By Daniel Choukroun, Yaakov Oshman, Julie Thienel, Moshe Idan

This publication offers chosen papers of the Itzhack Y. Bar-Itzhack Memorial Sympo-

sium on Estimation, Navigation, and Spacecraft keep an eye on. Itzhack Y. Bar-Itzhack,

professor Emeritus of Aerospace Engineering on the Technion – Israel Institute of

Technology, was once a well known and world-renowned member of the utilized estimation,

navigation, and spacecraft angle choice groups. He touched the lives

of many. He had a love for all times, a massive humorousness, and knowledge that he shared

freely with every body he met. To honor Professor Bar-Itzhack's reminiscence, in addition to his

numerous seminal expert achievements, a global symposium was once held

in Haifa, Israel, on October 14–17, 2012, lower than the auspices of the school of Aerospace

Engineering on the Technion and the Israeli organization for automated Control.

The e-book includes 27 chosen, revised, and edited contributed chapters written by

eminent overseas specialists. The booklet is equipped in 3 elements: (1) Estimation,

(2) Navigation and (3) Spacecraft tips, Navigation and keep watch over. the quantity was

prepared as a reference for examine scientists and working towards engineers from academy

and within the fields of estimation, navigation, and spacecraft GN&C.

**Read or Download Advances in Estimation, Navigation, and Spacecraft Control: Selected Papers of the Itzhack Y. Bar-Itzhack Memorial Symposium on Estimation, Navigation, and Spacecraft Control PDF**

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919–926 (2002) 8. : On Optimal Track-to-Track Fusion. IEEE Transactions on Aerospace and Electronic Systems 33(4), 1271–1276 (1997) 9. : Performance Evaluation of Track Fusion with Information Matrix Filter. IEEE Trans. on Aerospace and Electronic Systems 38(2), 455–466 (2002) 10. : Hierarchical Estimation. In: Proc. MIT/ONR Workshop on C3, Monterey, CA (1979) 11. : Distributed Multitarget Multisensor Tracking. In: Bar-Shalom, Y. ) Multitarget-Multisensor Tracking: Advanced Applications, ch. 8.

1) G G vT × aT ωT = G 2 ; vT G G G v ×j ω T = TG 2T vT G where wT represents the deviation of the actual behavior of the target from the constant angular turning acceleration and constant absolute value of the velocity assumptions. The state space representation in the State Dependent Coefficient Form is in three dimensions 52 I. Rusnak and L. Peled-Eitan ⎡ x⎤ ⎡ ⎢ x ⎥ ⎢ ⎢ ⎥ ⎢ ⎢ x ⎥ ⎢ ⎢ ⎥ ⎢ ⎢x⎥ ⎢ ⎢ y⎥ ⎢ ⎢ ⎥ ⎢ d ⎢ y ⎥ ⎢ = dt ⎢ y ⎥ ⎢ ⎢ ⎥ ⎢ ⎢y⎥ ⎢ ⎢z⎥ ⎢ ⎢ ⎥ ⎢ ⎢ z ⎥ ⎢ ⎢ z ⎥ ⎢ ⎢ ⎥ ⎢ ⎣⎢z⎦⎥ ⎢⎣ A 0 0 ⎡0 1 ⎢0 0 1 0 ⎢ ⎢0 0 0 1 ⎢ 3 ωy2 + ωz2 0 ⎢0 a4,2 ⎢0 0 0 0 ⎢ 0 0 0 0 ⎢ A= ⎢ 0 0 0 0 ⎢ ⎢0 a8,2 − 3ωxωy + 3ω z 3ωz ⎢0 0 0 0 ⎢ 0 0 ⎢0 0 ⎢0 0 0 0 ⎢ ⎣⎢0 a12,2 − 3ωxωz − 3ωy − 3ωy ( ⎡ x⎤ ⎢ y⎥ ⎢ ⎥ ⎣⎢ z ⎦⎥ m ⎤ ⎡ x ⎤ ⎡0 ⎥ ⎢ x ⎥ ⎢0 ⎥⎢ ⎥ ⎢ ⎥ ⎢ x ⎥ ⎢0 ⎥⎢ ⎥ ⎢ ⎥ ⎢x⎥ ⎢1 ⎥ ⎢ y ⎥ ⎢0 ⎥⎢ ⎥ ⎢ ⎥ ⎢ y ⎥ + ⎢0 ⎥ ⎢ y ⎥ ⎢0 ⎥⎢ ⎥ ⎢ ⎥ ⎢y⎥ ⎢0 ⎥ ⎢ z ⎥ ⎢0 ⎥⎢ ⎥ ⎢ ⎥ ⎢ z ⎥ ⎢0 ⎥ ⎢ z ⎥ ⎢0 ⎥⎢ ⎥ ⎢ ⎦⎥ ⎣⎢z⎦⎥ ⎣⎢0 ) 0 0 0 0 0 0 0 0 0 0 0 0⎤ 0 0⎥ ⎥ 0 0⎥ ⎥ 0 0⎥ 0 0⎥ ⎥⎡wx ⎤ 0 0⎥ ⎢ ⎥ wy 0 0⎥ ⎢ ⎥ ⎥ ⎢⎣ w z ⎥⎦ 1 0⎥ 0 0⎥ ⎥ 0 0⎥ 0 0⎥ ⎥ 0 1 ⎦⎥ 0 0 0 0 0 0 0 0 0 0 0 0 a4,6 − 3ωxωy − 3ω z − 3ωz 0 a4,10 − 3ωxωz + 3ω y 0 0 0 1 0 0 0 a8,6 0 0 ( 0 1 0 3 ωx2 + ωz2 0 ) 0 0 0 0 0 0 0 a12,6 − 3ωyωz + 3ω x 0 0 1 0 0 0 0 0 0 a8,10 − 3ωzωy − 3ω x 0 1 0 0 0 3ωx 0 0 0 0 0 0 0 0 a12,10 ⎡ x ⎤ ⎡1 ⎢ x ⎥ ⎢0 ⎢ ⎥ ⎢ ⎢ x⎥ ⎢0 ⎢ ⎥ ⎢ ⎢x⎥ ⎢0 ⎢ y ⎥ ⎢0 ⎡1 0 0 0 0 0 0 0 0 0 0 0 ⎤ ⎢ ⎥ ⎢ 0 y = ⎢⎢0 0 0 0 1 0 0 0 0 0 0 0⎥⎥ ⎢⎢ ⎥⎥ + ⎢⎢ y 0 ⎣⎢0 0 0 0 0 0 0 0 1 0 0 0⎦⎥ ⎢ y ⎥ ⎢0 ⎢ ⎥ ⎢ ⎢ z ⎥ ⎢0 ⎢ ⎥ ⎢ ⎢ z ⎥ ⎢0 ⎢ ⎥ ⎢ ⎢ z⎥ ⎢0 ⎣⎢z⎦⎥ ⎣⎢0 0 0 0 1 0 2 3 ωx + ωy2 ( 0 0⎤ 0 0⎥⎥ 0 0⎥ ⎥ 0 0⎥ 1 0⎥ ⎥ ⎡v x ⎤ 0 0⎥ ⎢ ⎥ vy 0 0⎥ ⎢ ⎥ ⎥ ⎣⎢vz ⎦⎥ 0 0⎥ 0 1⎥ ⎥ 0 0⎥ ⎥ 0 0⎥ 0 0⎦⎥ ) 0 ⎤ 0 ⎥ ⎥ 0 ⎥ ⎥ 3ωy ⎥ 0 ⎥ ⎥ 0 ⎥ 0 ⎥ ⎥ − 3ωx ⎥ 0 ⎥ ⎥ 0 ⎥ 1 ⎥ ⎥ 0 ⎥⎦ State Dependent Difference Riccati Equation Based Estimation ( ) = −((ω + ω + ω )ω + 2ω ω + ω ω ) = −(− (ω + ω + ω )ω + 2ω ω + ω ω ) a4, 2 = 3 ω yω y + ω z ω z a8, 2 a12, 2 2 x 2 y 2 x 2 z 2 y z 2 z x y y x x z y x z (( ) ) = 3(ω ω + ω ω ) = −((ω + ω + ω )ω + 2ω ω + ω ω ) = −((ω + ω + ω )ω + 2ω ω + ω ω ) = −(− (ω + ω + ω )ω + 2ω ω + ω ω ) = 3(ω ω + ω ω ) a4,6 = − − ω x2 + ω y2 + ω z2 ω z + 2ω xω y + ω xω y a8,6 a12,6 a4,10 a8,10 a12,10 x x z z 2 x 2 y 2 z x y z y z 2 x 2 y 2 z y x z x z x 2 x 2 y x y 2 z x z y z y y where G G G G G (vT × aT ) (vT × jT ) 1 ωT = G 2 = G 2 = 2 x + y 2 + z 2 vT vT In two dimensions this reduces to ⎡ y z − z y⎤ ⎢ z x − x z⎥ ⎥ ⎢ ⎢⎣ x y − y x⎥⎦ 53 54 I.

All vectors and matrices are of appropriate dimensions. 1 T xˆ (t ) as a Θ > 0. 4) The solution of the preceding problem is the Kalman filter [19, 20]. xˆ(t) = Axˆ(t)+K(t)[ z (t ) − Cxˆ(t)], xˆ(t o ) = xo , K (t ) = Q(t )CV −1 Q (t ) = AQ(t ) + Q(t ) AT + ΓWΓ T − Q(t )C T V −1CQ(t ), Q(t o ) = Qo . 5) 46 I. Rusnak and L. 2 Estimators for Nonlinear System For nonlinear systems there are several approaches. Here the State Dependent Riccati Equation (SDRE) [13-16] approach is considered. The SDRE approach is based on the dual of the SDRE based nonlinear control [16].