Basic GPS

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    Module 2 : Global Positioning Syste m L e c t ur e 1 1 : S a t e l l it e g e om e t r y a n d A c c u r a c y m e a s u r e s

    Geometrical interpretation of Dilution of PrecisionDOPAs mention ed earl ier DOP is an ind icator of three dime nsion al posi tioni ng accuracy as conseq uen ce of rela tive positio n of

    G P S s a t e l l l i t e s w i t h r e s p e c t t o a G P S r e c e i v e r . I n o r d e r t o a t t a c h a g e o m e t r i c a l i n t e r p r e t a t i o n t o t h i s , w e u s e a t e r m c a l l e dg e o m e t r i a c l d i l u t i o n o f p r e c i s i o n o r G D O P . F i g u r e 1 1 . 2 a n d 1 1 . 3 e x p l a i n a s i m p l e i n t e r p r e t a t i o n f o r t h i s . A c l o s e b u n c h i n g o r p o o r l y s p a c e d s a t e l l i t e s g i v e s p o o r G D O P v a l u e w h e r e a s w e l l d i s t r i b u t e d s a t e l l i t e s y i e l d g o o d G D O P . F o r a n i d e a l s i t u a t i o ni . e o n e s a t e l l i t e o v e r h e a d w i t h t h e o t h e r s s p a c e d a t e q u a l h o r i z o n t a l a n g l e s a b o u t t h e o b s e r v e r , w i l l g i v e t h e b e s t G D O P .

    Figure 11.2 Spatial geometry for GDOP values (Dana, 2000)

    Figure 11.3 Spatial geometry for GDOP values (Dana, 2000)

    I n l i t e r a t u r e , d i f f e r e n t t y p e s o f D O P d e s i g n a t i o n s a r e i s u s e . F o r e x a m p l e , G D O P , P D O P , e t c . T h e s e a r e g i v e b e l o w :G D O P : G e o m e t r i c a l D i l u t i o n o f P r e c i s i o n , ( m e a s u r e o f a c c u r a c y i n 3 - D p o s i t i o n a n d t i m e )P D O P : P o s i t i o n D i l u t i o n o f P r e c i s i o n ( m e a s u r e o f a c c u r a c y i n 3 - D p o s i t i o n ) , a l s o c a l l e d s p h e r i c a l D O PH D O P : H o r i z o n t a l D i l u t i o n o f P r e c i s i o n ( m e a s u r e o f a c c u r a c y i n 2 - D p o s i t i o n , f o r e x a m p l e L a t i t u d e a n d L o n g i t u d e )V D O P : V e r t i c a l D i l u t i o n o f P r e c i s i o n ( m e a s u r e o f a c c u r a c y i n 1 - D p o s i t i o n , H e i g h t )T D O P : T i m e D i l u t i o n o f P r e c i s i o n ( m e a s u r e o f a c c u r a c y i n T i m e )

    P D O P i s a l s o i n t e r p r e t e d a s i n v e r s e l y p r o p o r t i o n a l t o t h e v o l u m e , V, o f a t e t r a h e d r o n t h a t i s f o r m e d f r o m t h e s a t e l l i t e a n du s e r p o s i t i o n s ( P D O P 1 /V) . T h e s e D O P v a l u e s a r e r e l a t e d t o p o s i t i o n i n g e r r o r s a n d U E R E b y t h e f o l l o w i n g e x p r e s s i o n s

    w h e r e r i s U E R E , H, V , P a n d T a r e s t a n d a r d d e v i a t i o n s i n h o r i z o n t a l , v e r t i c a l , p o s i t i o n ( b o t h h o r i z o n t a l a n d v e r t i c a l ) ,a n d t i m e r e s p e c t i v e l y .

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