EE 570: Locaton and Navgaton: Thor & Practc Navgaton Snsors and INS Mchanaton Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 1 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton CASE : ECEF Fram Mchanaton Dtrmn th Poston, Vloct, and Atttud of th Bod fram wth rspct to th Earth Fram Dtrmn our PVA wrt th ECEF fram Poston: Vctor from th orgn of th od fram to th orgn of th arth fram rsolvd n th arth fram: r Vloct: Vloct of th od fram wrt th arth fram rsolvd n th arth fram: v Atttud: Orntaton of th od fram wrt th arth fram C Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton 1. Atttud Updat: Mthod A Start wth th angular vloct??? C C C C ( ) C ( ) t C ( ) T Sk C CSk C C C C C ( ) C ( ) t CC C ( ) C ( ) I t C ( ) t? Inrtal Fram? Bod Fram ECEF Fram Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 3 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton 1. Atttud Updat: Mthod B Start wth th angular vloct C C?? Bod Fram t C ( ) C ( ) C ( ) t Inrtal Fram ECEF Fram t K 3 kˆ 0 kˆ R K ˆ ( k, ) 0 kˆ kˆ 3 1 kˆ ˆ k1 0 K C( ) I sn( ) K 1 cos( ) C( ) Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 4 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton 1. Atttud Updat: Hgh Fdlt K C( ) I sn( ) K 1 cos( ) C( ) C ˆ t k Lowr Fdlt C( ) C( ) I t C ( ) t Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 5 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton. Spcfc Forc Transformaton: Smpl coordnat th spcfc forc 3. Vloct Updat ECEF & ECI hav th sam orgn v r r Cr r r 0 f C ( ) f r C r r Bod Fram C r C r C r C v r C v Inrtal Fram ECEF Fram Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 6 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton d dt r C v C v a v r C v v C v C v v r C v r a v f g a a C v r v g f a??? a f r a f g r v ( ) v ( ) a t v ( ) f g v ( ) t Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 7 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton 4. Poston Updat B smpl numrcal ntgraton t ( ) ( ) ( ) a r r v t Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 8 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton f C( ) C( ) I t C ( ) t f C ( ) f a f g v ( ) C ( ) v ( ) 1. Atttud Updat. SF Transform f 3. Vloct Updat Grav Modl g( r ) v ( ) v ( ) a t t ( ) ( ) ( ) a r r v t r ( ) 3. Poston Updat C ( ) v ( ) r ( ) Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 9 of 10
Navgaton Snsors and INS Mchanaton Navgaton Equatons Cas : ECEF Mchanaton In contnuous tm notaton: Atttud: C = C Ω Vloct: v Poston: r = C Ω Ω = C f + g Ω v = v??? Comnng nto a stat-spac quaton: r v v C f g v C C a f g v v Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 10 of 10