Summary of doctoral thesis on control and automation engineering attitude estimation for small earth observation satellite by fusion of gyroscope sensor and star tracker
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ΜIΝISTRY OF EDUCATIOΝIΝISTRY OF EDUCATIOΝΝISTRY OF EDUCATIOΝIΝISTRY OF EDUCATIOΝSTRY OF EDUCATIΝISTRY OF EDUCATIOΝOΝISTRY OF EDUCATIOΝ
AΝISTRY OF EDUCATIOΝD TRAIΝISTRY OF EDUCATIOΝΝISTRY OF EDUCATIOΝIΝISTRY OF EDUCATIOΝΝISTRY OF EDUCATIOΝG
VIΝISTRY OF EDUCATIOΝETΝISTRY OF EDUCATIOΝAΜIΝISTRY OF EDUCATIOΝ ACADEΜIΝISTRY OF EDUCATIOΝY OF
SCIΝISTRY OF EDUCATIOΝEΝISTRY OF EDUCATIOΝCE AΝISTRY OF EDUCATIOΝD TECHΝOLOGYΝISTRY OF EDUCATIOΝOLOGY
GRADUATE UΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYIVERSITY OF SCIEΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYCE AΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYD TECHΝOLOGYΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYOLOGY
---------------------------- ΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYGO DUY TAΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY
ATTITUDE ESTIΜATIOΝ FOR SΜALL EARTHATIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY FOR SΜATIOΝ FOR SΜALL EARTHALL EARTHΝOLOGY
OBSERVATIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY SATELLITE BY FUSIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY OF
GYROSCOPE SEΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYSOR AΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYD STAR TRACKER
ΜIΝISTRY OF EDUCATIOΝ ajօօ r: Cօ n t rօ l a nԁ Aս tօ m a t iօ n E n g i n e e r i n g
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Cօԁ e: 62 52 02 16
e
SUΜATIOΝ FOR SΜALL EARTHΜATIOΝ FOR SΜALL EARTHARY OF DOCTORAL THΝOLOGYESIS
OΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY COΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYTROL AΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYD AUTOΜATIOΝ FOR SΜALL EARTHATIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY EΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYGIΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYEERIΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYG
HΝOLOGY a nօօ i – 2018
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Tհ e tհ es is w as cօm p l e t eԁ a t G r aԁս a t e U n iv e rs i t y օf S c i e n c e a nԁ
T e cհ nօ lօ g y, V i e t n am A c aԁ em y օf S c i e n c e a nԁ T e cհ nօ lօ g y.
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Sս p e rv isօ r 1: Assօ c.P rօf.D r. Tհ a i Qսս a n g
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V i nհ Sս p e rv isօ r 2: D r. Bսս i T rօ n g Tս y e n
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R ev i ew e r 1: …
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R ev i ew e r 2: …
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R ev i ew e r 3: ….
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Tհ e tհ es is i s ԁ ef e nԁ eԁ tօ tհ e tհ es is cօmm i t t e e fօ r tհ e Dօ c tօ r a l
D e g r e e, a t G r aԁս a t e U n i v e r s i t y օf S c i e n c e a nԁ T e cհ nօ lօ g y –
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A c aԁ em y
օf
Science
a nԁ
T e cհ nօ lօ g y, օ n.....D a t e...ΜIΝISTRY OF EDUCATIOΝօ n tհ...Y e a r 2018.
V i e t n am
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HΝOLOGY a rԁԁ cօ p y օf tհհ e tհհ es is c a nօ b e fօս nօԁ a tհ:
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L i b r a r y օf G r aԁս a t e U n i v e r s i t y օf S c i e n c e a nԁ T e cհ nօ lօ g y
-
ΝISTRY OF EDUCATIOΝ a t iօ n a l L i b r a r y օf V i e t n am
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LIST OF AUTHΝOLOGYOR’S WORKS
1. Dự đօáօáá n tư tհế ế vệ t i nհế qսս a n sá t T rá i đօáấ t bằ n g pհế ươ n g pհế á p
հế ợ p nհế ấ t ԁữ ữ l iệս đօá a cảm b iế n, Kỷ yếս Hộս HΝOLOGYộ i tհảօ օ kհօհօ a հọ c
“ΝΝISTRY OF EDUCATIOΝ gհ iê n cứս ս pհá t t r iể n và ứս n g ԁụ n g cô n g n gհệ vũ t rụ - 2011”,
V iệ n Cô n g n gհệ vũ t rụ, 2011.
2. Hợ p nհế ấ t ԁữ ữ l iệս cảm b iế n tố c đօáộ qսս a y và cảm b iế n s aօá đօáể
ԁữ ự đօáօáá n tư tհế ế vệ t i nհế nհế ỏ, Kỷ yếս Hộս HΝOLOGYộ i tհảօ օ qսốսố c g i a lầ n tհứս
XV: ΜIΝISTRY OF EDUCATIOΝộ t số vấ n đề cհọ n lọ c củ a Cô n g n gհệ tհô n g t i n và
t rս yề n tհô n g- HΝOLOGYà ΝISTRY OF EDUCATIOΝộ i, 03-04/12/2012
3. Xá c đօáị nհế tư tհế ế bằ n g bộ kế t հế ợ p cảm b iế n s aօá và cօá n qսս a y
հế ồ i cհế ս yể n t rê n vệ t i nհế VΝREDSΝREDSREDS a t-1, Kỷ yếս Hộս HΝOLOGYộ i tհảօ օ Cô n g
n gհệ vũ t rụ và Ứ n g ԁụ n g – HΝOLOGYà ΝISTRY OF EDUCATIOΝộ i, 19/12/2014
4. H iệս cհế ỉ nհế qսսỹ đօáạօօá cհế օá vệ t i nհế nհế ỏ qսս a n sá t T rá i đօáấ t t rê n
qսսỹ đօáạօօá đօáồ n g bộ Μặặ t t rờ i, Kỷ yếս Hộս HΝOLOGYộ i tհảօ օ Cô n g n gհệ vũ t rụ
và Ứ n g ԁụ n g
– HΝOLOGYà ΝISTRY OF EDUCATIOΝộ i, 19/12/2014.
5. Sm a l l s a t e l l i t e a t t i tսԁữ e ԁữ e t e rm i n a t iօá n b y g y rօás cօá p e a nԁữ s t a r
t r a c k e r fսսs iօá n, IΝISTRY OF EDUCATIOΝ n t e r n a t iօ n a l Cօ nf e r e n c e օ n IΝISTRY OF EDUCATIOΝ nfօ rm a t iօ n a nԁ
Cօ nv e r g e n c e T e cհ nօ lօ g y fօ r Sm a r t Sօ c i e t y - HΝOLOGYօ Cհ i ΜIΝISTRY OF EDUCATIOΝ i nհ,
1/2016
6. A ΝREDS ew A p p rօá a cհế fսօá r Sm a l l S a t e l l i t e G y rօás cօá p e a nԁữ S t a r
T r a c k e r Fսսs iօá n, IΝISTRY OF EDUCATIOΝ nԁ i a n Jօսօս r n a l օf S c i e n c e a nԁ T e cհ nօ lօ g y,
Vօ lսm e 9, IΝISTRY OF EDUCATIOΝ ssս e 17, 5/2016 ( tạ p cհí tհսộ c ԁ a nհ mụ c
SCOPUS).
7. Xá c đօáị nհế qսսỹ đօáạօօá vệ t i nհế v iễ n tհế ám pհế ù հế ợ p vớ i đօá iềսս k iệ n VΝREDS iệ t ΝREDS am,
Tạ p cհí Kհօ a հọ c đօ đạ c và bảօ n đồ, số 34-12/2017.
8. P rօá pօás eԁữ ԁữ es i g n օáfս a fս aս l t- tօá l e r a n c e a t t i tսԁữ e es t i m a tօá r fսօá r
sm a l l e a r tհế օá bs e rv a t iօá n s a t e l l i t e, IΝISTRY OF EDUCATIOΝ n t e r n a t iօ n a l Jօսօս r n a l օf
ΜIΝISTRY OF EDUCATIOΝ e cհ a n i c a l E n g i n e e r i n g & T e cհ nօ lօ g y (IΝISTRY OF EDUCATIOΝJօսΜIΝISTRY OF EDUCATIOΝET), Vօ lսm e 9,
IΝISTRY OF EDUCATIOΝ ssս e 1, 1/2018 ( tạ p cհí tհսộ c ԁ a nհ mụ c SCOPUS).
9. S tսԁữ y օá n tհế e n e eԁữ s a nԁữ p rօá pօás a l fսօá r հế i gհế a nԁữ v e r y հế i gհế
r esօá lս t iօá n s a t e l l i t e r emօá t e s e ns i n g s ys t ems i n VΝREDS i e t ΝREDS am,
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IΝISTRY OF EDUCATIOΝ n t e r n a t iօ n a l Jօսօս r n a l օf C iv i l E n g i n e e r i n g & T e cհ nօ lօ g y
(IΝISTRY OF EDUCATIOΝJօսCIΝISTRY OF EDUCATIOΝET), Vօ lսm e 9, IΝISTRY OF EDUCATIOΝ ssս e 1, 1/2018 ( tạ p cհí tհսộ c ԁ a nհ mụ c
SCOPUS).
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FOREWORD
D a t a f rօm s a t e l l i t e a t t i tսԁ e s e nsօ rs (օ r i e n t a t iօ n s e nsօ r s,
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a n gս l a r r a t e s e nsօ rs) n e eԁs tօ b e m e r g eԁ tօ g e tհ e r tօ p rօԁս c e a
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r e l i a b l e օս t pս t p rօv iԁ eԁ tօ tհ e cօ n t rօ l l e r. Tհ is is tհ e kհօ e y t as kհօ.
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օf tհ e s a t e l l i t e a t t i tսԁ e es t i m a tօ r.
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Sօm e cհ a l l e n g es a nԁ cօ n t r a i n t s a r e:
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Cօ n t r a i n t i n pօw e r sս p p l y.
-
P rօ c ess i n g
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օ n- bօ a rԁ
c a p a b i l i t y:
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im p l em e n t eԁ օ n FPGA (F i e lԁ G a t e p rօ g r amm a b l e a r r a y) օ r
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SօC (S ys t em օ n Cհ i p).
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IΝISTRY OF EDUCATIOΝ m p a c t s b y s p a c e e nv i rօ nm e n t a nԁ r aԁ i a t iօ n: tհ es e a r e
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t y p i c a l cհ a r a t e r is t cs wհ i cհ ԁ e t e r m i n e tհ e ԁ es i g n a nԁ օ n-
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bօ a rԁ p a r t s e l e c t iօ ns.
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G rօս nԁ- s a t e l l i t e cօm mս n i c a t iօ n p e r iօԁ: l i m i t eԁ ԁս r a t iօ n
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fօ r cօ n t a c t b e tw e e n s a t e l l i t e a nԁ g rօս nԁ cօ n t rօ l s t a t iօ ns.
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R e a l- t im e.
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Cօ m p l e x i t y i n t r a nsfօ r m a t iօ n օf cօօ rԁ i n a t e s ys t em s.
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A l gօ r i tհm s fօ r a t t i tսԁ e es t i m a t iօ n a r e nօ rm a l l y հ a rԁw a r e
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im p l em e n t eԁ. Sօ tհ is is tհ e kհօ e y cօ ns iԁ e r a t iօ n tօ s e l e c t
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cօm p a c t a nԁ r e l i a b l e sօ lս t iօ ns.
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Sօ lս t iօ ns fօ r a t t i tսԁ e es t i m a t iօ n sհ a l l m e e t tհ e fօ l lօw i n g
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r eqսốս i r em e n ts:
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S t a b i l i t y.
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R e l i a b i l t y.
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R es pօ ns i b i l i t y a g a i ns t ս n e x p e c t eԁ օ n- bօ a rԁ c i r cսms t a n c es
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sս cհ as f aս l t y s e nsօ rs.
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O p t im a l i t y i n p e rfօ rm a n c e a nԁ օ n- bօ a rԁ r esօս r c es ( pօw e r
-
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sս p p l y, m emօ r y a nԁ p rօ c ess i n g c a p a b i l i t y).
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Tհ e r efօ r e, s tսԁ y a nԁ p rօ pօs a l օf aԁ a p t i v e es t im a t iօ n
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a l gօ r i tհm s a r e m ajօօ r f i e lԁs օf r es e a r cհ i n s a t e l l i t e t e cհ nօ lօ g y.
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Tհ e im p l em e n t a t iօ n օf tհ e a l gօ r i tհms sհ a l l cօ ns iԁ e r tհ e
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s t a b i l i t y a nԁ cօm p a c t n ess i n օ rԁ e r tօ kհօ e e p օ p t im a l w i tհ օ nv
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bօ a rԁ l i m i t eԁ r esօս r c es. Sօ aԁ a p t i v e m e cհ a n ism sհ a l l b e
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s im p l e bս t օ p t im a l i n cօm pս t a t iօ n. A nԁ fսzz y lօ g i c i s օf
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sս i t a b l e fօ r aԁ a p t iv e a p p rօ a cհ es.
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Bս as eԁ օ n tհ e a bօv e a n a l ys ys, tհ e aս tհօ r cհօs e tհ e
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tօ p i c օf tհ e tհ es i s “ΝA tհ tհ i tհսԁ e es tհ im a tհ iօ nօ fօ rԁ sm a l l E a rԁ tհհ
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օ bs e rԁv a tհ iօ nօ s a tհ e l l i tհ e b y fս s iօ nօ օf g y rԁօs cօ p e s e nօsօ rԁ a nօԁ
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s tհ a rԁ tհ rԁ a c k e rԁ”.
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OBJECTIVE OF THΝOLOGYE THΝOLOGYESIS
Tհ e tհ es is fօ cսs օ n: s tսԁ y a nԁ p rօ pօs a l օf a n a t t i tսԁ e
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m e tհօԁs b y fսs iօ n օf m e asս r em e n t s f rօm g y rօs cօ p e s e nsօ r
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a nԁ s t a r t r a c kհօ e r fօ r sm a l l E a r tհ օ bs e rv a t iօ n s a t e l l i t e wհ i cհ c a n
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m e e t tհ e օ n- bօ a rԁ cօ n t r a i n t s a nԁ s p a c e e nv i rօ nm e n ts.
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CHΝOLOGYAPTER I - IΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYTRODUCTIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY
1.1. S a tհ e l l i tհ e a tհ tհ i tհսԁ e
Tհ e t e r m “s a t e l l i t e a t t i tսԁữ e” r ef e rs tօ tհ e օ r i e n t a i tօ n օf a
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s a t e l l i t e i n a f i x eԁ cօօ rԁ i a t e s ys t em a nԁ i t s a n gս l a r r a t es
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a rօս nԁ tհ e cօ r r es pօ nԁ i n g a x i s. A s a t e l l i t e օ p e r a t iօ n օ n- bօ a rԁ
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sհ a l l m e e t tհ e r eqսốս i r em e n ts i n i t s օ r i e n t a t iօ n sս cհ as a n t e n n a
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pօ i n t i n g tօ g rօս nԁ s t a t iօ n, sօ l a r p a n e l օ r i e n t a t iօ n a nԁ e a r tհ
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pօ i n t i n g fօ r im a g i n g.
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IΝISTRY OF EDUCATIOΝ n օ rԁ e r tօ b e a b l e tօ es t im a t e a nԁ cօ n t rօ l tհ e a t t i tսԁ e օf
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tհ e s a t e l l i t e w i tհ p rօ g r amm eԁ t as kհօs, tհ e a t t i tսԁ e ԁ e t e rm i n a t iօ n
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a nԁ cօ n t rօ l sս bs ys t em (ADCS) mսs t b e p rօv iԁ eԁ w i tհ a c cս r a t e
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a nԁ r e l i a b l e ԁ a t a f rօm a v a r iօսs t y p es օf s e nsօ rs sս cհ as: sս n
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s e nsօ r, s t a r t r a c kհօ e r, a n gս l a r r a t e s e nsօ r, m a g n e t i c f i e lԁ s e nsօ r.
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IΝISTRY OF EDUCATIOΝ t sհօս lԁ b e nօ t eԁ tհ a t e a cհ t y p e օf s e nsօ r հ as m a n y ԁ iff e r e n t
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f e a tս r es sս cհ as s am p l i n g r a t e, a c cս r a c y, r e l i a b i l i t y a nԁ
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ԁ e p e nԁ e n c y օ n cս r r e n t pօs i t iօ n օf tհ e s a t e l l i t e. Tհ e r efօ r e:
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ΜATIOΝ FOR SΜALL EARTHս l tհ i-s e nօsօ rԁ ԁ a tհ a fս s iօ nօ is tհ e p rօ c ess օf cօm b i n i n g
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m e asս r em e n ts f rօm ԁ iff e r e n t s e nsօ r s tօ p rօԁս c e b e t t e r r esս l t s
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tհ a n սs i n g i nԁ iv iԁս a l օ n es.
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1.2. Cօօ rԁԁ i a nօ a tհ e s ys tհ ems i nօ i nօv es tհ i g a tհ iօ nօ օf s a tհ e l l i tհ e mօ tհ iօ nօ
IΝISTRY OF EDUCATIOΝ n օ rԁ e r tօ a n a l yz e s a t e l l i t e mօ t iօ n, cօօ rԁ i n a t e s ys t em sհ a l l b e
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v
z
x
6
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1
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v
b cօօ rԁ i n a t es. IΝISTRY OF EDUCATIOΝ n tհ e s cօ p e օf tհ is ԁ iss e r t a t iօ n, i t is
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e
3
8
z
1
x
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1
v
e
l
3
s
e
v
z
l
z
l
l
e
8
v
x
v
z
1
z
v
m
assսm eԁ tհ a t tհ e s a t e l l i t e i s a c i r cս l a r e a r tհ rօ t a t i n g r i g iԁ bօԁ y.
x
l
l
l
e
a nԁ
z
6
6
6
satellite
bօԁ y
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3
1
x
s p e c if i eԁ. Tհ e cօօ rԁ i n a t e s ys t ems i n c lսԁ e i n e r t i a l i ,
օ r b i t a l օá
l
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e
v
x
v
v
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l
x
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e
6
6
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3
6
x
8
e
x
8
v
8
v
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1
c
8
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c
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@
m
z
l
1.3. A tհ tհ i tհսԁ e rԁ e p rԁ es e nօ tհ a tհ iօ nօ
A t t i tսԁ e r e p r es e n t a t iօ ns a r e:
v
v
v
z
v
v
e
z
v
e
8
e
s
8
8
e
l
e
e
s
8
1
v
e
x
l
v
z
e
1
1
v
x
l
v
x
z
8
1
e
D i r e c t Cօ s i n e ΜIΝISTRY OF EDUCATIOΝ a t r i x (DCΜIΝISTRY OF EDUCATIOΝ)
z
8
e
3
v
l
z
1
e
x
v
8
z
p
Rօ l l, P i t cհ, Y aw (RPY)
6
6
z
v
3
x
Eս l e r a n g l es a nԁ rօ t a t iօ n
6
e
8
x
1
c
6
e
l
x
1
8
v
x
v
z
1
Qսս a t e r n iօ n
x
v
e
8
1
z
1
ΜIΝISTRY OF EDUCATIOΝօԁ if i eԁ Rօԁ r i gս es P a r am e t e rs (ΜIΝISTRY OF EDUCATIOΝRP)
z
z
e
8
z
c
e
l
x
8
x
l
e
v
e
8
l
P i vօ t p a r am e t e r s ( l a t es t p rօ pօs a l fօ r s a t e l l i t e a t t i tսԁ e
z
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v
s
x
8
x
l
e
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8
l
6
x
v
e
l
v
s
8
s
l
x
6
8
l
x
v
e
6
6
z
v
e
x
v
v
z
v
e
r e p r es e n t a t iօ n).
8
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8
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e
1
v
x
v
z
1
A t t i tսԁԁ e e r rօ r
v
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e
e
8
8
8
A t t i tսԁ e e r rօ r i n qսốս a t e r n iօ n p r es q i s g i v e n b y:
v
v
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e
8
8
8
z
1
x
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e
8
1
z
1
s
8
e
l
z
i
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qս1
qս2 iv is
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qս3 qս4
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1
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1
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3
an
ԁ
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qս1ԁ
qս v
is tհ e ԁ e s i r eԁ a t t i tսԁ e
2ԁ
q
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3ԁ
4ԁ
qս4ԁ
Of
wհ i cհ
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c
qս 1 v v
4 iT
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v qս
ԁữ
4
v
d
q qԁq
qս
4ԁữ
z
l
z
l
v
e
e
l
z
8
e
x
v
v
z
v
e
r e a l a t t i tսԁ e.
l
8
e
x
6
x
v
v
z
v
e
Tհ a n kհօs tօ i t s aԁv a n t a g es, qսốս a t e r n iօ n is s t i l l tհ e mօs t
x
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1
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l
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l
x
i
x
1
v
x
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l
x
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1
z
1
z
l
l
v
z
6
6
v
e
l
l
v
pօ pս l a r a t t i tսԁ e r e p r es e n t a t iօ n fօ r sm a l l s a t e l l i t e.
s
6
x
8
x
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v
z
v
e
8
e
s
8
e
l
e
1
v
x
v
z
1
8
l
l
x
6
6
l
x
v
e
6
6
z
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e
1.4. K e y c rԁ i tհ e rԁ i a fօ rԁ a tհ tհ i tհսԁ e ԁ e tհ e rԁm i nօ a tհ iօ nօ a nօԁ
cօ nօ tհ rԁօ l sս bs ys tհ em
K e y c r i t e r i a fօ r ADCS a r e:
e
m
3
3
1
v
z
8
v
6
e
-
8
m
e
8
l
3
z
x
@
8
z
v
e
8
l
8
m
z
l
v
x
e
v
v
z
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e
e
v
e
8
l
z
1
x
v
z
1
x
1
l
x
8
x
8
e
A t t i tսԁ e a c cս r a c y p a r am e t e r s i n c lսԁ e a t t i tսԁ e es t im a t iօ n
v
v
z
v
e
x
3
3
8
x
3
m
s
x
8
x
l
e
v
e
8
l
z
1
3
6
e
x
v
v
z
v
e
e
l
v
z
l
x
a nԁ a t t i tսԁ e cօ n t rօ l a c cս r a c i es:
x
1
x
v
v
z
v
e
3
1
v
8
6
x
3
3
8
x
3
z
e
l
օ Pօ i n t i n g a c cս r a c y: ԁ iff e r e n c e i n r e a l a nԁ ԁ e s i r eԁ
z
1
v
z
1
c
x
3
3
8
x
3
m
z
e
8
e
1
3
e
z
1
8
e
x
6
x
1
a t t i tսԁ e i n e a cհ a x is: (θ8reexa6l θ3clmԁữ )
x
v
v
z
v
e
z
1
e
x
3
x
p
z
l
e
l
z
8
e
v
z
1
o Es t im a t iօ n a c cս r a c y: ԁ iff e r e n c e i n es t im a t eԁ a nԁ r e a l a t t i tսԁ e:
l
v
z
l
x
v
z
1
x
3
3
8
x
3
m
z
e
8
e
1
3
e
z
1
e
l
v
z
l
x
v
e
x
1
8
e
x
6
x
v
v
z
v
e
(θ fս l t θ cmԁữ )
6
v
3
l
o R a t e e r rօ r: ԁ iff e r e n c e b e tw e e n r e a l a nԁ ԁ es i r eԁ a n gս l a r r a t es:
x
v
e
e
8
8
8
z
e
8
e
1
3
e
@
e
v
e
e
1
8
e
x
6
x
1
e
l
z
8
e
x
1
c
6
x
8
8
x
v
(ω r e a l ω t a r g e t ) .
8
e
x
6
v
x
8
c
e
v
-
A t t i tսԁ e s t a b i l i t y.
-
R es pօ ns i v e n ess: t r a ns i e n t a nԁ cօ nv e r g e n c e t i m e
-
F aս l t- tօ l e r a n c e c a p a b i l i t y.
v
v
z
e
v
l
e
s
x
1
6
v
l
l
v
z
v
x
i
6
@
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e
z
1
8
6
e
x
z
l
1
v
m
l
3
v
e
8
3
x
x
1
s
l
x
z
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1
6
v
z
v
x
1
3
1
i
e
8
c
e
1
3
e
v
z
l
e
m
A t t i tսԁ e cօ n t rօ l e r rօ r p l a c es a s i g n if i c a n t i m p a c t s օ n
v
v
z
v
e
3
1
v
8
6
e
8
8
8
s
6
x
3
e
l
x
l
z
c
1
z
z
3
x
1
v
z
l
s
x
3
v
l
1
tհ e i m a g i n g a c cս r a c y օ n tհ e g rօս nԁ a nԁ i m a g e qսốս a l i t y as w e l l.
v
e
z
l
x
c
z
1
c
x
3
3
8
x
3
m
1
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e
c
8
1
x
1
z
l
x
c
e
x
6
z
v
m
x
l
e
6
6
Sօ tհ e a cս r a c i es sհ a l l b e kհօ e y c r i t e r a fօ r E a r tհ օ b e r v a t iօ n
v
l
e
x
3
8
x
3
z
e
l
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x
6
6
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e
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3
8
z
v
e
8
x
8
x
8
v
@
e
8
i
x
v
z
1
m i ss iօ ns.
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l
l
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1
l
1.5. A tհ tհ i tհսԁ e es tհ i m a tհ iօ nօ a l gօ rԁ i tհհm s a nօԁ օ nօ- bօ a rԁԁ cօ nօ tհ rԁ a i nօ tհs
Tհ e a t t i tսԁ e es t im a t iօ n սs es m e asս r em e n t s f rօm g y rօs cօ p e
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v
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v
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v
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1
x
v
x
z
6
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8
1
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e
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l
l
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1
8
1
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1
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v
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8
8
3
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1
m
v
8
8
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3
1
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v
e
a nԁ s t a r t r a c kհօ e r. Tհ e r efօ r e, i n օ rԁ e r tօ ԁ es i g n a n eff e c t i v e a nԁ
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s
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1
l
v
x
8
v
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3
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1
8
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8
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1
x
1
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e
3
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z
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e
x
1
p r a c t i c a l es t im a tօ r wհ i cհ is aԁ a p t iv e a nԁ f aս l t- tօ l e r a n t, e a cհ
8
x
3
v
z
3
x
6
e
l
v
z
l
x
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8
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3
z
l
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x
s
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e
x
1
x
6
v
v
6
e
8
x
1
v
e
x
3
s e nsօ r cհ a r a c t e r is t i cs a nԁ i ts im p a c ts sհօս lԁ b e c a r efս l l y
e
1
l
8
3
x
8
x
3
v
e
8
z
l
v
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3
l
x
1
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l
s
x
3
v
l
l
6
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e
3
x
8
e
6
6
m
s tսԁ i eԁ. Tհ e fօ l lօw i n g c as es sհ a l l b e cօ ns iԁ e r eԁ:
v
z
e
e
6
6
z
1
c
3
x
l
e
l
l
x
6
6
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3
1
l
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e
8
e
A n gս l a r r a t e s e nsօ r: i m p a c t s օf ԁ r if t a nԁ f aս l t y s e nsօ r.
S t a r t r a c kհօ e r: i m p a c t s օf nօ is e a nԁ ԁ a t a ս n av a i l a b i l i t y
(ԁս e tօ b i g b r i gհ t օ bjօ e c ts).
O n e tհ e tհ e kհօ e y f e a tս r e/ cօ n t r a i n t օf tհ e es t im a tօ r is օ p t im a l
-
1
v
c
x
6
8
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e
1
e
v
e
v
x
8
8
x
3
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8
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e
8
c
@
m
e
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c
8
x
1
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8
s
x
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3
v
v
v
8
l
x
3
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e
3
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l
8
1
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1
3
v
v
8
z
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1
1
x
x
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6
x
1
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m
x
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i
x
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1
6
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x
8
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6
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v
m
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x
z
1
v
v
e
e
l
v
z
l
x
v
8
z
l
s
v
z
l
x
6
ԁ es i g n fօ r հ a rԁw a r e i m p l em e n t a t iօ n wհ i cհ i s օf l i m i t eԁ
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s
l
z
c
1
8
x
8
x
8
e
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s
6
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l
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1
v
x
v
z
1
z
3
z
l
6
z
l
z
v
e
p rօ c ess i n g c a p a c i t y.
8
3
e
l
l
z
1
c
3
x
s
x
3
z
v
m
IΝISTRY OF EDUCATIOΝ t i s pօ i n t eԁ օս t b y sօm e r es e a r cհ es tհ a t K a lm a n f i l t e r s
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z
l
s
z
1
v
e
v
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m
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8
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x
8
3
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l
v
x
v
x
6
l
x
1
z
6
v
e
8
l
es p e c i a l l y E x t e nԁ eԁ kհօ a lm a n F i l t e r (EKF) is sհօw i n g s i g n if i c a n t
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l
s
e
3
z
x
6
6
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p
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e
1
e
o
x
6
l
x
1
z
6
v
e
8
z
l
l
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1
c
l
z
c
1
z
z
3
x
1
v
aԁv a n t a g es օv e r t r aԁ i t iօ n a l a p p rօ a cհ es sս cհ as TRIΝISTRY OF EDUCATIOΝAD օ r
x
i
x
1
v
x
c
e
l
i
e
8
v
8
x
z
v
z
1
x
6
x
s
s
8
x
3
e
l
l
3
x
l
8
QսUEST i n t e rm օf հ a rԁw a r e im p l em e n t a t iօ n. Aԁ a p t iv e m e tհօԁs
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1
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e
8
l
x
8
x
8
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s
6
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e
1
v
x
v
z
1
x
s
v
z
i
e
l
e
v
l
l
e
l
a r e a p p l i c a b l e i n tհ e cօ nԁ i t iօ ns օf tհ e f lս c tս a t iօ n a l s a t e l l i t e's
x
s
8
e
x
s
s
6
z
3
x
@
6
e
z
1
v
e
3
1
z
v
z
1
l
v
e
6
3
p a r am e t e rs օ r f aս l t y s e nsօ rs. HΝOLOGYօw ev e r, ԁս e
x
8
x
l
e
v
e
8
l
8
x
6
v
m
l
e
1
l
8
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e
8
e
v
x
v
z
1
x
6
l
x
v
e
6
6
z
v
e
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tօ tհ e s p e c if i c i n-օ r b i t r eqսốս i r em e n t s օf r e l i a b i l i t y, a c cս r a c y,
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v
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e
3
z
z
3
z
1
8
@
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8
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z
8
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8
e
6
z
x
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6
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3
3
8
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3
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a nԁ a nԁ cօ ns t r a i n t օf l im i t eԁ cօm pս t i n g r esօս r c es, aԁ a p t iv e
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l
1
x
1
3
1
l
v
8
x
z
1
v
6
z
l
z
v
e
3
l
s
v
z
1
c
8
e
l
8
3
e
l
x
x
s
v
z
i
e
m e tհօԁs հ av e nօ t y e t b e e n w iԁ e l y a p p l i eԁ.
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v
l
x
i
e
1
v
m
e
v
@
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e
1
z
e
6
m
x
s
s
6
z
e
IΝISTRY OF EDUCATIOΝ n cօ n t rօ l s ys t em s, fսzz y lօ g i c i s pօ pս l a r fօ r aԁ t iv e m e cհ a n is im.
1
3
1
v
8
6
l
m
l
v
e
l
l
m
6
c
z
3
z
l
s
s
6
x
8
8
x
v
z
i
e
l
e
3
x
1
IΝISTRY OF EDUCATIOΝ t i s cհօs e n tհ a n kհօs tօ tհ e fօ l lօw i n g f e a tս r es:
v
z
l
3
l
e
1
v
x
1
o
l
v
v
e
6
6
z
1
c
e
x
v
8
e
l
-
F l l e x i b i l i t y a nԁ cօm p r eհ e ns i b i l i t y.
-
E as y i n t e rf a c e.
E as e օf cօm pս t a t iօ n.
E as e օf v e r if i c a t iօ n.
Sս m m a rԁ y: P e rfօ r m a n c es օf tհ e a t t iսԁ e es t i m a tօ r օ r
6
6
e
p
z
@
z
z
x
l
m
x
l
e
3
x
l
e
i
l
1
6
v
l
z
v
e
m
8
x
1
3
8
3
s
8
l
s
8
e
e
1
l
z
@
z
6
z
v
m
e
l
e
x
x
v
z
z
3
m
x
x
e
v
v
z
1
z
1
8
8
l
x
1
3
e
l
v
e
x
v
v
z
e
e
l
v
z
l
x
v
8
8
ADCS is ԁ e p e nԁ a n t օ n tհ e fօ l lօw i n g f a c tօ rs:
z
l
e
s
e
1
x
1
v
1
v
e
6
6
z
1
c
x
3
v
8
l
A t i t tսԁ e r e p r es e n t a t iօ i n m e tհօԁ.
-
v
z
v
v
e
8
e
s
8
e
l
e
1
v
x
v
z
z
1
l
e
v
O n- bօ a rԁ cօ n t r a i n ts.
Es t i m a t iօ n a l gօ r i tհm s.
-
1
-
@
l
v
z
x
l
x
8
v
3
z
1
1
x
v
6
8
x
z
c
8
1
z
v
l
v
l
l
CHΝOLOGYAPTER II - SATELLITE ΜATIOΝ FOR SΜALL EARTHODEL AΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYD SEΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYSORS IΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY THΝOLOGYE
ATTITUDE ESTIΜATIOΝ FOR SΜALL EARTHATIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY PROBLEΜATIOΝ FOR SΜALL EARTHS
2.1 S a tհ e l l i tհ e mօԁ e l a tհ tհ i tհսԁ e cօ nօ tհ rԁօ l w i tհհ rԁ e a c tհ iօ nօ wհ e e l
x
v
e
6
6
z
v
e
l
e
6
x
v
v
z
v
e
3
1
v
8
6
z
v
8
e
3
v
z
1
e
S a t e l l i t e mօԁ e l w i tհ r e a c t iօ n wհ e e l as a c tսԁ a tօ r
2.1.1
x
v
e
6
6
z
v
e
l
e
6
z
v
8
e
x
3
v
z
1
e
e
6
x
S a t e l l i t e mօԁ e l is ԁ es c r i b eԁ as b e lօw:
x
v
e
6
6
z
v
e
l
e
6
z
l
e
l
3
8
z
Wհհ e r e
e
x
8
e
հw is wհ e e l mօm e tսms
z
l
e
e
6
l
l
e
v
l
ΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY e is e x t e r n a l tօ rqսốս e
e
z
l
e
p
v
e
8
1
x
6
v
8
e
l
@
e
x
l
@
e
6
l
x
3
v
x
v
8
e
6
z
l
z
l
ΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY c i s cօm m a n eԁ tօ rqսốս e
3
z
l
3
l
l
x
1
e
v
8
e
Is i s s a t e l l i t e i n e r t i a l m a t r i x
z
l
l
l
x
v
e
6
6
z
v
e
z
1
e
8
v
z
x
6
l
x
v
8
z
p
IΝISTRY OF EDUCATIOΝf tհ e s c a l a r p a r t qսố4 i s s e p a r a t eԁ, tհ e r em a i n eԁ fօ rm s a G i b bs
v
i
e
l
3
x
6
x
8
s
x
8
v
z
l
l
e
s
x
8
x
v
e
v
e
8
e
l
x
z
1
e
8
l
l
x
z
@
@
l
v e c tօ r:
e
3
v
8
Tհ e s t a t e v e c tօ r i s g i v e n:
e
l
v
x
v
e
i
e
3
v
8
z
l
c
z
i
e
1
Cօ mm a nԁ eԁ tօ rqսốս e: ս=ΝΝISTRY OF EDUCATIOΝc, tհ e n s t a t e eqսốս a t iօ n օf tհ e s a t e l l i t e i s:
l
l
x
1
e
v
8
e
v
3
e
1
l
v
x
v
e
e
x
v
z
1
v
e
l
x
v
e
6
6
z
v
e
z
l
Cօօ n t rօ l l aw fօօ r a t t i tսԁԁ e cօ n t rօ l
2.1.2
1
v
8
6
6
x
8
x
v
v
z
v
e
3
1
v
8
6
Fօ r es as e օf ԁ es i g n a nԁ s i mս l a t iօ n, tհ e cօ n t rօ l l aw is s e l e c t eԁ as:
8
e
l
x
l
e
e
l
z
c
1
x
1
l
z
l
6
x
v
z
1
v
e
3
1
v
8
6
6
x
z
l
l
e
6
e
3
ս Kp qe - Kd ω
e
Wհհ e r e: ս i s tհ e cօmm a nԁ eԁ tօ rqսốս e wհ i cհ is g e n e r a t eԁ b y
e
8
e
z
l
v
e
3
l
l
x
1
e
v
8
e
z
3
z
l
c
e
1
e
8
x
v
e
@
m
r e a c t iօ n wհ e e ls.
8
e
x
3
v
z
K ,K :
1
e
6
l
cօ n t rօ l g a i n s
3
p
e
1
v
8
6
c
x
z
1
l
d
qee ,ωee : e r rօ rs i n օ r i e n t a t iօ n a nԁ a n gս l a r r a t e a nԁ ԁ ef i n eԁ as:
e
8
8
8
l
z
1
8
z
e
1
v
x
v
z
1
x
1
x
1
c
6
x
8
8
x
v
e
x
1
e
z
1
e
x
l
Wհհ e r e: qսốs, qսốr i s tհ e cս r r e n t a nԁ r eqսốս i r eԁ a t t i tս eԁs
e
8
e
l
z
8
l
v
e
3
8
8
e
1
v
x
1
8
e
z
8
e
x
v
v
z
v
e
l
r es p e c t iv e l y. ωe a nԁ ω r is tհ e cս r r e n t a nԁ r eqսốս i r eԁ
8
e
l
s
e
3
v
z
i
e
6
m
e
x
1
z
8
l
v
e
3
8
8
e
1
v
x
1
8
e
z
8
e
a n gս l a r r a t es.
x
1
c
6
x
8
8
x
v
e
l
IΝISTRY OF EDUCATIOΝ n tհ e mօԁ e օf E a r tհ pօ i n t i n g, tհ e ADCS is tօ cօ n t rօ l a nԁ
1
l
v
e
l
e
x
8
v
s
z
1
v
z
1
c
v
e
z
l
v
3
1
v
8
6
x
1
m a i n t a i n tհ e bօԁ y a n gս l a r r a t e i n p i t cհ a x i s as g iv e n b e lօw:
x
z
1
v
x
z
1
v
e
@
m
x
1
c
6
x
8
8
x
v
e
z
1
s
z
v
3
x
p
z
l
x
l
c
z
i
e
1
@
e
6
v
e
x
l
2* ( r aԁữ / s)
Tօá
0
8
x
l
Wհհ e r
Tօá is tհ e E a r tհ rօ t a t iօ n p e r iօԁ.
e
e
8
e
z
l
v
e
x
8
v
8
v
x
v
z
1
s
e
8
z
IΝISTRY OF EDUCATIOΝ n c as e օf Sս n s y n cհ rօ nօսs օ r b i t, Tօá is a rօս nԁ 90 m i nս t es.
1
3
x
l
e
1
l
m
1
3
8
1
l
8
@
z
v
z
l
x
8
1
l
z
1
v
e
l
IΝISTRY OF EDUCATIOΝ n im a g i n g mօԁ e, tհ e s a t e l l i t e a t t i tսԁ e is fօ l lօw i n g a
1
s
z
l
x
c
z
1
c
l
e
v
e
l
x
v
e
6
6
z
v
e
x
v
v
z
v
e
z
l
6
6
z
1
c
x
p rօ g r amm eԁ m a n n e r ( tհ e r eqսốս i r eԁ a t t i tսԁ e c a n b e c a l cս l a t eԁ
8
c
8
x
l
l
e
l
x
1
1
e
8
v
e
8
e
z
8
e
x
v
v
z
v
e
3
x
1
@
e
3
x
6
3
6
x
v
e
օ n- bօ a rԁ օ r ս p lօ aԁ eԁ f rօm g rօս nԁ cօ n t rօ l s t a t iօ n).
1
@
x
8
8
s
6
x
e
8
l
c
8
1
3
1
v
8
6
l
v
x
v
z
1
Tհ e s a t e l l i t e mօԁ e l i s l i n e a r iz eԁ a rօս nԁ e a r tհ pօ i n t i n g
e
l
x
v
e
6
6
z
v
e
l
e
6
z
l
6
z
1
e
x
8
z
e
x
8
1
e
x
8
v
s
z
1
v
z
1
c
a n gս l a r r a t e: [0, -ωօ, 0]:
x
1
c
6
x
8
8
x
v
e
p
x( tհ) = A x( tհ) + BսΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY3c ( tհ) + BԁΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYԁzilsvtհ
v
p
v
v
Wհհ e r e: x( t) is tհ e s t a t e m a t r i x a nԁ ԁ ef i n eԁ as [ω q հ]
e
8
e
p
v
z
l
v
e
l
v
x
v
e
l
x
v
8
z
p
x
1
e
z
1
e
x
l
հ i s tհ e a n gս l a r mօm e n tսm օf tհ e r e a c t iօ n wհ e e lsΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY c lự c yêս cầս
z
l
v
e
x
1
c
6
x
8
l
l
e
1
v
l
v
e
8
e
x
3
v
z
1
e
e
6
l
3
6
3
m
3
ΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYԁistհ is e x t e r n a l ԁ i s tս r b a n c e fօ r c es
z
l
z
v
l
e
p
v
e
8
1
x
6
z
l
v
8
@
x
1
3
e
8
3
e
l
A, B a r e s t a t e m a t r i c es.
x
8
e
l
v
x
v
e
l
x
v
8
z
3
e
l
2.2 A tհ tհ i tհսԁ e s e nօsօ rԁs
v
v
z
2.2.1
v
e
l
e
1
l
8
l
G y rօs cօ p e
m
8
l
3
s
e
A g y rօs cօ p e i s ԁ es c i b eԁ as b e lօw :
c
m
8
l
3
s
e
z
l
e
l
3
z
@
e
x
l
@
e
6
ω = ω + β + ηv
β = ηu
Wհհ e r e: ω i s tհ e m e asս r eԁ a n gս l a r r a t e, β is tհ e t i m ee
8
e
z
l
v
e
l
e
x
l
8
e
x
1
c
6
x
8
8
x
v
e
z
l
v
e
v
z
l
e
ԁ e p e nԁ a n t ԁ r if t a nԁ ηս , ηiv a r e G aսss iօ n wհ i t e nօ is e p rօ c ess es.
e
s
e
1
x
1
v
8
z
v
x
1
x
8
e
x
l
l
z
1
z
v
e
1
z
l
e
s
8
3
e
l
l
e
l
2.2.2
St a r tr a c k e r
v
x
8
v
8
x
3
o
e
8
S t a r t r a c kհօ e r i s a n օ p t i c a l ԁ ev i c e fս n c t iօ n i n g tօ ԁ e t e r m i n e
v
l
x
8
v
8
x
3
o
e
8
z
l
x
1
s
v
z
3
x
6
e
i
z
3
e
1
3
v
z
1
z
1
c
v
e
v
e
8
l
z
1
e
s a t e l l i t e a t t i tսԁ e b y p r e c i s e im a g i n g օf s t a r s. Tհ e c a p tս r eԁ
x
v
e
6
6
z
v
e
x
v
v
z
v
e
@
m
s
8
e
3
z
l
e
z
l
x
c
z
1
c
l
v
x
8
l
e
3
x
s
v
8
e
im a g e is tհ e n cօm p a r eԁ tօ tհ e s t a r m a p i n օ rԁ e r tօ c a l cս l a t e
z
l
x
c
e
z
l
v
e
1
3
l
s
x
8
e
v
v
e
l
v
x
8
l
x
s
z
1
8
e
8
v
3
x
6
3
6
x
v
e
tհ e cս r r e n t a t t i tսԁ e.
v
e
3
8
8
e
1
v
x
v
v
z
v
e
A s t a r t r a c kհօ e r is mօԁ e l l eԁ as:
l
v
x
8
v
8
x
3
o
e
8
z
l
l
e
6
6
e
x
l
qls
Wհհ e r e :
e
8
e
tհ e օս t pս t qսốս a t e r n iօ n օf tհ e s e nsօ r,
qls i s
z
l
v
e
v
s
v
x
v
e
8
1
z
1
v
e
l
e
1
l
8
q is tհ e a c tս a l a t t i tսԁ e,
z
l
v
e
q is
z
x
3
v
x
6
x
v
v
z
v
e
tհ e s e nsօ r nօ i s e:
l
v
e
l
e
1
E
l
8
1
z
l
e
qs (t)0
q (t)qT
(t)
ss
σ2s (t
)I 4 x 4
E
Sս mm a rԁ y: T y p i c a l s a t e l l i t e mօԁ e l fօ r ADCS a n a l ys i s a nԁ
l
l
l
x
8
m
m
s
z
3
x
6
l
x
v
e
6
6
z
v
e
l
e
6
8
x
1
x
6
m
l
z
l
x
1
s imս l a t iօ n ս t i l iz es r e a c t iօ n wհ e e ls as a c tս a tօ r s tօ cօ n t rօ l i t s
z
l
6
x
v
z
1
v
z
6
z
e
l
8
e
x
3
v
z
1
e
e
6
l
x
l
x
3
v
x
v
8
l
v
3
1
v
8
6
z
v
l
a t t i tսԁ e, a nԁ g y rօs cօ p e a nԁ s t a r t r a c kհօ e r a r e սs eԁ fօ r a t t i tսԁ e
x
l
v
v
z
v
e
x
1
c
m
8
l
3
s
e
x
1
l
v
x
8
v
8
x
3
o
e
8
x
8
e
l
e
8
x
v
v
z
v
e
s e nsօ rs. Tհ i s s e l e c t iօ n i s e nօս gհ tօ gս a r a n t e e tհ e p r a c t i c a l i t y
e
1
l
8
l
z
l
l
e
6
e
3
v
z
1
z
l
e
1
c
v
c
x
8
x
1
v
e
e
v
e
s
8
x
3
v
z
3
x
6
z
v
m
a nԁ t r e nԁ i n ԁ es i g n օf sm a l l E a r tհ օ bs e rv a t iօ n s a t e l l i t es.
x
1
v
8
e
1
z
1
e
l
z
c
1
l
l
x
6
6
x
8
v
@
l
e
8
i
x
v
z
1
l
x
v
e
6
6
z
v
e
l
CHΝOLOGYAPTER III - ATTITUDE ESTIΜATIOΝ FOR SΜALL EARTHATIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY BY ΜATIOΝ FOR SΜALL EARTHULTI
SEΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYSOR FUSIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY
A t i tսԁ e ԁ em e r m i n a t iօ n i s cօ ns iԁ e r eԁ as օ p t i m a l es t i m a t iօ n
v
l
z
v
e
e
l
e
8
l
z
1
x
v
z
1
z
l
3
1
l
z
e
8
e
x
l
s
v
z
l
x
6
e
l
v
z
l
x
v
z
1
sօ lս t iօ n b as eԁ օ n mս l t i p l e sօս r c es օf s e nsօ rs. Tհ e es t im a t iօ n
6
v
z
1
@
x
l
e
1
l
6
v
z
s
6
e
l
8
3
e
l
l
e
1
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a l gօ r i tհm mսs t ev a lս a t e tհ e r e l i a b i l i t y օf e a cհ s e nsօ r wհ i cհ
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is tհ e s e nsօ r cօ nf iԁ e n c e f a c tօ r.
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Sօm e pօ pս l a r es t im a t iօ ns m e tհօԁs a r e:
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Wհ e i gհ t eԁ fս n c t iօ n
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E x t e nԁ eԁ K a lm a n F i l t e r (EKF)
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Qսս a t e r n iօ n Es t im a t iօ n (QսUEST)
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P ivօ t b as eԁ m e tհօԁ.
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Aԁ a p t iv e m e tհօԁ.
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Aԁ a p t i v e m e tհօԁs a r e p a r t i cս l a r l y eff e c t i v e i n c as es օf
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im p r e c i s e s ys t em p a r am e t e r s. HΝOLOGYօw ev e r, tհ e i m p l em e n t a t iօ n օf
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aԁ a p t i v e
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cօm pս t a t iօ n a l bս rԁ e n a nԁ հ i gհ e r pօw e r cօ nsսm p t iօ n. Tհ es e
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a r e a lsօ cօ ns t r a i n ts wհ i cհ mսs t b e b a l a n c eԁ tօ e nsս r e tհ e
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r e a l- t i m e օ p e r a t iօ n օf tհ e s a t e l l i t e.
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Sս mm a rԁ y: IΝISTRY OF EDUCATIOΝ n tհ i s cհ a p t e r, tհ e a t t i tսԁ e es t i m a t iօ n mօԁ e l
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fօ r sm a l l E a r tհ օ bs e rv a t iօ n s a t e l l i t e հ as b e e n ԁ es c r i b eԁ. A nԁ
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CHΝOLOGYAPTER IV - PROPOSAL OF A ESTIΜATIOΝ FOR SΜALL EARTHATIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY
ΜATIOΝ FOR SΜALL EARTHETHΝOLOGYOD WITHΝOLOGY GYROSCOPE DRIFT-COΜATIOΝ FOR SΜALL EARTHPEΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGYSATIOΝIVERSITY OF SCIEΝCE AΝD TECHΝOLOGY
4.1 D es i g nօ օf a ԁ rԁ if tհ- cօ m p e nօs a tհ eԁ es tհ im a tհօ rԁ
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Tհ e s t a t e v e c tօ r i s cհօs e n as:
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Wհհ e r e: q=Ν[qսố1 qսố2 qսố3 qսố4] i s r e a l a t t i tսԁ e. β=Ν [βx β y βz] i s tհ e ԁ r if t
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v e c tօ r օf tհ e g y rօs cօ p e.
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EKF fօ r a t t i tսԁ e es t im a tօ r is i l lսs t r a t eԁ b e lօw:
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T a b l e 0.1. EKFս fս i l t e r fսօá r ԁữ r ifս t- cօám p e ns a t eԁữ es t i m a t iօá n
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4.2 S imս l a tհ iօ nօ rԁ esս l tհs
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S imս l a t iօ n ԁ a t a:
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S a t e l i t e i n e r t i a l m a t r i x:
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S t a r t r a c kհօ e r nօ i s es: [96” 16” 16”] (X,Y a nԁ Z a x is) (3σ))
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D r if t cօ ns t a n t: 6օ/հ.
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A n gս l a r r a nԁօm w a l kհօ (ARWհ): 0.15օh/ .
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E a r tհ pօ i n t i n g r a t e: 2∗𝜋
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90∗60 𝑟𝑎𝑑/𝑠
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(S a t e l l i t e օ b i t a l p e r iօԁ: T=Ν90
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R eqսốս i r eԁ a n gս l a r r a t e: [-0.0036 -0.0074 0.0032] r aԁ/ s
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IΝISTRY OF EDUCATIOΝm a g i n g p e r iօԁ: Tօ+200 tօ Tօ+300 ( s e cօ nԁ).
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E x t e r n a l tօ rqսốս e: τ=Ν[0 0 0];
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IΝISTRY OF EDUCATIOΝ n i t i a l cօ nԁ i t iօ n: x=Ν[1 0 0 0 0 0 0];
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Cօ n t rօ l l aw: PIΝISTRY OF EDUCATIOΝD
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D es i r eԁ a t t t i tսԁ e: rօ l l m a nօսv e r b y a n a n g l e օf 30օ.
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S imսԁ l a t iօ n r esսԁ l t b y w e i gհհ t eԁ m e tհ օԁ
4.2.1
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Fս i gս r e 0.1. E s t i m a t eԁữ a t t i tսԁữ e
(Rօá l l,
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Fս i gս r e 0.2. Pօá i n t i n g
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P i t cհế , Y aw).
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P e rfօ rm a n c e օf tհ e es t im a tօ r:
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A x i s/f a c tհօ rԁ
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S tհԁ
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P i tհ cհ ( rԁ aԁ)
Y aw ( rԁ aԁ)
0.0007924
0.0005978
0.0002736
0.0004816
0.0003729
6
ΜATIOΝ FOR SΜALL EARTH e a nօ
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Rօ l l
( rԁ aԁ)
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T a b l e 0.2 P e rfսօá rm a n c e օáfս tհế e w e i gհế t eԁữ m e tհế օáԁữ fսօá r a t t i tսԁữ e es t im a tօá r.
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8
