EE 570: Locatio ad Naigatio: Thory & Practic Naigatio Ssors ad INS Mchaizatio NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 1 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio CASE 3: Na Fram Mchaizatio Dtrmi th Positio, Vlocity, ad Attitud of th Body fram with rspct to th Naigatio Fram Dtrmi our PVA wrt th Na fram Positio: Typically dscrid i curiliar coordiats: L, λ, h T Vlocity: Typically th locity of th ody wrt th arth fram rsold i aigatio fram coords: Attitud: Typically th oritatio of th ody dscrid i th a fram: C NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 2 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio Dtrmi our PVA wrt th Na fram Na Fram? Irtial Fram? i i z z i y y z x x i z? y y x x ECEF Fram Body Fram Body & Na fram ha th sam origi Irtial & Earth fram ha th sam origi NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 3 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio 1. Attitud Updat: Mthod A Not that: Now C C???? i ii C i i i i C C C i i C i i C T Sk C C Sk C C Sk Sk C C S xt slid Masurd y th gyro C i i * * * 0 cos( L ) * * * 0 i 0 cos( L ) 0 si( L ) i si( L ) T NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 4 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio C C Last trm: Ω cos( L) -L -si( L ), E RE h, N - RN h ta( L), E - RE h T C C = Sk ω Courtsy of Mathmatica y 0 si( L ) -L, -si( L, ) z 0 -cos( L ) L cos( L ) 0, x C ( ) C ( ) tc From hadout #2 i i, N RN h L, E Cos( L ) RE h h D, C ( ) I t C ( ) t NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 5 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio 1. Attitud Updat: Mthod B Not that: Ω = Ω i Ω i Ω Hc, C (+) = C ( ) Ω Δt C C C C i i T Sk C C Sk C i C Sk i Sk Sk C i 2 K C( ) C( ) I si( ) K 1 cos( ) C t K i i NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 6 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio 1. Attitud Updat: High Fidlity ˆ t k 2 K C( ) C( ) I si( ) K 1cos( ) i i i Ci C Lowr Fidlity i i C ( ) C ( ) I t C ( ) t NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 7 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio 2. Spcific Forc Trasformatio: Simply coordiatiz th spcific forc f C ( ) f i i NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 8 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio 3. Vlocity Updat Not that: = C a f g 2 i i C C C C f g 2 f g 2 i i i i f g 2C i i f g 2 C i i T Sk C C Sk C C Sk Sk C C Fially, ( ) ( ) t fi g 2 i ( ) NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 9 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio 4. Positio Updat Rcallig th rlatioship tw ad th curiliar coordiats (s hadout #2), N ( ), N L( ) L( ) t RN h RN h L, E Cos( L ) RE h h D,, E ( ) ( ) ( ) t RE h cos( L) h( ) h( ) t, D( ) NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 10 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio i i C ( ) C ( ) I t C ( ) t i f i f C ( ) f i ( ) ( ) i t fi g 2 i ( ) h( ) h( ) t, D( ), N ( ) L( ) L( ) t RN h, E ( ) ( ) ( ) t RE h cos( L) C ( ) ( ) h ( ) L ( ) ( ) 1. Attitud Updat 2. SF Trasform f i 3. Vlocity Updat Gra Modl g 3. Positio Updat C ( ) ( ) h( ), L( ), ( ) NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 11 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio I cotiuous tim otatio: Attitud: C = C Ω i Ω i + Ω Vlocity: C = f i + g Ω + 2Ω i,n Positio: L λ = R N +h,e h Cos(L ) R E +h,d NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 12 of 13
Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na Mchaizatio Comiig ito a stat-spac quatio:, N RN h L, E h Cos( L ) RE h, D 2 C f i g i C i i C NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 13 of 13