16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde er(t=e+v, cosy(t-t,) =已 en()=eH. -v, siny(t-t,)=0 (1-L)= sIn =eg. cot yeH The transformation which relates rhterrors at the nominal end time to r and t errors when h=o e4 Pe If the e defined earlier, based on integration of perturbed trajectories, measured in R, Tcoordinates, then the sensitivity matrix defined at that point is equivalent to e16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 4 of 8 3 3 3 ( ) cos ( ) ( ) ( ) sin ( ) R Rn n T T H Hn n et e v tt et e et e v tt γ γ =+ − = =− − Impact: 3 3 3 3 3 3 3 ( ) sin ( ) 0 1 ( ) sin cos ( ) sin cot ( ) Hi H n i n in H n n Ri R H n R H Ti T et e v t t tt e v v et e e v e e et e γ γ γ γ γ = − −= − = = + = + = The transformation which relates R,H,T errors at the nominal end time to R and T errors when H=0 is: 3 3 3 4 3 3 ( ) ( ) cot 1 0 cot 01 0 R i T i R H T e t e e t e e e e Pe γ γ ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ + = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ = ≡′ ′ ⎢ ⎥ ⎣ ⎦ If the s e defined earlier, based on integration of perturbed trajectories, is measured in R,T coordinates, then the sensitivity matrix defined at that point is equivalent to s 1 r e Se S PR = = Φ