THE IMPACT OF VERY STABLE OSCILLATORS ON NAVIGATION SYSTEMS

HAL Id: jpa-00221743

https://hal.archives-ouvertes.fr/jpa-00221743

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

NAVIGATION SYSTEMS

R. Moreau

To cite this version:

R. Moreau. THE IMPACT OF VERY STABLE OSCILLATORS ON NAVIGATION SYSTEMS.

Journal de Physique Colloques, 1981, 42 (C8), pp.C8-415-C8-426. �10.1051/jphyscol:1981847�. �jpa-

00221743�

JOURNAL DE PHYSIQUE

CoZZoque C8, suppZQment au nO1 2, Tome 42, d6cembre 1981 page C8-415

T H E I M P A C T OF VERY S T A B L E O S C I L L A T O R S ON N A V I G A T I O N SYSTEMS

R. Moreau

Office NationaZ drEtudes e t de Recherches AQrospatiaZes ( O N E R A ) , 92320 ChGtiZZon, France

A b s t r a c t . - The h i g h s t a b i l i t y a c h i e v e d by o s c i l l a t o r s d r i v e n by q u a r t z o r by a t o m i c t r a n s i t i o n s i s such t h a t t h e i r t i m e s c a l e s , when used i n n a v i g a t i o n systems, remain c o h e r e n t a t a l l l o c a t i o n s . For t h a t reason, i t i s no l o n g e r necessary t o p r o v i d e e i t h e r f o r t r a n s f e r o f t h e t i m e parameter by r a d i o waves from s t a t i o n t o s t a t i o n and f r o m s t a t i o n t o v e h i c l e , o r f o r i t s t r e a t m e n t as an a d d i t i o n a l unknown i n t h e e q u a t i o n s . T h i s s i t u a t i o n makes i t p o s s i b l e t o c o n s t i t u t e t i m e f r e q u e n c y n a v i g a t i o n systems w i t h many advantages, namely d i r e c t access t o c i r c u l a r o r s p h e r i c modes, t h i s p o s s i b i l i t y g i v i n g h i g h e r accuracy and reduced s e n s i t i v i t y t o g e o m e t r i c parameters.

I n t r o d u c t i o n . - N a v i g a t i o n systems aim a t making i t p o s s i b l e f o r a m o b i l e t o determine i t s p o s i t i o n r e l a t i v e t o landmarks r e l a t e d t o a r e f e r e n c e frame ( t e r r e s t r i a l , s o l a r , a b s o l u t e ) . These landmarks may have been e s p e c i a l l y e s t a b l i s h e d t o t h i s end ; i t i s t h e case i n p a r t i c u l a r i n t h e OMEGA, LORAN C o r NAVSTAR systems ; th e y may a l s o be n a t u r a l , b u t i d e n t i f i a b l e t h r o u g h a p p r o p r i a t e t e c h n i q u e s .

Two groups o f systems may be d i s t i n g u i s h e d :

a ) a c t i v e systems, w i t h on-board t r a n s m i t t e r : beacons, r a d a r t r a n s p o n d e r s , b ) p a s s i v e systems, w i t h o u t t r a n s m i t t e r , b u t o n l y r e c e i v e r on-board.

The second group o f d e v i c e s i s d i s c r e e t , i.e. i t does n o t r i s k t o e n t a i l spot- t i n g o f t h e v e h i c l e by d e t e c t i o n o f i t s RF emission.

P o s i t i o n i n g d e v i c e s a r e t h e r e c i p r o c a l o f n a v i g a t i o n d e v i c e s ; t h e i r f u n c t i o n i s t o a l l o w an Earth-bound o r space s t a t i o n w i t h p r o p e r r e f e r e n c e t o d e t e r m i n e t h e p o s i t i o n o f a m o b i l e ( n a v i g a t i o n i n c h a n n e l s ) , and p o s s i b l y t o send back i t s p o s i - t i o n t o t h e m o b i l e .

A l t h o u g h t h e ranges, p o s i t i o n s and v a r i o u s o t h e r c h a r a c t e r i s t i c s a r e o f t e n q u i t e d i f f e r e n t f o r p o s i t i o n i n g and n a v i g a t i o n systems, t h e i r f u n c t i o n a l s t r u c t u r e s a r e v e r y s i m i l a r and t h e g e o m e t r i c a l and p h y s i c a l p r i n c i p l e s i n v o l v e d a r e t h e same, so t h a t we s h a l l n o t s e p a r a t e them h e r e and t h i s paper, which aims a t b r i n g i n g t o l i g h t t h e i n f l u e n c e o f o s c i l l a t o r s t a b i l i t y on t h e i r performance, w i l l make no d i f - f e r e n c e between them.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981847

General p r i n c i p l e s used.- A p o i n t i n space i s d e f i n e d by t h e i n t e r s e c t i o n o f n s u r f a - ces, w i t h n 3. These s u r f a c e s a r e e i t h e r hyperbolae, o r e l l i p s e s , o r spheres.

Most o f t e n , i n t h e p r e s e n t s t a t e o f a f f a i r s , t h e y a r e h y p e r b o l a e ; i t i s t h e case i n p a r t i c u l a r f o r t h e LORAN C and OMEGA systems.

The s u r f a c e s a r e c o n c r e t i z e d by e q u a l i t i e s o f phase when t h e systems o p e r a t e i n CW (Continuous Wave), o r o f p r o p a g a t i o n t i m e when t h e y o p e r a t e w i t h p u l s e s o f RF s i g n a l s , I t o f t e n happens t h a t a g i v e n system uses q u a s i s i m u l t a n e o u s l y b o t h modes.

The systems d i f f e r by t h e t y p e o f s u r f a c e generated and t h e means implemented f o r measuring e i t h e r phases o r p r o p a g a t i o n t i m e s f o r s p h e r i c a l systems, o r d i f f e r e n - ces o r sums o f phases o r p r o p a g a t i o n t i m e s f o r h y p e r b o l i c o r e l l i p t i c systems.

S m y o f t h e r& f - p a l la t o r s i n n a v i g a t i o n systems and t h e i r d e r i v a t i v e s . - O s c i l - l a t o r s are d e v i c e s whose s u c c e s s i v e and p e r i o d i c a l changes o f s t a t e s e r v e as a b a s i s t o two broad c l a s s e s o f a p p l i c a t i o n s [ I ] .

I n t h e f i r s t c l a s s , t h e rythms t h e y g e n e r a t e a r e used f o r t r i g g e r i n g sequences o f o p e r a t i o n s ; i t i s f o r i n s t a n c e t h e case o f c l o c k s c o n t r o l l i n g t h e d i s t r i b u t i o n o f t i m e i n t e r v a l s d u r i n g m u l t i p l e x i n g o p e r a t i o n s .

I n t h e second c l a s s , t h e c h a r a c t e r i s t i c s o f t h e s i g n a l s generated (phases frequency, a m p l i t u d e ) c a r r y t h e i n f o r m a t i o n i t i s i n t e n d e d t o a c q u i r e o r t r a n s m i t .

The RF waves which c o n c r e t i z e t h e s u r f a c e s whose i n t e r s e c t i o n s d e f i n e t h e v e h i c l e p o s i t i o n a r e generated by o s c i l l a t o r s , so t h a t t h e i r c h a r a c t e r i s t i c s happen t o be t r a n s f e r r e d t o t h o s e o f t h e RF waves ; i n p a r t i c u l a r t h e s t a b i l i t y o f t h e e m i t - t e d wavelengths -hence of t h e network o f RF r e f e r e n c e p o i n t s e x p l o i t e d by t h e naviga- t i o n systems- i s o b v i o u s l y r e l a t e d i n a d i r e c t manner t o t h e f r e q u e n c y and phase s t a - b i l i t y o f t h e p i l o t used.

Phase o r t i m e a r e l i n k e d t o t h e frequency s t a b i l i t y o f o s c i l l a t o r s by t h e r e l a t i o n s h i p :

' w i t h : = t i m e e r r o r a t t i m e t,

A t 0

= i n i t i a l t i m e e r r o r ,

fo

= i n i t i a l frequency a t t i m e t = 0 fr = r e f e r e n c e f r e q u e n c y ( d e s i r e d ) , a = aging, o r d r i f t r a t e ,

v a r l a n c e o f t i m e f l u c t u a t i o n s , due t o v a r i o u s k i n d s o f n o i s e

'

^(')= ( w h i t e , f l i c k e r , random w a l k ) ;

i n p a r t i c u l a r , a l i n e a r frequency d r i f t c r e a t e s a q u a d r a t i c t i m e d r i f t [81.

Moreover, t h e r e e x i s t s t a b i l i t y t h r e s h o l d s a u t h o r i z i n g s t r u c t u r e s more advanta- geous t h a n o t h e r s . I t i s i n p a r t i c u l a r t h e case o f d e v i c e s where t h e p o s i t i o n o f t h e m o b i l e i s d e f i n e d by t h e i n t e r s e c t i o n o f t h r e e spheres.

I n f a c t , t h e consequences o f t h e performance o f t h e o s c i l l a t o r s used i n n a v i - g a t i o n systems a r e m u l t i p l e and complex, and we s h a l l emphasize them b r i e f l y , s t a r - t i n g by a l i s t i n g o f t h e m a i n c h a r a c t e r i s t i c s o f r a d i o l o c a t i o n systems.

We may d i v i d e t h e c h a r a c t e r i s t i c s i n t o two groups : 1

-

f u n c t i o n a l c h a r a c t e r i s t i c s , c o n p r i z i n g :

.

range,

.

p r e c i s i o n

r e l a t i v e ,

.

s p a t i a l homogeneity ( d i l u t i o n ) ,

I

.

r e l i a b i l i t y ;

2

-

l o g i s t i c c h a r a c t e r i s t i c s :

.

a v a i l a b i l i t y ,

.

e x p l o i t a t i o n c o n s t r a i n t s ,

.

e x i s t e n c e o f downgraded modes,

.

d i s c r e t i o n (one way),

.

v u l n e r a b i l i t y (codes, s t a b i l i t y , e t c . ) .

Impact o f o s c i l l a t o r e formance on na i g a t i o n s stem c h a r a c t e r i s t i c s . - We s h a l l b r i e f l y a n a l y z e t h e iip:ct o f t h e perfLrmance o f Y v e r y s t a b l e o s c i l l a t o r s on each o f t h e s e c h a r a c t e r i s t i c s .

&nge,gye_cQion and d i l u t i o n ( o r s p a t i a l inhomogeneity o f e r r o r ) a r e h a r d l y d i s - s o c i a b l e parameters w h i c h a r e s i m u l t a n e o u s l y a f f e c t e d by o s c i l l a t o r s t a b i l i t y , as w i l l be shown by t h e f o l l o w i n g comments.

The p r i n c i p a l parameters which govern t h e s e f a c t o r s a r e :

-

t r a n s m i t t e r power,

-

wavelength r e t a i n e d ,

-

r e c e i v e r d e t e c t i v i t y ,

-

system s t r u c t u r e ,

-

s t a t i o n l o c a t i o n ,

-

o s c i l l a t o r s t a b i l i t y .

The f i r s t t h r e e p o i n t s w i l l n o t be d i s c u s s e d and w i l l be assumed once and f o r a l l , and we s h a l l a n a l y z e b r i e f l y t h e i n f l u e n c e and i m b r i c a t i o n o f t h e o t h e r t h r e e on t h e performance o f a n a v i g a t i o n o r p o s i t i o n i n g system.

I f we c o n s i d e r a t r a j e c t o g r a p h y system o f h y p e r b o l i c t y p e and i f , f o r s i m p l i - f i c a t i o n , we examine t h e problem i n a p l a n e ( f i g . I ) , we can see t h a t t h e p r e c i s i o n w i t h which t h e p o s i t i o n o f a m o b i l e i s determined

-

^{i f} we n e g l e c t f o r t h e moment t h e o t h e r causes o f e r r o r , i n p a r t i c u l a r those due t o p r o p a g a t i o n , t o r e l a t i v i t y and t o t h e s i g n a l l n o i s e r a t i o

-

i s r e l a t e d t o t h e a n g l e between hyperbolae a t t h e i r i n t e r s e c t i o n : i t r a p i d l y g e t s downgraded whenever t h e m o b i l e i s f u r t h e r from t h e p o l y g o n made by t h e t h r e e s t a t i o n s A, B, C. T h i s f a c t i s p a r t i c u l a r l y c l e a r f o r p o i n t s l o c a t e d i n t h e .hatched zone.

Fig 1

I n a more p r e c i s e way, c a l c u l a t i o n s p e r f o r m e d i n t h e case o f a t h r e e - d i m e n s i o n a l s t r u c t u r e 121 such as t h a t r e p r e s e n t e d on f i g u r e 2 e n a b l e one t o d e f i n e e r r o r c o e f - f i c i e n t s , f i g u r e s by w h i c h s h o u l d be m u l t i p l i e d t h e w a v e l e n g t h used i n o r d e r t o o b t a i n t h e e r r o r , i n metres, f o r a g i v e n p r e c i s i o n o f phase o r p r o p a g a t i o n t i m e measurement.

Fig

2

Figure 3 i s graduated i n reduced space s c a l e ( t h e measuring u n i t being t h e d i s t a n c e between s t a t i o n s ) . The dotted curves correspond t o t h e hyperbolic s t r u c t u r e , and show how f a s t t h e p o s i t i o n i n g i s downgraded when t h e mobile g e t s f u r t h e r from t h e s t a t i o n s . The s o l i d l i n e curves correspond t o a s t r u c t u r e e x p l o i t i n g a t r a n s - ponder on t h e mobile, which l e a d s t o defining i t s p o s i t i o n by t h e i n t e r s e c t i o n o f t h r e e spheres.

Fig

3

The comparison of t h e c o e f f i c i e n t s o f t h e two networks shows t h e enormous advantage o f s p h e r i c a l ( o r c i r c u l a r ) s t r u c t u r e s over hyperbolic s t r u c t u r e s , and

j u s t i f i e s t h e present general trend towards c r e a t i n g c i r c u l a r o r s p h e r i c a l naviga- t i o n systems.

I t i s easy t o show t h a t t h e s e s t r u c t u r e s a r e a l l the e a s i e r t o implement as t h e o s c i l l a t o r s generating t h e R F waves a r e more s t a b l e . The simplest s p h e r i c a l device may indeed be made of t h r e e s t a t i o n s equipped with very s t a b l e , mutually synchronized o s c i l l a t o r s , t h e mobile carrying i t s e l f a f o u r t h o s c i l l a t o r , a l s o synchronized with those of t h e s t a t i o n s ; i n t h e s e c o n d i t i o n s , t h e operation of t h e system i s i l l u s t r a t e d by t h e diagram of f i g u r e 4.

I t 0

^{Fig 4}

Because o f t h e supposedly p e r f e c t s t a b i l i t y o f t h e o s c i l l a t o r s , t h e t i m e i s t h e same o n each s t a t i o n and on t h e m o b i l e ; th u s , a t a t i m e t o known o n t h e m o b i l e , t h r e e RF p u l s e s a, b, c a r e t r a n s m i t t e d by t h e s t a t i o n s A, B, C ; th e s e a r e r e c e i v e d on t h e m o b i l e a f t e r d e l a y s

, ZZ , Zc

depending on t h e r e l a t i v e p o s i t i o n s o f t h e m o b i l e and s t a t i o n s .

I t i s o b v i o u s t h a t t h e m o b i l e p o s i t i o n l o o k e d f o r i s a t t h e i n t e r s e c t i o n o f t h r e e spheres o f r e s p e c t i v e r a d i i C%

,

C

c8 ^{, c gC}

^{( C} b e i n g t h e speed of 1 ig h t ) .

We t h u s have t h e s i m p l e s t s p h e r i c a l system, b u t t h i s depends e n t i r e l y on t h e r e l a t i v e s t a b i l i t y o f t h e o s c i l l a t o r s c o n s t i t u t i n g them.

A l l p r e s e n t - d a y systems a r e based on a compromise between o s c i l l a t o r s t a b i l i t y and t h e s y n c h r o n i z a t i o n frequency r e q u i r e d f o r o b t a i n i n g t h e d e s i r e d p r e c i s i o n : t h e b e t t e r i s t h e s t a b i l i t y , t h e l e s s f r e q u e n t may be t h e s y n c h r o n i z a t i o n s .

The n e c e s s i t y o f s y n c h r o n i z a t i o n s i s anyway v e r y p e n a l i z i n g as ^{i t} c o n s i d e r a b l y c o m p l i c a t e s t h e systems, and may even sometimes be i n c o m p a t i b l e w i t h l o g i s t i c r e q u i - reme n t s

.

To i l l u s t r a t e t h i s we may say t h a t t h e t y p i c a l v a l u e o f p r e c i s i o n g a i n t o be expected by p a s s i n g f r o m a h y p e r b o l i c t o a s p h e r i c a l s t r u c t u r e f o r d i s t a n c e s of 3 t o 4 i n t e r v a l s between s t a t i o n s i s o f t h e o r d e r o f 10.

I f t h e s t r u c t u r e i s elementary, such as t h a t d e s c r i b e d abave, t h e r e l a t i a n s h i p between o s c i l l a t o r s t a b i l i t y and p o s i t i o n i n g p r e c i s i o n i s immediate ; i t i s i l l u s t r a - t e d f o r a p a r t i c u l a r case on f i g u r e 5. I n t h i s diagram t h e f i g u r e s marked on t h e curves a r e metres p e r nanosecond o f e r r o r , whether t h i s e r r o r i s due t o measurement u n c e r t a i n t y on p r o p a g a t i o n t i m e o r a s y n c h r o n i z a t i o n d e f e c t due t o a r e l a t i v e i n s t a - b i l i t y o f t h e o s c i l l a t o r s . I t can be seen t h a t , f o r d i s t a n c e s o f 3 t o 4 i n t e r v a l s between s t a t i o n s , t h e e r r o r i s o f t h e o r d e r o f 2 m e t r e p e r nanosecond.

Fig 5

To have an i d e a o f t h e r e q u i r e d s t a b i l i t i e s we must d e f i n e t h e m i s s i o n dura- t i o n : f o r a e r o n a u t i c a l m i s s i o n s , i t i s counted i n hours, b u t f o r m a r i t i m e o r space mis- s i o n s , i n months o r y e a r s . I t i s easy t o c a l c u l a t e t h a t f o r such an elementary

system t h e r e q u i r e d l o n g - t e r m s t a b i l i t i e s may reach one microsecond p e r y e a r i n t h e o p e r a t i n g c o n d i t i o n s c r e a t e d by t h e environment : such a v a l u e , t o my knowledge, i s n o t easy t o o b t a i n w i t h t h e p r e s e n t technology,

The m a i n n a v i g a t i o n systems o p e r a t i n g now o r i n t h e near f u t u r e a r e :

-

DECCA, v e r y much used by fishermen, has a medium p r e c i s i o n and w i l l n o t be commented h e r e .

-

LORAN C (Long Range A i d t o N a v i g a t i o n ) : t h e ground s t a t i o n s a r e m o s t l y equipped w i t h cesium c l o c k s s y n c h r o n i z e d b y groups o f 3 o r 4 by c l o c k t r a n s p o r t s e v e r a l t i m e s a y e a r . S y n c h r o n i z a t i o n i s m a i n t a i n e d t o w i t h i n about 1 microsecond.

I t i s a h y p e r b o l i c system which, i n some p a r t i c u l a r cases, may be r e n d e r e d c i r c u l a r

[Ll

( f i g . 6).

Fig 6

-

OMEGA i s a v e r y l o n g range n a v i g a t i o n system, h y p e r b o l i c i n p r i n c i p l e , ( f i ~ . 7 ) . The t r a n s m i t t i n g s t a t i o n s comprise f o u r cesium j e t o s c i l l a t o r s , and t h e combined o u t p u t o f these f o u r standards forms a s i g n a l whose r e l a t i v e d r i f t i s o f t h e o r d e r o f 10-12. But t h i s system can a l s o be used i n c i r c u l a r mode. Two t e c h n i - ques can be used [41 : d i r e c t phase measurement o f t h e s i g n a l s from each s t a t i o n used (which r e q u i r e s a v e r y s t a b l e c l o c k s y n c h r o n i z e d t o t h e A. t r a n s m i s s i o n s ) , o r phase measurements o f t h e s i g n a l s from s t a t i o n p a i r s . The r e s u l t o f t h e f i r s t method i s a f a m i l y o f c i r c u l a r l i n e s o f p o s i t i o n (LOP'S) c e n t e r e d about t h e s t a t i o n and spaced one wavelength a p a r t . The second t e c h n i q u e y i e l d s a f a m i l y o f h y p e r b o l i c 1 in e s o f p o s i t i o n spaced one h a l f wavelength a p a r t .

-

TRANSIT i s a n a v i g a t i o n system by quasi p o l a r s a t e l l i t e s : t h e r e a r e 5 s a t e l - l i t e s i n o r b i t and t h e user, t o g e t a f i x , must remain i n c o n t a c t w i t h t h e s a t e l l i t e o v e r a n a r c o f o r b i t o f s e v e r a l m i n u t e s o f t i m e . The s a t e l l i t e i s equipped w i t h a q u a r t z o s c i l l a t o r o f good q u a l i t y (10-ll). T h i s system i s deemed i n s u f f i c i e n t and i s t o be r e p l a c e d by NAVSTAR ( N A V i g a t i o n S a t e l l i t e Time And Ranging system) o r GPS ( G l o b a l P o s i t i o n i n s System). T h i s system i n v o l v e s 18 s a t e l l i t e s so t h a t

s e v e r a l o f them can be heard s i m u l t a n e o u s l y by t h e users. Each o f t h e f o u r s a t e l l i t e s launched c o n t a i n s t h r e e r u b i d i u m a t o m i c c l o c k s [ 3 1 ; t h e f o u r t h s a t e l l i t e a l s o has an e x p e r i m e n t a l cesium a t o m i c c l o c k . The c o r r e c t i o n can o n l y be made when t h e s a t e l l i t e i s i n view o f t h e c o n t r o l c e n t e r about e v e r y 12 hours.

Shaded zone Covering in 1974 Existing stations

Stations in development Planned stations

Tests station ( N e w York )

Fig 7

The system i s such t h a t many modes o f u t i l i z a t i o n , i n c l u d i n g s p h e r i c a l modes, a r e p o s s i b l e , a c c o r d i n g t o t h e u s e r ' s equipment.

The s t a b i l i t y r e q u i r e d f o r t h e spaceborne o s c i l l a t o r s i s d e f i n e d by t h e neces- s i t y o f 1 im i t i n g t h e u p d a t i n g frequency and o f a1 l o w i ng an autonomous o p e r a t i o n , w i t h o u t c o n t r o l from t h e ground, f o r a t l e a s t two weeks.

The c o n t r i b u t i o n o f t h e spaceborne c l o c k s t a b i l i t y t o p o s i t i o n i n g p r e c i s i o n i n t h e case o f t y p e

P

( P r e c i s i o n ) s i g n a l s i s s t i l l under s t u d y . I t i s e s t i m a t e d a t 5 metres w i t h a 68% p r o b a b i l i t y two hours a f t e r update, and 12 metres t w e n t y - f o u r hours a f t e r C51, C61, [71.

As f o r t h e ground ( u s e r ) c l o c k , t h e r e q u i r e d q u a l i t y o b v i o u s l y depends on t h e u t i l i z a t i o n mode, b u t t h e most i n t e r e s t i n g c h a r a c t e r i s t i c i s i n t h i s case t h e medium-term (30 seconds t o 10 m i n u t e s ) s t a b i l i t y : t h i s s h o u l d be o f t h e o r d e r o f 20.10-9/600

=

3.10-l1 t o be c o h e r e n t w i t h t h e space segment ; t h i s means t h a t a good q u a l i t y q u a r t z may be s u i t a b l e .

R _ e l i a _ b i l i t y . Thus, t h e o s c i l l a t o r s used i n t h i s system have a s t a b i l i t y j u s t s u f f i - c i e n t f o r t h e expected o b j e c t i v e s ; on t h e o t h e r hand, t h e p r e s e n t - d a y r e l i a b i l i t y i s n o t y e t s a t i s f a c t o r y .

I t i s i n d e e d a m a j o r problem i n n a v i g a t i o n systems t o be a b l e t o guarantee t h e p i l o t s t a b i l i t y i n t h e e n v i r o n m e n t a l c o n d i t i o n s imposed by t h e system, and t h e i r p r o p e r o p e r a t i o n d u r i n g t h e whole d u r a t i o n o f t h e planned m i s s i o n s , w i t h a s u f f i c i e n t p r o b a b i l i t y . I n t h e case o f GPS, t h e planned l i f e t i m e i s s i x y e a r s , and t h i s v a l u e seems t o be a b l e t o be reached o n l y t h r o u g h redundancy ( 3 o r 4 c l o c k s p e r s a t e l l i t e ) . Moreover, t h e i r b e h a v i o u r s h o u l d be m o d e l l e d so as t o account f o r t h e d r i f t s i n t h e n a v i g a t i o n message.

Thus i t i s c l e a r t h a t a t t h e p r e s e n t t i m e t h e c r i t i c a l p a t h as r e g a r d s r e l i a b i - l i t y passes t h r o u g h t h e o s c i l l a t o r s , t h e r e l i a b i l i t y o f t h e n a v i g a t i o n system b e i n g f i n a l l y t h a t o f t h e c l o c k . I t would be u s e f u l t o i n v e s t i g a t e , b u t t h i s i s o u t s i d e t h e scope o f t h i s paper, whether t h e c l o c k s t a b i l i t y i s c o n d i t i o n e d by t h e resona- t o r s , q u a r t z o r a t o m i c c e l l , o r by a n c i l l a r y equipment, such as e l e c t r i c s u p p l y .

There i s no q u e s t i o n t o r e v i e w h e r e a l l t h e n a v i g a t i o n systems, which a r e v e r y many ( s e v e r a l t e n s ) , which anyway means t h a t t h e r e i s no u n i v e r s a l one and t h a t t h e f i e l d o f a p p l i c a t i o n o f each i s o f t e n l i m i t e d (such as TORAN f o r o i l e x p l o r a t i o n ) .

The a v a i l a b i l i t y o f a n a v i g a t i o n system can be numerized by t h e t i m e percentage d u r i n g which an u s e r l o c a t e d anywhere on E a r t h i s a b l e t o compute h i s p o s i t i o n .

I t t h u s e x i s t s a space a v a i l a b i l i t y and a t i m e a v a i l a b i l i t y ; t h e former i s d e f i n e d once and f o r a l l , and t h u s accepted once t h e r e f e r e n c e segment i s s e t i n p l a c e : ground segment f o r OMEGA [ 4 1 , space segment f o r GPS [ 5 1 ; o n l y GPS, when f u l l y o p e r a t i o n a l , w i l l o f f e r a w o r l d w i d e c o v e r i n g , hence a 100% space a v a i l a b i l i t y . I t s t i m e a v a i l a b i l i t y i s a l s o expected t o be

loo%,

^{b u t} i t i s d i r e c t l y r e l a t e d t o t h e r e l i a b i l i t y o f t h e space segment hence, as a l r e a d y mentioned, t o o s c i l l a t o r r e l i a - b i l i t y .

For comparison, t h e t i m e a v a i l a b i l i t y o f t h e TRANSIT system i s a t b e s t 10%

(10 m i n u t e s e v e r y 2 h o u r s ) , and t h e space a v a i l a b i l i t y ( c o v e r i n g ) o f t h e o r d e r o f 30% ( ? ) .

U n s e r v i c e a b i l i t y o f one s a t e l l i t e , f o r i n s t a n c e t h r o u g h c l o c k breakdown, i s expressed i n GPS by a l o s s o f p r e c i s i o n , due t o t h e e x i s t e n c e o f downgraded o p e r a t i o n modes, w h i l e i n t h e TRANSIT system t h e r e would be a c o n c o m i t t a n t r e d u c t i o n o f a v a i l a -

b i l i t y .

One o f t h e m a i n o p e r a t i o n a l c o n s t r a i n t s o f t h e above n a v i g a t i o n systems i s t h e n e c e s s i t y t o p e r f o r m p e r i o d i c a l l y e i t h e r c l o c k s y n c h r o n i z a t i o n -case o f LORAN C o r ONEGA- o r m o n i t o r i n g and m o d e l l i n g o f t h e i r d r i f t - case o f GPS- by means o f a s o p h i s - t i c a t e d and c o s t l y c o n t r o l segment. I t i s obvious t h a t t h i s c o n s t r a i n t i s reduced when t h e l o n g - t e r m o s c i l l a t o r s t a b i l i t y i s i n c r e a s e d .

For t h e users, t h e o p e r a t i o n a l c o n s t r a i n t w h i c h seems most d i r e c t l y r e l a t e d t o t h e s t a b i l i t y o f t h e v e h i c l e borne c l o c k s i s t h e computing c a p a c i t y necessary f o r o b t a i n i n g a g i v e n p r e c i s i o n . Indeed i f we may c o n s i d e r t h e t i m e and frequency genera- t e d b y t h e v e h i c l e borne o s c i l l a t o r as e x a c t l y known, a p p r o x i m a t e l y known o r t o t a l l y unknown, t h e r e q u i r e d computing c a p a c i t y i n c r e a s e s c o n s i d e r a b l y , and one passes from t h e microcomputer t o t h e heavy m i n i c o m p u t e r . Whereas t h i s i s o f l i t t l e i m p o r t a n c e f o r a submarine o r an a i r l i n e r , i t i s n o t s o f o r a t r a w l e r o r f o u r t h - l e v e l a i r c r a f t . D i s r x t j ? ~ , i.e. t h e f a c u l t y o f a m o b i l e t o g e t a f i x w i t h o u t e m t t t i n g any RF

-

s i g n a l , i s a q u a l i t y much a p p r e c i a t e d by t h e m i l i t a r y . I t i s t h e case o f t h e a s t r o - nomical f i x , and a l s o o f p a s s i v e systems where t h e u s e r i s o n l y equipped w i t h a r e c e i v e r . T h i s c o n s t r a i n t imposes t o t h e d i s c r e e t n a v i g a t i o n system t o be h y p e r b o l i c i f i t i s equipped w i t h o n l y medium s t a b i l i t y o s c i l l a t o r s , o r p o s s i b l y s p h e r i c a l i f i t c a r r i e s h i g h s t a b i l i t y ones.

Consequently, d i s c r e e t and p r e c i s e systems must be equipped w i t h v e r y s t a b l e o s c i l l a t o r s .

Thus, t h e d i s c r e t i o n concept imp1 i c i t l y assumes t h a t t h e RF i n f o r m a t i o n t r a v e l s from s t a t i o n s t o v e h i c l e i n one sense o n l y ( t h e r e i s no t r a n s p o n d e r ) : d i s c r e e t systems a r e "one way" systems, w i t h a l l t h e advantages t h i s i m p l i e s [ I ] , b u t i t s h o u l d n o t be f o r g o t t e n t h a t , a t t h e p r e s e n t t i m e , t h e most p r e c i s e systems make use o f t h e

"two way mode" t e c h n i q u e as soon as t h e m i s s i o n d u r a t i o n exceeds a few days.

~ l ~ ~ ~ a b i l i t . i s a concept c o r r e s p o n d i n g t o t h e s e n s i t i v i t y o f t h e system, o r

i t s components, t o e x t e r n a l agents, whether t h e s e a r e n a t u r a l - a n d i n t h i s case t h i s concept i s none o t h e r t h a n t h e r e a c t i o n t o i n f l u e n c e parameters (temperature, vacuum, r a d i a t i o n s , magnetic f i e l d , e t c . ) ; we s h a l l n o t emphasize t h i s aspect- o r t h e y a r e a r t i f i c i a l , i .e. p u r p o s e l y c r e a t e d w i t h a view t o r e n d e r t h e n a v i g a t i o n system i n o p e r a t i v e : t h i s i s i n p a r t i c u l a r t h e case o f RF jamming. Very s t a b l e o s c i l l a t o r s

a r e more j a m - p r o o f , as t h e i r s t a b i l i t y makes i t p o s s i b l e t o generate codes o p t i m i z e d f o r t h i s o b j e c t i v e w i t h o u t f e a r i n g t h a t t h e r e s i d u a l i n s t a b i l i t y o f t h e p i l o t s j e o p a r d i z e t h e i r e f f i c i e n c y , p a r t i c u l a r l y b y c r e a t i n g secondary rebounds i n t h e a m b i g u i t y f u n c t i o n s [ 9 ] , which i s expressed by a l o s s o f p r e c i s i o n due t o a d e t e r i o - r a t i o n o f t h e s i g n a l / n o i s e r a t i o .

&wtgrxJedm&da. It s h o u l d a l s o be emphasized t h a t t h e use o f v e r y s t a b l e

o s c i l l a t o r s i n n a v i g a t i o n systems makes e a s i e r t h e c o n s t i t u t i o n o f redundant d e v i c e s indeed i f t h e o s c i l l a t o r s t a b i l i t y i s s u f f i c i e n t f o r t h e source f r e q u e n c i e s (and phases) t o be c o n s i d e r e d as known, i t i s no more necessary t o t r a n s m i t them, so t h a t t h e systems comprise l e s s f u n c t i o n a l components and hence a r e e a s i e r t o be made r e - l i a b l e by m u l t i p l i c a t i o n o f modules.

Moreover, t h e s t r u c t u r e o f t h e systei:~ may i t s e l f be s i m p l e r -one way system- so t h a t i t i s p o s s i b l e t o c o n s i d e r downgraded o p e r a t i o n modes w i t h o u t e x c e s s i v e c o m p l i c a t i o n ; th e downgraded mode o f a s p h e r i c a l system, f o r i n s t a n c e , may be t h e h y p e r b o l i c system t o which we would have t o r e s o r t i f , f o r any reason, t h e s t a b i l i t y o f t h e s o u r c e became i n s u f f i c i e n t : t h e r e would r e s u l t a l o s s of p r e c i s i o n , b u t n o t a t o t a l l o s s o f i n f o r m a t i o n .

T h i s b r i e f a n a l y s i s c l e a r l y shows t h a t t h e performance o f n a v i g a t i o n systems i s l a r g e l y dependent o n t h e c h a r a c t e r i s t i c s o f t h e o s c i l l a t o r s t h a t g o v e r n them, b u t t h e s e do n o t possess y e t a l l t h e d e s i r a b l e q u a l i t i e s .

P r o s p e c t i v e . - I n t h e v e r y near f u t u r e most n a v i g a t i o n systems w i l l be o f t h e " t i m e - frequency" t y p e ; t h i s means t h a t t h e y w i l l be a b l e t o e x p l o i t s i m u l t a e n o u s l y o r suc- c e s s i v e l y t h e i n f o r m a t i o n c a r r i e d by t h e phase o f an RF s i g n a l ( t i m e ) and t h a t c a r r i e d by t h e t i m e d e r i v a t i v e o f t h e phase ( f r e q u e n c y ) o f t h i s same s i g n a l .

The denomination " t i n e - f r e q u e n c y " i s a1 so o f t e n used f o r some s y n t h e t i c systems i n c l u d i n g , on-board an a i r c r a f t , a s p a c e c r a f t o r a s h i p , many f u n c t i o n s such as telecommunications, n a v i g a t i o n , i d e n t i f i c a t i o n , a n t i c o l l i s i o n , e t c . These are, i n f a c t , m u l t i f u n c t i o n systems u s i n g " t i m e - f r e q u e n c y " t e c h n i q u e s . They a r e o r g a n i z e d around t h r e e m a i n modules :

-

a v e r y s t a b l e o s c i l l a t o r ,

-

a minicomputer,

-

a t r a n s m i t t e r - r e c e i v e r module.

The g e n e r a l i z e d use o f t h e s e concepts supposes t h a t p r e s e n t - d a y components, p a r t i c u l a r l y o s c i l l a t o r s , p r o g r e s s r a p i d l y .

I t i s d e s i r a b l e t h a t , i n t h e near f u t u r e , v e r y s t a b l e o s c i l l a t o r s be more com- pact, b u t above a l l more r e l i a b l e and e a s i e r t o model ; t h i s means t h a t t h e i r b e h a v i o u r s h o u l d be s t u d i e d i n v a r i o u s e n v i r o n m e n t a l c o n d i t i o n s ( a c c e l e r a t i o n s , v i b r a t i o n s , m a g n e t i c f i e l d s , temperatures, e t c . ) , and t h a t t h e laws o f t h e i r e v o l u t i o n i n t i m e be e s t a b l i s h e d w i t h a v i e w t o be a b l e t o i n p u t i n t o t h e memories o f t h e i r a s s o c i a t e d computers t h e necessary c o r r e c t i o n f a c t o r s . I t s h o u l d be remarked t h a t i t i s anyway i n d i s p e n s a b l e t o t a k e i n t o account some c o r r e c t i o n s , i n p a r t i c u l a r r e l a t i v i s t i c c o r r e c t i o n s which a r e f a r from n e g l i g i b l e : t h e y can r e a c h on E a r t h s e v e r a l hundreds o f nanoseconds ; b y way o f i n d i c a t i o n , t h e f o r m u l a p r o v i d i n g t h e c a l c u l a t i o n o f t h e r e l a t i v i s t i c d r i f t s

6

o c c u r i n g between a f i x e d c l o c k and a m o b i l e c l o c k t r a v e l l i n g around t h e E a r t h a t a l a t i t u d e A and a n a l t i t u d e

h

may be expressed i n t h e f o l l o w i n g way [ l o , 111 :

6 - ~ ~ ~ / c ~ ) - [ ( z R R c o s h t o) v-/.c']

Furthermore, a p a r t i c u l a r e f f o r t s h o u l d be made t o improve t h e l o n g - t e r m s t a b i - l i t y j u s t s u f f i c i e n t f o r a p p l i c a t i o n s t o n a v i g a t i o n ; an o v e r a l l v a l u e o f 10-l3 f o r A t / f s h o u l d be ensured o v e r a y e a r i n " a v i a t i o n " t y p e e n v i r o n m e n t a l c o n d i t i o n s .

F i g u r e 8 shows t h e p r e d i c t a b l e medium t e r n e v o l u t i o n o f t h e most common o s c i l l a t o r s .

1950 1960 1970 1980 1990 2000

Date 10-l4

l o t 3 - 10-l2

*'

^lo-11-

-

f

"-

l o - * - 10 -7

AC: Atomic clock O W :Quartz oscillators weight L T : Long term ACW: Atomic clocks weight S T : Short term AAB : Accelerated ageing boxes

Q :Quartz Ex.

:

Example

Fig 8

I t seems t o me d e s i r a b l e t h a t t i m e d i s t r i b u t i o n be o r g a n i z e d a t a w o r l d w i d e b a s i s a t t h e l e v e l o f one (maybe t e n ) nanosecond, so t h a t t h e many a p p l i c a t i o n s o f

v e r y s t a b l e o s c i l l a t o r s , p a r t i c u l a r l y t h o s e r e l a t e d t o n a v i g a t i o n , m i g h t develop ap- p r o p r i a t e l y . I f such a network e x i s t e d -GPS i s l i k e l y t o p r o v i d e t h i s p r e c i s i o n . .

.

b u t GPS i s c o n s i d e r e d as v u l n e r a b l e - , and p r o v i d e d t h a t t h e l o n g - t e r m s t a b i l i t y o f v e r y s t a b l e o s c i l l a t o r s had been improved t o c l o s e t o

loe1'+,

n o t h i n g would h i n d e r anymore t h e f u l l e x p l o i t a t i o n o f t h e "time-frequency'' p r i n c i p l e s ; t h e problem o f s y n c h r o n i z a t i o n u p d a t i n g would be suppressed, and n a v i g a t i o n d e v i c e s would be e x t r e m e l y s i m p l e and economical ; under t h e e f f e c t o f i n c r e a s i n g number o f users, v e r y s t a b l e o s c i l l a t o r s ( n o t n e c e s s a r i l y a t o m i c ) m i g h t become i n e x p e n s i v e and ap- p l i c a t i o n s i n t h e g e n e r a l p u b l i c c o u l d be c o n s i d e r e d : g e n e r a l a v i a t i o n , t r a w l e r s , p l e a s u r e boats, etc., w i t h a d i r e c t impact o n t h e t r a f f i c s a f e t y .

\

- \,ACW

\\

-

- -

AAB

-

- <---- ^{EX. - -}

- -

I 1 I I

On t h e s c i e n t i f i c v i e w p o i n t t h e i n c r e a s e o f t h e s h o r t - a n d l o n g - t e r m s t a b i l i t y o f v e r y s t a b l e o s c i l l a t o r s c o n d i t i o n s i n a l a r g e measure t h e p r o g r e s s i n t h e knowledge o f cosmic laws and t h e p o s s i b i l i t y o f c a r r y i n g o u t t h e necessary experiments by c o n t r o l l i n g w i t h a p r e s e n t l y i n a c c e s s i b l e accuracy t h e t r a j e c t o r y o f space probes : l e t us m e n t i o n as an example t h a t a "one way" n a v i g a t i o n d e v i c e f o r a Mars r o b e a i i r i n g a t a p r e c i s i o n o f a few meters r e q u i r e s a l o n g - t e r m s t a b i l i t y o f

lbP5.

A

60 50 40 30 20 10

On t h e m i l i t a r y v i e w p o i n t , a p a r t f r o m t h e " c o n v e n t i o n a l n a v i g a t i o n " m o t i v a t i o n which r e q u i r e s o s c i l l a t o r s w i t h an e x c e l l e n t l o n g - t e r m s t a b i l i t y , r e q u i r e m e n t s appear on s h o r t - t e r m s t a b i l i t y f o r n a v i g a t i o n systems u s i n g p a t t e r n r e c o g n i t i o n techniques, such as systems d e r i v e d from "Side L o o k i n g Radars".

Conclusion.- The b r i e f s t u d y w h i c h has been p r e s e n t e d l e a d s t o two remarks, which w i l l s e r v e as c o n c l u s i o n :

1

-

N a v i g a t i o n system p r o g r e s s as r e g a r d s p r e c i s i o n , simp1 i c i t y , r e 1 i a b i l i t y and u n i v e r s a l i t y i s c o n d i t i o n e d by p r o g r e s s on v e r y s t a b l e o s c i l l a t o r s .

2

-

The performance a t t a i n e d a t p r e s e n t by a t o m i c o r q u a r t z v e r y s t a b l e o s c i l - l a t o r s a r e n o t o n l y n o t superabundant, as sometimes b e l i e v e d , b u t s t i l l i n s u f f i c i e n t f o r t h e i r u t i l i z a t i o n i n n a v i g a t i o n systems t o be f u l l y g e n e r a l i z e d .

E l l Moreau, R. : A p p l i c a t i o n s a 6 r o s p a t i a l e s des oscillateurs,T.P.ONERA 1979-48.

[ 2 ] Zakheim, J. : Etude comparative de quel ques d i s p o s i t i f s de t r a j e c t o g r a p h i e , Note Technique ONERA n o 63 (1961).

[ 3 1 NAVSTAR s h o u l d improve t h e e f f e c t i v e n e s s o f m i l i t a r y m i s s i o n s , General ac- c o u n t i n g o f f i c e , Washington DC, Procurement and Systems A c q u i s i t i o n Div.

PSAD 80-21.

[41 P r i n c i p l e s and o p e r a t i o n a l aspects o f p r e c i s i o n p o s i t i o n d e t e r m i n a t i o n systems, AGARDOGRAPH no 245 (1979), (TYLER J.S., p. 1, 1, 2 ) .

[51 P r e c i s i o n p o s i t i o n i n g and i n e r t i a l guidance sensors, AGARDOGRAPI-I no 298 (1981).

[61 IEEE P o s i t i o n L o c a t i o n and N a v i g a t i o n Symposium, San Diego, 6-9/11/1978.

[71 G l o b a l P o s i t i o n i n g System, The I n s t i t u t e o f F l a v i ~ a t i o n , Washington 1980, (Easton R.L., p . 1 5 ) .

181 Time Keeping and Frequency C a l i b r a t i o n , Hewlett-Packard, A p p l i c a t i o n N o t e 52-2 (1975).

[9] Moreau, R. : Cornparaison des o s c i l l a t e u r s u l t r a - s t a b l e s , I n t e r s t r e l a t i f des mesures t e m p o r e l l e s e t f r e q u e n t i e l l e s , T.P. ONEPA no 1977-120.

[ I 0 1 Moreau, J.P. : S y n c h r o n i s a t i o n d ' h o r l o g e dans l e domaine 100 ps, Note Techni- que ONERA 1978-1.

[ I 11 H a f e l e , J.C. : R e l a t i v i s t i c Time T e r r e s t r i a l C i r c u m n a v i g a t i o n s , AJP Volume 40/81 (1972).