t h e r e f o r e i m p os s ib l e t o e l i m i n a t e p o r-
t i o n s o f t h e n o i s e s pe ct ru m b y u s i n g d i f f e r e n t f i l t e r i n g i n ea ch ch an ne l. T he re a r e some e r r o r r e d u c t i o n
benef i ts , however .
the system.
g a i n due t o t h e c o r r e l a t i o n be tw ee n t h e t r u e q u a n t i t i e s a nd t h e l a c k o f c o r r e l a t i o n b etw ee n t h e t wo n o i s es .
F i g u r e 2 shows a s i m p l i f ie d d iagram o f a redundant sys tem.
One may choose t o shape the composi te tr an sf e r fu nc-
Recent
I n many sys te ms t h e e q u i v a l e n t i n p u t n o i se i s l a r g e l y d u e t o p r oc es se s i n t e r n a l t o
I n t h i s c ir cu m st an ce , as w e l l as i n ca se s i n v o l v i n g q u i t e i nd ep e nd en t se ns or s, t h e r e i s a
F i g u r e 2. Redundant System
Subsystems I nd I 1 a r e t a ke n t o b e s i m i l a r .
example.
added. The s u b t r a c t i o n i s v a l ua b l e f o r f a i l u r e d e t e c t i o n as di s cu s se d l a t e r . The
ns
e r r o r i n t h e co mbined
o ut pu t i s
R adar a l t im e te r s f o r a i r c r a f t l an d ing sy stems w ou ld be a good
The we igh t in g o f each channe l would normal ly be equa l , and th e ou tpu ts a re bo th sub t ra c ted and
1+P 112
"canbi ned = (7)
where
no ises o f th e two subsystems.
w i t h i ndependent i n pu t s ( p = O ) t h e r e i s a n o i s e r e d u c t io n t o
70%
o f the s i n g l e system va lue . The sys tem de-
s i g n e r ,
as a lw ay s, s eeks des igns w h ic h m in im iz e c m o n e r r o r modes and c m o n fa i l u r e modes.
Through a combinat ion
o f m on i to r i n g and c ompar is on i t s p os s i b l e f o r the user t o make a much more accura te asses .sment o f th e
c o n d i t i o n o f h i s e qu ip m en t and t h e p r o b a b i l i t y f o r s u c ce s s f ul c o m p l et i o n o f a m i s s i o n ca n be s u b s t a n t i a l l y
inc reased.
d i s c us s ion .
i s the rms e r r o r i n each s ubs ys tem ou tpu t and
i s t h e c o r r e l a t i o n c o e f f i c i e n t between t h e i n p u t
W i th c omp le te l y c o r r e la t ed no i s e ( p = l ) t he r e i s no imp rovement i n ac cu r ac y ;
The c h ie f adv an tages o f r edundan t sy stems l i e i n imp rovements i n depen dab i l i t y .
F i g u r e 3 shows a s im p l i f i e d d iag ram o f a dua l mon i to r ed sy stem app r op r i a t e f o r depend ab i l i t y
M ode rn m o n i t o r i n g s ys te ms n o r m a ll y c o n s i s t o f s e v e r al i n d i v i d u a l m o n i t or s w h ic h t e s t a v a i l a b l e s i g n i -
f i c a n t q u a n t i t i e s .
i n the o the r s ubsy stems.
u r e r a te c anno t be i gno r ed .
an a t t em p t i s made t o i d e n t i f y t h e s i g n i f i c a n t f a i l u r e modes and t h e p r o b a b i l i t y o f t h e i r o cc ur ra nc e.
summing the p r o ba b i l i t i e s o f thos e th a t a r e mon i to r ed and thos e th a t a r e no t , an es t im a te c an be made o f
t he p r o b a b i l i t y o f d e t e ct i ng a f a i l u r e
i f
one does occur.
th r es h o ld o f some ty pe t o be s e t w h i c h i nv o l v e s a t r a de o f f be tw een the numbe r o f fa l s e f a i l u r e a la r ms and the
number o f missed alarms.
t h e t r ad e o ff i s q u i t e d i f f e r e n t i n d i f f e r e n t s i t ua t io n s .
few r e a l f a i l u r e s i t n e v i t a b l y g i v e s m ore f a l s e a l ar ms .
o b j e c t i v e r e q u i r i n g t h e s yst em ) i s g i v e n g r e a t p r i o r i t y i t s c us tomar y t o ac c ep t a s ubs tan t i a l unnec es sa ry
equipment r emov al r a te i n o r de r t o hav e a h ig h deg ree o f c on f idenc e i n the equ ipment .
Some o f thes e t es ts may ac t ua l l y i n v o l v e c ompa ri sons w i t h th e c o r r espond ing quan t i t y
The mon i to r i ng c i r c u i t r y and mechanisms may be r a th e r c omplex , s o th a t i t s f a i l -
The m o n i t o r c an n e ve r t e s t a l l p o s s i b l e f a i l u r e m odes.
I n most modern systems
By
I n t h e " s o f t " f a i l u r e modes t h e r e i s u s u a l l y a
V ery l i t t l e can be s a i d ab ou t t h i s t r a d e o f f i n a g e ne r al way as t h e c h a r a ct e r o f
O f course,
as
t h e m o ni t o r i s s e t t o m is s ve ry
I n o p er a ti o ns
i n
w h ic h s a f e ty ( o r some m is s io n
Unnecessary removal
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-
I1
F i g u r e
3.
Dual Monitored System
acc ounts fo r about ha l f o f t he remov al s i n a i r l i n e ope r a t i ons . W he ther thes e remov al r a tes a r e es s e n t i a l
i n h i g h l y m o n i to r e d d u al s yste ms w o ul d be a w o r th w h il e s u b j e c t f o r f u r t h e r i n v e s t i g a t i o n .
adequate i n many c ircu mstan ces.
Sys tem c ha r a c te r i s t i c s w hi ch tend t o make th i s app roach p r ac t i c a l a r e :
( 1 ) H i g h r e l i a b i l i t y f o r t h e i n d i v i d u a l s ys te ms ; ( 2 ) N ormal o u t p u t f l u c t u a t i o n s s m a l l c om pa red w i t h t h e
opera t iona l accuracy requ i rement
s o
e f fec t i v e c ompa r i s on c an be made w i thou t h i gh fa l s e a la r m r a te ; ( 3 )
Outpu t c h a r a c te r i s t i c s wh i ch c ause the ou tp u t t o r ev ea l the most p r ev a len t f a i l u r e modes; and ( 4 ) P o s s i b i l -
i t y
o f a l t e r n a t e o p e r a t i o n p ro ce du re s. I n t h i s c o n ne c ti o n
i t
s hou ld be no ted tha t th e ope r a to r o f most
sys tems ac ts as a mon i to r f o r many fa i l u r e modes, by in te rp re t i ng
w ould be imp r ac t i c a l t o au toma te .
i s t i c , o r t o r e pl ac e
i t
adequate ly .
I n genera l , however, the dua l m on i to red and compared system has sup er i o r opera t in g ch ar ac te r is t i cs ,
b o t h i n c on ve yi ng t o t h e u s e r a mo re p r e c i s e k no wle dg e o f i t s o p e r a t i n g c o n d i t i o n a nd i n i n c r e a s i n g t h e
p r ob ab i l i t y o f s uc c es s fu l l y c omp let i ng a m is s ion . The w hole s ub jec t o f mon i to r i ng i s v e ry c omplex and
c an no t b e ta k en u p i n d e t a i l
he re . We
w i l l
make only a few observat ions.
F i r s t , we have the p rob lem o f
i n f or m i n g t h e us er o f t h e o p e r at i o na l c o n d i t io n . Second, t h e r e i s t h e m a t t e r o f r e l i a b i l i t y , o r p ro ba -
b i l i t y o f m i ss io n success. W it h re ga rd t o t h e f i r s t ,
i t
s i n t e r e s t i n g t o n ot e th e f o l l o w i n g s i t u a t i o n :
suppose t he mo n i to r ing per fo rmed by each mon i to r and compara to r were comple te and per f ec t , th a t m on i t o r
f a i l u r e a l wa ys c aused a n a l a rm ( i d e n t i c a l w i t h s y st em f a i l u r e a l a rm ) , and th a t c ompa ra tor f a i l u r e s w er e
ne g l i g i b l e . Then a dua l mon i to r ed s ys tem c ou ld be i n any one o f 16 pos s ib le ope r a t i ng c ond i t i on s : a l l
u n i t s o p e ra bl e, a l l u n i t s o p er a bl e e xc e pt m o n i t o r 1
,
.
,
a l l u n i t s i n op e ra b le .
p a r a t o r ca n o n l y i n d i c a t e
8
d i f f e r e n t c o n d i t i o n s ,
s o
t h ey a r e o b v io u s ly u na bl e t o g i v e a f u l l d e s c r i p t i o n
o f the s ys tem. H owever, t he amb igu i t i e s a r e g rouped i n s uc h a way t ha t the c o r r ec t ope r a t i ona l dec i s i ons
are made.
Dev ia t ions
from
t h i s i d e a l s i t u a t i o n a re a s s o ci a te d w i t h i n co m p le t e and i m p e r f e c t m o n i t o r i n g ,
l ac k o f a l a rm when a mon i to r f a i l s , and fau l t y ou tp u t due to f au l t y i n pu t th a t c anno t be ass es sed by the
mon i to r ing sys tem (comon mode er ro rs ) .
eac h i nd i v i dua l s y s tem
A ,
o f ea ch m o n i t o r Am, and o f the comparato r
x
.
f a i l u r e
w i l l
r e s u l t i n e rro ne ou s f a i l u r e i n d i c a t i o n and t h a t m o n i to r f a i l u r e s f a i l t o g i v e a la rm s.
t h e p r o b a b i l i t y t h a t t h e f u n c t i o n
w i l l
be l o s t d u ri n g a m i s s i o n o f l e n g t h
t
i s
The c o m bi n at i on o f - tw o i d e n t i c a l s ys te ms w i t h o u t p u t c o m pa ri so n b u t w i t h o u t i n d i v i d u a l m o n i t o r i n g i s
t h e n a t ur e o f t h e o u t p ut i n ways t h a t
I n combining systems i t s q u i t e i m p o r ta n t t o p re s er ve t h i s c h ar ac t er -
The monitors and the com-
T ur ni ng now t o t h e p r o b a b i l i t y o f l o s s o f f u n c t i o n d u r i n g a m i ss io n , we d e f i n e t h e f a i l u r e r a t e o f
We a ls o assume th a t compara tor
Then
(3)
-it
s i n g l e m on i to red system: 1 - e = ~ t
dual unmonitored system
corn pa ra
t
o r
:
dua l mon i to red sys tem w
comparator :
t h
( 4 )
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5
For numerical comparison, assume x
=
0 . 2 4 ~ 1 0 - ~ er hour , x = 0 . 1 5 ~ 1 0 - ~e r hou r ,
x C =
0 . 0 5 ~ 1 0 - ~er hour ,
and
t =
1.75 hours.
t h r e e c o n f i g u r a t i o n s . T hu s, we w ou ld e f f e c t an or d e r o f m a gn it ud e r e d u c t i o n i n m i s s i o n f a i l u r e s w i t h t h e
assumed dual monitored system.
W i th the i nc r eas ed use o f m ic r oe lec t r on i c c i r c u i t r y we c an ex pect t o s ee c on t i nued dev elopmen t o f mon i-
to r i ng techn iques and gre a t er use o f dua l mo n i to red systems.
F o r m i s si o n s o f c r i t i c a l n a t ur e o r o f l o n g d u r a t i o n , w here a l t e r n a t e s yst em s a r e n o t a v a i l a b l e ( e. g.
,
ca tegory
I11
a i r c r a f t l a n d i n g s y s t e m s
,
nuc lea r s ubmar ine nav iga t i on )
,
e x t en s i on s o f t h e s e t e ch n iq u es i n t o
t r i p l e and dual-dua l systems have been made.
b r a t i o n o f i n t e r n a l f u n c t i o n s w h i l e o p e ra ti n g, and f u r t h e r i n cr ea s e t h e p r o b a b i l i t y f o r m i s s io n su cce ss .
Widespread use o f such sys tems depends upon cont inu a t ion o f th e min ia tu r i za t i on t ren d , and the development
o f a u to m a ti c t e s t t e ch n iq u e s t o h o l d m a in te na nc e c o s ts t o d e f e n s i b le l e v e l s . T re nd s i n th o se d i r e c t i o n s
are very encourag ing, and we can look fo rward t o a new era o f dep end ab i l i ty i n gu idance and nav i ga t i on .
we o b ta in an ou tpu t w h ic h i s n o t measu red d i r e c t l y by e i th e r s ubsy stem.
meaning t o work toget her .
c our ses o f t r ea tmen t r e i n f o r c e each o the r .
An im po rta nt example i s th e a irb orn e do pple r system which measures speed over th e ground, and combines
t h i s w i t h t ime and head ing t o c ompute eas t and no r th d i s tanc e t r av e led .
ga t ion sys tem wh ich uses angu la r da ta f rom the
VOR,
range f rom DME a n d a l t i t u d e
from
t h e a l t i m e t e r t o com-
pu te a 3 -d imensiona l f i x .
o r inc re as in g r e l i a b i l i t y as the redundant and complementary sys tems do .
a b i l i t y t o p r o v id e a needed o u t p u t w hi ch i s n o t a v a i l a b l e d i r e c t l y from any sensor. I n some systems re-
dundacy i s i n t r oduc e d by us ing m u l t i p l e o r a l te r na te s ubsy stems t o i n s u r e th a t the needed measu red pa ra -
meters
w i l l
b e a v a i l a b l e .
redundant, complementary and sy ne rg is t i c .
and u t i l i t y , an d o f f e r p o s s i b i l i t i e s f o r r e d uc in g common mode f a i l u r e s a nd e r r o r s .
w i t h m u l t i p l e i n p u ts , m u l t i p l e o u tp u ts , and c on s id e ra b le a b i l i t y f o r d a ta s m oo th in g w i t h o u t i n t r o d u c i n g
lags , f o r pe r fo r m ing i n t e r na l c a l i b r a t i on s and ad justmen ts, and f o r c omplex p r oc es s ing to ac c omp li sh de-
s i r e d c o m bi n at i on s . Such s yst em s t y p i c a l l y e x h i b i t a l l o f t h e c h a r a c t e r i s t i c s we ha ve been d e s c r i b i n g .
F igure
4
i s a gene r a l i z ed b loc k d iag ram o f s uc h a s ys tem.
Here the s ig na l l i n e s may represent more than
one qu an ti ty , and th er e cou ld be more than two subsystems.
I t
s f r e q u e n t l y c o nv e ni e nt t o p e r fo r m t r a n s -
form ation s repre sente d by th e b locks M1 and M2 so th a t t he d at a coming from subsystems
I
and I 1 represent
the same parameters, even though derived from d i f f e r e n t s e n s o r s ,
s en t th e d i f f e r en c e i n meas urement e r r o r i n the two s ubsy stems and the e f fe c t o f any e r r o r s i n any assumed
parameters i n th e t rans fo rmat ion s . Any no ise less component o f t h i s d i f f e re nc e shou ld be a s low ly vary in g
qu an t i t y , and smooth ing p rocesses
w i l l
no t c ause app r ec iab le l ag i n the main da ta f l o w .
tem des ign enough systems and enough ou tp u ts shou ld be chosen t o pe rmi t t he d a ta f i l t e r t o make a un ique
s o l u t i o n f o r s lo w a dj u st m e nt o f p ar am et er s t h a t a r e s u b j e c t t o d r i f t , o r a r e b a s i c a l l y unknown a nd r e q u i r e
de te r m ina t ion . The ou tpu t o f the da ta f i l t e r i s shown as making ad jus tmen ts i n the s ubsy stems ( the b loc k
M i
and M2 cou ld be inc lud ed) and al so sending da ta t o K1 and K2.
and e r r o r su b t ra c t i on p rocesses, and th e f i n a l o u tpu t da ta may no t be combined. There may be f i n a l t ra ns -
f o rm a ti on s i n t o o t h e r q u a n t i t i e s
so
t h a t t h e two s ys tem ou tpu ts may no t hav e pa i r s o f s im i l a r q uan t i t i e s .
I f
t he da ta f i l t e r c an be s upp l i ed w i t h a ma thema t ic a l mode l o f t he dy namics o f the s y s tem and a model
o f the r e l a t i ons h ip between the measu rement e r r o r s and the s t a t e o f the s ys tem
i t
i s p os s i bl e f o r t h e f i l t e r
t o pe r fo r m an op t ima l es t ima t i on p r oces s w h i c h m in im izes e r r o r s i n the l e as t s qua res s ens e and r ede te rm ines
parameters used i n th e mode l o f the sys tem.
F or a l i n e a r s ys te m such a f i l t e r i s c a l l e d a Kalman f i l t e r ( 1,
2 ) . Non l ine ar sys tems, may o f te n be l i ne ar iz ed by in t ro du c in g a model
o f the nomina l des i red per fo rmance
and fo rm ing th e s ys tem as a l i n ea r app rox ima ti on u t i l i z i n g the s ma l l d i f f e r enc es between nomina l and actua
.
T h i s i s e x p e c i a l l y u s e f u l i n space n a v i g a t i o n ( 3 ) .
Then i n 10,000 f l i g h t s we wou ld expec? 4.4, 9.6, and 0.9 l os se s o f f u n c t i o n f o r t h e
These i n c re a s e t h e p o s s i b i l i t i e s f o r m o n it o r in g a nd c a l i -
We
turn
now t o t h e t h i r d m a j o r c l a s s o f h y b r i d s yst em s -- t he s y ne r g i s t i c s y s tems .
I n these sys tems
It
s u sed i n me di ca l p r a c t i c e t o d e s cr ib e a s i t u a t i o n i n w hi ch t wo d i f f e r e n t
The word comes from a Greek word
The e x t e n s io n t o h y b r i d sys te ms i s s t r a i g h t f o r w a r d .
Another example i s an a rea nav i -
I n th e i r mos t r ud imen ta r y fo rm, s y n e r g i s t i c s ys tems do no t hav e any s pec ia l means f o r r educ ing e r r o r s
T h e i r b e n e f i ci a l f e a t u r e i s t h e
I t s p o s s ib l e
- -
indeed, de s ir ab le, t o make compound hy br id systems which are
Such s ys tems can be designed f o r g r e a t p r ec i s i on , r e l i a b i l i t y ,
Rapid improvements i n data tra nsm iss ion and computer tec hniques have made
i t
pos s ib l e t o fo r m s ys tems
The d i f fe ren ce s shou ld be smal l and repre-
I n t h e h y b r i d s ys -
These represen t bo t h ga in ad jus tments
Th is method o f system org an iz a t io n has many des i ra b l e fea t u res bes ides the accuracy b en ef i t o f th e op t
ma l es t imate p rocess .
w h i c h i nv o l v es da ta r a tes s l ow e r than the ma in s i gna l
f low , and the math ematica l models can be changed i n
the computer t o implement var ious modes inv o lv ed i n s t a r t up, use o f a l t e r na te subsys tem inp ut s , degraded
subsystem performance, s toppage o f data i n one subsystem, et c .
c o r r ec t i ons c an be made i n bo th the 84 m inu te and 24 hour l oops on an i n te r m i t ta n t bas i s w i tho u t e x c i t i n g
osc i 11a t i ons.
Th e d a t a f i l t e r i n g i s n o r m a ll y i mp le me nt ed
with
an i t e r a t i v e , s amp led p r oc edu r e
I f one subsystem i s an in e r t i a l sys tem,
Futu re Hyb r id Sys tems
I n the pas t th e r e have been r easons f o r av o id ing h y b r i d c omb ina ti on o f s ys tems , and the c omb ina t i on
o f t e n was l e f t t o t h e o p e ra t or s.
au toma ti on i nv o l v ed was one de t e r r e n t , and the r e l i a b i l i t y r equ i r ed o f th e common elemen ts w ere tw o
imp or ta n t fac to rs . Wi th cons iderab le ga ins i n bo th o f these areas we can expec t t o see more use made o f
hy br id sys tems.
Tab le 1 l i s t s some examples o f au tomat ic h yb r i d systems deve loped i n the Un i ted Sta tes .
A cons iderab le t im e span ex is ts f rom concept ion to comple t ion , and
i t
was n o t p o s s i b l e t o o b t a i n e q ui va -
l e n t da tes f o r each sys tem.
The c anp le x i t y , w i th a t tendan t c os t and ma in tenanc e r equ i r emen ts , o f t he
No
c la im o f completeness i s made, and
i t
s r e a l i z e d t h a t many e q u i v a l e n t
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t
- 1 -
M l
F ig ure 4. Genera l i zed Hyb r id Sys tem.
* K l I
c
-
sys tems were deve loped i n o th e r coun t r i es , i n some cases ear l ie r .
comp l ex i t y and the i n c re as i ng use o f redundancy and op t i ma l e s t i m a t i on t echn i ques i n r e c e n t y e a r s .
Exper ience w i t h these systems has been so fave rab le t h a t these t rends can be expected t o cont inu e.
Landing acc idents
s t i l l a r e t h e ma jo r s a fe t y h az ar d i n c i v i l a v i at io n , and t he y a r e q u i t e i m p or ta n t i n m i l i t a r y a v i a t io n .
V a r i a t io n i n a i r p o r t a cce pta nce r a t e s w i t h v a r i a b l e w e ath er c o n d i ti o ns i s a s e r i o us p ro ble m i n a i r t r a f f i c
c o n t r o l .
D i ve r s io n t o a l t e r n a t e a i r p o r t s i s c o s t l y t o a i r c r a f t o p e r at o r s an d p as se ng er s. R es er ve f u e l
r e qu ir e me n ts i n a n t i c i p a t i o n o f d i v e r s i o n i s a c o n t i n u a l o p e r a ti o n a l c o s t . Rough l a n d i ng i n l a r g e a i r -
c r a f t causes su bs t an t i a l mai ntenance cos t . The inc rease i n a i r c r a f t w i t h d i f f e r e n t g l i d e s lo p e ch ara c-
t e r i s t i c s a nd t h e ne ed f o r o p e r a t i o n w i t h c l o s e r r un wa y s p a c in g an d c u r ve d p a th s on f i n a l a pp ro ac h a l l
r e q u i r e a d i f f e r e n t t y p e o f r e fe r e nc e s i g n a l . A s u b s t a n t i a l n um ber o f a c c id e n t s o c c u r c lo s e i n , b u t
b ef or e a c q u i r i n g g l i d e s l o p e s i g n a l .
deve lopment e f for t w i l l be needed du r i ng t he nex t decade . Landi ng requ i remen ts a re pa r t i c u l a r l y s u i t ed
f o r h y b r i d sy st em s. M u l t i p l e r ed u nd a nt s o ur ce s o f d a ta , p r oc e ss ed i n a c om p le m en ta ry f a s h i o n i n m u l t i p l e
c h an n el s w i t h e x t e n si v e o u t p u t c o m pa ri so ns a r e t y p i c a l o f new f l i g h t c o n t r o l s ys te ms .
i n p u t s a r e u se d i n t h e f l a r e phase.
a nd c a r e f u l m o n i t o r i n g t o d e t e c t f a i l u r e s a r e a l s o b e in g d ev el op ed .
degree o f r e l i a b i l i t y a nd p r e c i s io n w i t h t h e p r es en t I L S and permi t land ings under Category I11 c o n d i t i o n s .
As new r a d i o g u id a nc e sy st em s p r o v i d e f l e x i b l e a nd p r e c i s e g l i d e s lo p e s , t h e f l i g h t c o n t r o l s ys te ms o f
t h e f u t u r e s h o ul d p r o v i d e a l l t h e d e s i r e d f ea t ur e s.
t e r r a i n avo idance and runway su rv e i l l an ce system. T h i s depends upon the r ad i o gu i dance sys tem u t i l i z e d
i n t h e f u t u r e.
The a re a o f a i r t r a f f i c c o n t r o l , b o th m i l i t a r y and c i v i l , i s an ot he r f i e l d r e q u i r i n g h y b r i d system s.
I n t h e U n i t e d S t a t es t h e o v e r a l l a i r t r a f f i c c o n t r o l s y st em c an n ot r e a l l y be co n s id e r ed a sy st em fr om t h e
con t ro l t heo ry v i ewpo i n t . Some aspec ts o f i t s ope ra t i on can be mode led as sys tems, some i nv o l v i ng i n te r -
a c t i o n s w i t h p i l o t s and c o n t r o l l e r s . The m os t u r ge n t need i s , o f co ur se , t o i n cr e a s e a i r p o r t c ap a c i t y i n
major t ra ns po r t a t io n hubs. The lan d in g sys tem improvements c i te d above
w i l l
be q u i t e h e l p f u l
,
e s p e c i a l l y
i f accompanied w i t h compa t i b l e cons t ru c t i o n o f runways and tax i ways . F u r th e r e f f o r t s a re needed t o
u pg ra de t h e c o n t r o l s y ste m b y t i g h t e r c o n n ec t io n o f s u r v e i l la n c e , n a v i g a t i o n , p i l o t a nd c o n t r o l l e r .
B e si de s t h e u p g ra d i ng o f s u r v e i l l a n c e a nd n a v i g a t i o n , i t seems es se n t i a l t o i mprove th e comnun i ca t i on
between the p i l o t and co n t ro l l e r , as we l l as be tween co n t ro l l e r s . An i n teg ra t ed message sw i t ch i ng and
p r o ce s s in g ne tw o rk i n c o r p o r a t i n g a p o l l e d a i r - g r o u n d - a i r d i g i t a l d a t a tr a n s m i ss i o n l i n k a pp ea rs a p p r o p r i a t e .
Such a l i n k c o ul d t r a n s m i t i d e n t i t y , p o s i t i o n , a l t i t u d e , ETA f o r t h e n e x t c he c k p oi n t, a nd p er ha ps o t h e r
pa rameters , and pe rm i t s ho r t p i l o t messages.
and c o n t r o l l e r i n s t r u c t i o n s .
t rans ce i ve r s and th e remote g round UHF s ta t i o ns i n such a way t h a t cou l d be ex tended t o s a t e l l i t e use
l a t e r i f t ha t became feas i b l e .
It i s i n t e r e s t i n g t o n o te t h e g ro wi ng
One o f t h e a re as w i t h i n t e n s e h y b r i d s ys te m a c t i v i t y
i s
a i r c r a f t l a n d in g s ys te ms .
I n v ie w o f a l l t he s e p ro ble ms
i t
seems ev i den t t ha t i n tens i ve
R a d a r a l t i m e t e r
E xt en si ve c a p a b i l i t y f o r s ys te m r e c o n fi g u r a t io n i n case o f f a i l u r e s
These new systems
w i l l
bring a new
I t
may be necessary t o add some ty pe o f independent
The up l i nk c ou l d t ran sm i t i n f o rm a t i o n such as weathe r da ta
It w ou ld s eem m o st p r a c t i c a l t o s t a r t b y m o d i f i c a t i o n o f a i r b o r n e VHF
DATA
FILTER.
I t s h o u ld be p o s s i b l e by t i g h t e n i n g t h e c o mn u ni ca ti on , p o s i t i o n r e p o r t i n g , s u r v e i l l a n c e , a nd d a t a
p rocess i ng l oops t o
fo rm
f u n c t i o n a l s ubs yste ms w i t h a b i l i t y t o h a nd le m ore t r a f f i c s a f e l y . W i th t h i s
f u n c t i o n a l c a p a b i l i t y i t shou l d be pos s i b l e t o deve l op and imp lement a more canprehens ive s t r a te gy o f
a i r t r a f f i c c o n t r ol ( 4) .
c o n t r o l e n vi ro nm e nt a n a re a n a v i g a t i o n c a p a b i l i t y u t i l i z i n g VOR/DME and a i r d at a, as w e l l a s i n e r t i a l
n a v i g a t i o n i n some i n s t a n c e s, w o ul d a pp ea r t o be q u i t e u s e f u l .
More a i rways f o r en rou te use cou l d be
reduced. Stud ies have shown (5 ) t h a t s i g n i f i c a n t im pro ve me nt s i n a c c ur a cy an d c o n t r o l c h a r a c t e r i s t i c s
c an b e o b t a in e d b y o p t im a l c o m b in a t io n o f a i r d a t a w i t h VOR/DME, and even greater improvements are
a v a i l a b l e w i t h i n e r t i a l n a v i g a t i o n com bin ed w i t h t h e r a d i o d a t a ( 6 ) .
A i r c r a f t n a v i g a t i o n i s i n need o f u pg ra di ng f o r s ev er al a p p l i c a ti o n s .
I n t h e do me st ic a i r t r a f f i c
-
1 - 2
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I
' K2
c
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I - 7
One o f t h e m aj o r s te p s f o r i n c r e a s in g c a p a ci t y l i e s i n ac h ie v in g g r e a t e r r e g u l a r i t y i n a r r i v a l
s pac ing a t the l and ing dec i s i o n po i n t . W i thou t hav ing a f u l l y deve loped theo r y as a bas i s i t s t i l l
seems pos s ib le t o foresee some use fu l aspects . The runway capa c i ty inc rea ses as the r eg u la r i ty o f.
a r r i v a l i n c r e a s e s .
des ign.
I t
w o u l d u s u a l l y b e b e n e f i c i a l i f a i r c r a f t c o ul d a r r i v e a t a d e ci s io n p o i n t a t t h e ass ig ne d
t i m e w i t h a s t a n d ar d d e v i a t i o n o f a b ou t 3
-
5 s ec onds . S inc e the c os t o f as s ign ing and c o n t r o l l i n g
a i r c r a f t t hr ou gh o ut t h e a ir sp a ce t o t h i s p r e c i s i o n wo uld b e p r o h i b i t i v e ,
i t
seems e ss en t ia l t o seek
means f o r i m p ro v i ng t h e r e g u l a r i z i n g f u n c t i o n as a i r c r a f t n e a r t h e a i r p o r t . I f a w ides p r ead s t r a teg i c
s c h ed u l in g o f a i r c r a f t ( i n c l u d i n g t h e e f f e c t o f a ny u n c o n t r o l l e d f l i g h t wh ic h w o ul d be p e r m i t t e d ) c o u l d
p r ev e nt s e v er e pe ak s i n a r r i v a l r a t e s and p a r t i a l l y r e g u l a r i z e t h e t r a f f i c ,
i t
m i g h t b e f e a s i b l e t o
b u i l d an e f f ec t i v e r eg u la r i z i ng p r ocedu r e a round a r ea nav iga t i on s ys tems . D i s c r e te , p r ede f i n ed r ou tes ,
w i th s ho r t c u t and s t r e tc hed a l te r na tes , and a s ma l l amoun t o f s peed c on t r o l
cou l d be used w i th an a rea
n a v i g a t i o n sy st em c ap ab le o f c a n p u t in g E TA'S and d e r i v i n g s t e e r i n g i n f o r m a t i o n f o r a s m a l l s e t o f p r e -
d e f i n e d t h re e -d i m en s io n a l r o u te s . The r o u t e - s t r u c t u r e s h o u ld i n c l u d e t r a n s i t i o n s t o o t h e r ru nw ays s i n ce
sh i . f ts i n runway use cause severe de lays a t conges ted a i rp or ts .
and h e l i c o p t e r s i n c i v i l o p e r a ti o n may p o s s i b l y
f i t
i n t o the a r ea nav iga t i on comnen ts above , bu t th e r e
may be a p rob lem o f adequate geograph ica l coverage due t o the lower a l t i t u d e ope ra t io n .
g e og r ap h ic a l e x tr em e t h e r e s t i l l e x i s t s a n eed f o r i m pr ov ed a i r c r a f t n a v i g a t i o n o ve r o cea n ar ea s.
i t
s v e ry d i f f i c u l t t o p r e d i c t wh ic h ap proaches
w i l l
b e f a v o re d i n t h e f u t u r e .
i n e r t i a l s y s t e m s w i l l be used by many a i r c r a f t , and tha t the to ta l s ys tem w i l l be a hyb r i d system.
T he re a r e p o i n t s made i n f a v o r o f m u l t i p l e i n e r t i a l system s, o r i n e r t i a l i n c om b in at io n w i t h L o ra n
C y
Omega, o r sa t e l l i t e systems.
Pre fe rence w i l l depend upon economic fac to rs , th e ex t en t to wh ich ra d i o
a id coverage i s ex tended, and the va lue p laced on su rve i l l an ce and communica t ion .
Dependence
u p o n i n e r t i a l t e c h n i q u e s
w i l l
c o n ti n u e t o expan d. The p r e c i s i o n o f t h e p o s i t i o n , a t t i t u d e , a nd v e l o c i t y
da ta d es i re d requ i re s augmenting da ta f rom one o r more o t he r sources .
most used systems.
p r ov ide p r ac t i c a l augmen ta t i on .
S t r a nd i n gs and c o l l i s i o n s s t i l l c au se he av y
l o s se s i n b o t h c i v i l an d n a va l o p e r a ti o n s.
a t t e n t i o n a nd r e so u rc e s t o n a v i g a t i o n a l e q ui pm en t, t h a t a s i g n i f i c a n t a mount o f t r a f f i c c o n t r o l s h ou l d
be us ed i n c onges ted a r eas , and t ha t au toma t i c means o f c o l l i s i o n haz ar d ev a lua t i on s hou ld be a ttac hed
t o ma r ine r ada rs .
A l l
o f thes e a reas c ou ld b en e f i t f r om hy b r i d s ys tems .
We ha ve se en s i g n i f i c a n t d e m o n st r at i on s o f s pa ce n a v i g a t i o n c a p a b i l i t y i n t h e p a s t y e a r . The u se
o f s e ve r al
s en so rs i n v a ri o u s c om b in at io ns i n t h e d i f f e r e n t m i s s io n p ha ses i s e s s e n t i a l .
I t
i s i n te r -
e s t i n g t o n o t e t h a t we a r e l e a r n i n g t o u se man m ore e f f e c t i v e l y
i n
s pace nav ig a t i o n w h i l e we a r e l e a r n ing
t o a ut om at e more e x t e n s i v e l y i n a i r c r a f t n a v i ga t i o n.
The p o i n t o f d i m i n i s h i n g r e t u r n i n r e g u l a r i t y d epends u pon a i r c r a f t m i x an d run way
There are,
o f
course, ot he r na v i ga t i on al needs which should be met. The sp ec ia l needs o f V/STOL
A t
t h e o t h e r
Here
I t i s e v id en t t h a t
T he re i s c o ns id e ra b le need f o r im provem ent i n t a c t i c a l m i l i t a r y a i r c r a f t n a v i ga t i o n.
Doppler and Loran have been the
We aw a i t t he r e s u l t s o f the 6216 deve lopmen t p rogr am t o s ee i f t h a t s y s t e m w i l l
We s hou ld make b r i e f men t i on o f ma r i ne r equ i remen ts .
I t would seem t h a t s hi p operato rs shou ld devote more
I ave a t temp ted t o i l l u s t r a t e h y b r i d s ys tem appr oaches w i t h examp les o f common i n te r e s t t o bo th
c i v i l and m i l i t a r y o pe ra ti on s.
d e t a i l e d t o t r e a t h e re . We ca n l oo k f o r w ar d t o an e xt e n si v e s a m pl in g o f p r es e n t p r og r es s i n t h e pa pe rs
t o f o l lo w .
There a re , o f course , many o the r , more spec ia l ize d requ i rements too
References
( 1 )
R. E . Kalman,
A
New App roac h t o L in ea r F i l t e r i n g and Pr ed i c t i o n P roblems.
J .
Basic Engr . gJ:
35-45. 1960.
( 2 ) H.
W .
Sorenson, Kalman F i l t e r i n g Techniques .
-
: 219-292. Academic Pre ss, New York. 1966.
( 3 ) S.
F.
Schmid t , Ap p l ica t io n o f Sta te-space Methods t o Nav i ga t i on Problems.
Advances i n Contr o l
S
stems 3: 293-340. Academic Pre ss. 1966.
I n Leondes,
C.
T. ed. Advances i n Co nt ro l Systems
I n Leondes, C. T. ed.
' - T o r n o T k 3 -
an Gene
R.
Marner , Separa t ion Hazard C r i te r i a . Co l l in s Radio ReDort . Dec. 1968.
(5 )
Norber t B. Hemesath, The Optimum Com plem entatio n o f
VOR/DME
w i t h
A i r
Data, Jo in t Au tomatic
( 6 )
D. H.
Meyer,
N. B.
Hemesath and
H. M.
Schweighofer, Complementing
VOR/DME
w it h INS--an improved
Contro l Conference, Pr inceton, August 1969.
na v i ga t io n sys tem, Nat iona l Business A i r c r a f t Meet ing , Wich i ta , March 1969.
Acknowledgements
Ack nowledgemen t i s g i v en f o r as s i s tanc e f rom, and s t im u la t i n g d i s c us s ion w i th , c o l leagues
E. 0.
Frye,
N. B . Hemesath, J . M. H o l t and R. L. Sebeny.
q u e s t i o n n a i r e .
Thanks are a ls o due many f r ie nd s who re p l ie d t o a sys tem
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2
I
CHARACTERISTICS
OF
A SATELLITE NAVIGATION SYSTEM
OPERATED
IN
CONJUNCTION WITH A USER INERTIAL SYSTEM
B
P . Leonard* and
J
B Woodford**
* Syste ms Engineerin g Operations, Aer ospa ce CorporAtion,
E l
Segundo, California
**
Advanced Orbi tal Sys tems Direc torate , System Planning Divis ion,
Aero spac e Corp orati on, E l Segundo, Califo rnia
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2 - 1
CHARACTERISTICS O F A SA TE LL ITE NAVIGATION SYSTEM
OPERATED I N CONJUNCTION WITH A USER INER TIAL SYSTEM
B. P. Leonard*,
J.
B. Woodford
The Aerospace Corporation
t
1 .
Introduction
Navigation sys tem s, b ecau se of thei r relat ively high cost,
a re
preferably designed to serve
a
broad
class of u s e r s .
navigation syste ms a r e given below:
Wide Are a o r Global Coverage
Continuous Availability
Three- dimens ion Posit ion and Velocity Fixes
Rea l T ime Measurements
Accuracy to
a
Few Tens of Feet in Positio n
Accuracy to
a
Fra ctio n of
a
Foot P e r Second in Velocity
Usable on Rapidly Maneuvering Vehicles
No Radiation from U s e r -
-
No Sys tem Sa turat ion
Equipment Adaptable to Many Cl ass es of U ser s
Tot ally Self -Contained
A set of sys te m proper t ie s which wi l l sa t is fy the requ irements
of
virtually al l u se r s of
No s y s te m p o s s e s s es al l of thes e feat ure s.
sate ll i te -based navigation aid coupled with a n inerti a l navigator can provide
a
viable approximation to
them.
perfor mance of this sys tem when coupled with an inertia l pla tform .
However, a hybri d sy st em composed of a high precis io n
This paper will
f i rs t
descr ibe such
a
sate ll i te -based navigation aid and will indicate the a tta inable
2. Satell ite -Based Navigation Aid
Many possible satellite-based navigation systems have been defined.
This sec t ion desc r ibes a
specific syst em concept which posse sses all but the
las t
feature l is ted above, and al so
is
availa ble with
pres ent technology. The syste m uses what
is
term ed pseudo range and rang e-ra te me asur eme nts which
a re
defined
as
one-way range and range-rate measurements made by the use
of
a
non-synchronized u se r
clock.
four sa te l l i te s in o rd er to ob ta in a 3-dimensional
fix.
orde r to m aintain deployment flexibil ity .
establi shed which can be extended to global coverage .
Four
satellites
are placed in 24 hour orbits , thre e of which a r e e ll iptical inclined orbits , so phased that
The use r
is
pass ive while making a navigational fix.
Simultaneous measurements
a r e
made on
Twenty-four hour sate l l i te periods ar e used in
By the use of these orbits , wide ar ea cove rage can init ia lly be
A conceptual diag ram of the sys tem approach as deployed for regional coverage
is
shown in Fig. 1.
//-COMMAND
8
TR A C K I N G
Fig.
. l .
Navigation System Configuration
*
Vice Pr eside nt and Genera l Manager, Systems Engineering Operations , Aerosp ace Corporation,
El Segundo, Calif.
Aer ospa ce Corp oratio n, E l Segundo, Calif.
'Associate Group Dir ecto r, Advanced Orb ital Syst ems Dir ecto rat e, System Planning Division,
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2 -2
\y......
....,.
.......
......
ARTH-FIXED COORDINATES ......
INERTIAL COORDINATES
Fig.
2 .
Orb ital Deployment--Two Views
Fig. 3 . Pseudo-Ranging to Four S atel l i tes
they appear f ro m the ea r th to fo llow
a
common c i rcu lar path.
equatorial orb i t appea rs to be in the center of the configuration.
Y
n the sky.
Figure
2
shows two views.of the orbital deployment.
cons te l lat ion to an ob server ro tat ing wi th the ear th .
iner t ia l coord ina tes .
that the ir posi t ions be accu rately determined in geodetic coordinates. Figure 1 indicates the method by
which sa te l l it e pos i t ions a r e de te rmined .
t ia l ly acqui res the four sa te l l i t es and ,
fo r
a
period
of
sev era l minutes, me asu res range and range- ra te
us ing the 2-way pa th f ro m the ma s te r s ta t ion to the sa te l l i t es .
grav i ta t iona l po ten t ia l , the sa te l l i t e ephemer ides a re de te rmined .
An a rb i t r a ry
se t of coordinate s, X, Y, and Z ,
are
introduced in which the s ate l l i t e posi t ions a r e assu med to be known
and in which the u se r w ishes t o obtain his posi t ion and velocity.
u s e r .
modulation.
modulation.
in or der tha t the s igna ls may be d is tinguished by the user .
posi t ion
fix
is determined f ro m these s igna ls .
t he s a me s igna l as generated by the user 's unsynchronized clock.
quali ty quar tz cr ys tal osci l lator of the type commonly incorp orated in high-grade f ield equipment.
The four th sa te l l it e in nea r synchronous-
The four s a te l l i t es appear
as a
rotat ing
Such a constella tion of satell ites provid es
a
nea r opt imum geom etry fo r naviga tion.
The left hand drawing show s the ap pear ance of the
The r ight hand f igure shows the s am e si tuat ion in
Since the satellite posi t ions for m the ref erenc e fr om which navigat ion is per formed, i t is es sen t i a l
A
ma ste r t racking s ta t ion contain ing
a
t racking antenna sequen-
Fr om these da ta and
a
model of the -ear th ' s
F igure 3 i l lus t ra tes the pro ces s by which the us er ob ta ins a position and velocity fix.
Each s a t e l li t e t r ansm i t s
a
signal to the
These sig nals contain identifiable range codes modulated upon the ca rr ie r , typical ly by biphase
The signals al so contain the equivalent of satel l i te e pheme rides a s a low data rate , addit ipnal
The signals a r e e i t he r at di f fe ren t car r ie r f requencies or a r e modulated by orthogonal codes
Figure 4 i l lu stra tes the method by which
a
This clock typic ally would be
a
high
By
A
typical s ignal fr om one satel l i te
is
shown together with
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2 - 3
I
- -TINE
IGNAL
FROM
1 1 1 L I 1 1 1 1 I
ONE SATELLITE
S I GN A L
FROM
tT-i
USER CLOCK
a
SEUDO-RANGE Tj *C = J(X-X j) ' t ( Y- Yj ) '+ ( Z - Z j ) * - 6 . C
C IS SPEED
OF
LIGHT
'IiERE A IS
LAG OF USER CLOCK
SINCE Xj,Yj,Zj:S ARE KNOW N, 4 Tjk ALLOW SOLUTION FOR
USER POSITION
(
X ,Y, Z AND
A
Fig. 4. Position Determination
WHERE THE DOT INDICATES TIME DIFFERENTIATION
0 SINCE X,Y,Z , X j ,y i ,Z j , Xj,j,ij, RE KNOWN,4 i's ALLOW SOLUTION
FOR USER VELOCITY
(
X , i , Z
)
AND
A
(USER CLOCK FREOUENCY BIAS )
Fig. 5. Velocity Deter mina tion
means of a corr elat ion dete ctor , t he time shift between
a
sate ll i te s ignal and the user c lock is determined.
This time shift ("T" in Fig. 4) is the difference between the time of tra vel of light fr om e satelli te to the
tions of the four sa tell ites can be expr esse d as a s et of four non-l inear algebr aic equations in four unknowns
(th ree components
of
user position and the clock bias).
chronized a s one of the ground s tation functions, the us er clock bias i s the sam e in each of the se equations.
If
the geometry of the us er re la tive to the sate ll i te s is appropria te , these equations can be solved for the
us er position and the clock bia s. In part icul ar,
the sat elli te geo met ry shown in Fig. 2 insures the ex is -
tence of this solution.
Doppler extrac tion techniques, four equations with use r velocity a s unknown may be wri tten and solved for
the use r velocity in thre e dimensions .
position and velocity is normally made in a modest digital computer of the so rt used in an integrat ed
avionics system.
in mor e modest u ser equipment.
The de si re d accu ra cy of a few tens of feet in position and
a
frac tion of a foo t-per -second in velocity
re q u i re s a more careful sy stem calibration than has
s o far
been implied.
by which this can be accomplished. The sam e navigation signal which is re ceived by the use r is received
at the mast er s ta tion and at two or m ore calibration s ta tions . Although Fig.
6
shows the re cept ion of th e
s ignal f rom
a
s ingle sate ll i te , in actuali ty the s ignals ar e received at each s ta t ion f rom a l l four sa te l l i te s .
Pseudo range measurem ents 'a t each s ta tion ar e made and the results of these measurements a r e re turned
using a data link through the center s ate ll i te to the master s ta tion. At the ma ste r s ta tion,
the implied
position of each statio n is computed in the same manner as a us er would compute his position. These a r e
compared with the surveyed position of each s ta tion and correctio ns a r e made in the assumed sate ll i te
posit ions and sate ll i te c lock biases in ord er t o e lim inate the difference between apparent and surveyed
station locations . This proc ess , in addition, removes res idu al er r or s due to ionospheric propagation
anomalies . The syst em calibration procedure is summariz ed in Fig.
7 .
ibility of fou r sat ell ite s allows continuous 3 -di me nsio nal navigation.
a r e continuously visible pr ovides navigation all
of
the tim e providing u se r altitude i s independently known,
and provides continuous 3-dimensional navigation during portions of the day when four s atel lite s a r e vis
-
ible. Figur e 9 shows global sys tem covera ge when thr ee constellations of five sate lli tes each a r e
deployed. In each constellation, four sa tell ites a r e placed in the inclined elliptic orbit and the additional
sate llit e is in near synchronous-equatorial orbit.
Fig. 10.
introduction can be achieved using pres ent technology.
us er and the lag of the user c lock. Four T. 's as measu red fro m the four sate ll i t es toget
4R
e r with the posi-
Since the signals fr om the four sa tell ites a 're sy n-
If,
at the sam e t ime as the pseudo ranges a r e measured, the ra te of change is measured by normal
This proce ss is sum marize d in Fig. 5.
The computation of us er
If les s than full accuracy is required, many simplifications ar e possible which result
1
Figure 6 i l lus t ra tes a means
Figure
8
shows the coverage fr om a s ingle constella tion as described .
The a r ea of continuous vi s-
The are a in which thre e sate ll i tes
The e rr or pe rformance'
of
this syste m has been analyzed considering the er r or sources l is ted in
It has been determined that, within the ar ea of coverage, the desired accuracy a s given in the
1
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2 - 4
Fig.
6.
System Calibration
0
ORBITS DETERMINED FROM MASTER STATION
RANGE MEASUREMENTS
oSATfLLITE CLOCK BIAS DETERMINED AT MASTER
STATION BY COMPARING NAVIGATION SIGNAL
WITH
MEASURED RANGE
Fig. 8.
Continuous Coverage'Contours and Satell i te Ground Tr ac e
f o r
a
Four-Satell i te Constella tion
0 O R B l T
AND CLOCK PARAMETERS ADJUSTED
TO
GIVE CORRESPONDENCE BETWEEN REAL AND
APPARENT LOCA TION OF MASTER AND
CALIBRATION STATIONS
Fig. 7. System Calibration Summary
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2 - 5
01
4
TO
7
I3-DIMENSIONS
iNTERYITrENl COVERAGE
WVERAGE FOR i =
30&,
8 = a30
MINIMUM ELEVATION M G L E 3
5d89
THREE C O N S W T I O N S OF FIVE SATELLITES EACH
Fig.
9.
Coverage for Fifteen Deployed Satellite s
SATELLITE TRACKING ERRORS
3.
Hybrid System s
STATION LOCATION
RANGE MEASUREMENT
0 E A R T H M O M L
SATELLITE CLOCK DRiFT
AUXIL IARY STATION CLOCK DRIFT
As has
been
mentioned,
a
satellite naviga-
t ion syste m possesses many desirable features,
but is not completely self-contained. Reliance
on external signal sour ces makes the sy stem
vulnerable to
loss
of sate llit e signals through
ground station or satellite failure, interference,
or
other causes.
sys tem is totally self-contained but has irreduo-
ible
drift c ha rac ter isti cs which become signific-
MULTIPATH
ant over a few tens of min utes to a few hours of
IONOSPHERIC UNCERTAINTIES operation depending upon user requirements.
A
TROPOSPHERIC UNCERTAINTIES
hybrid syste m in which an iner tial system is
updated by means of a satellite-based radio navi-
gation system possess es a number of features
ECEIVER NOISE
RECEIVER PRECISION
which neither system
bas
alone.
In
particular,
the high accurac y
and
freedom fro m drift of the
satellite-based system ar e retained and the
ine rtia l sys tem provides the means for continued
navigation if the sa telli te signals should be lost.
Owing to the precision with which an i ner tia l
sy ste m can be aligned by
making
use of he satel-
On he other
hand an
inertial
RANGE MEASUREMENT ERRORS
GEOMETRIC DILUTION OF PRECISION
Fig. 10.
E rro r
Sources
Considered
lite system, the ine rti al navigation accuracy, even with the
loss
of the satellit e signal, exceeds that of
the inertial platform alone.
Figure 11 shows a simplified block diagram of such a hybrid system . The
position and veloc ity outpu ts of the two systems a re applied to a Kalman filter. In the example illustrated.
a 21-element s tat e vector is used.
the 21
parameters.
The
nitial e rr o rs ar e then subtracted fro m the inertially derived position and veloc-
i ty
to obtain a beet preeent estim ate of position
and
velocity.
In
addition,
the estima tes of the other
er ro rs can be used to align and calibrate the ine rtial system and to make fine corrections to the satellite
navigation receiver clock.
4.
The state vector consists of the optimum entimate of the e r ro r s of
Performance
of
the Hybrid System
A covariant matrix er ro r analysis
of
the hybrid system has been performed.* The er ro rs utilimed
in
this
analysis ar e listed in Fig.
12.
These values arm considered repres enta tive of attaina blep erfor-
mance, but should not be considered to be the performanc e of any specific system.
Figure
13 shows the hybrid wvigation syetem e rr or s for
400
seconds. Also shown is the ine rtia l
system performance from 200 o 400 seconds assuming the s atelli te system is not i n use during that
period.
the
400-second period the velocity accuracie s approach the ord er of 0.1 foot-per-second.
ations
in
the c ar rie r re sult from the sequential
filter
update process used
in
the analysis.
It can
be seen
that the position accuracie s rapidly approach the level
of
a few tens of feet.
Over
The undul-
With the loss
*
The author s acknowledge the contribution of Dr. L. L. Hagerman, Aerosp ace Corporation, who
performed the error analyeis.
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STATE VECTOR
P L A TFOR Y E R R OR S
0
INERT IAL SYSTEM
fl5
PARAMETERS)
I
3
POSITIONS
3 VELOCITIES
3
TILTS
3
GYRO DRIFTS
3
ACCELEROMETER BIASES
1 1
I i
VELOCITY
F I L TE R
0 SATELLITE SYSTEM (6 PARAMETERS)
4 RANGE BIAS ES I
CLOCK TIME
CLOCK FREQUENCY
Fig. 11. Kalman Fi lte r Used With Hybrid System
INERTIAL SYSTEM
S AT EL L ll E S m E M
of
the
satellite system, the ine rtia l system errorB
grow rapidly.
later.
MEASU REMEW UNCERTAINTIES
Figure
14
shows the inertial system alignment
oRn mmow
141
n RANGE 5 F l
e rr or s utilising the satellite system.
ERT
POSITION lWF l
RANGE RITE 0.2 FPS
HORlZ
V U O C m 1.4 FPS
ar e the er ro rs assuming
loss
of the satel lite sys tem
VERT VELOCIW IO F K at
200
seconds. With the satellite system. the
