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Non-linear state error based extended Kalman filters with applications to navigation

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Table 2.1 – Formulas for most frequent matrix Lie groups in navigation G SO (3) (R dim g = R 3 ) SE (3) (R dim g = R 6 ) Embedding of G R ∈ M 3 (R), R T R = I 3 R v 0 1 ! , R ∈ SO(3), u ∈ R 3 Embedding of g A 3 : ψ ∈ M 3 (R), ψ T = −ψ ψ u 0 0 ! , ψ ∈ A 3 ,
Figure 3.1 – Example illustration of the log-linear property of the error propagation
Figure 5.1 – Static alignment of an IMU planted in a car at stand with engine running
Figure 5.2 – Prolonged static pose during which a "small movement" measure is pro- pro-vided to the EKF
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