4.1 The Process ModelThe state equations described by (8) can be rewritten by𝑞˙=𝛺[𝜔]𝑞(11)where 𝛺[𝜔]=12[0−𝜔𝑇𝜔[𝜔×]] .(12)ω = [ωx ωy ωz]T denotes the tri-axis gyroscope output; [ω ×] is a 3 × 3 skew symmetric matrix given by [𝜔×]=[0𝜔𝑧−𝜔𝑦−𝜔𝑧0𝜔𝑥𝜔𝑦−𝜔𝑥0] .(13)The next step is to convert continuous-time model represented by (11) into a discrete-time model. Let the system sampling time be Ts, then the discrete-time model is given by
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4.1 The Process ModelThe state equations described by (8) can be rewritten by𝑞˙=𝛺[𝜔]𝑞(11)where 𝛺[𝜔]=12[0−𝜔𝑇𝜔[𝜔×]] .(12)ω = [ωx ωy ωz]T denotes the tri-axis gyroscope output; [ω ×] is a 3 × 3 skew symmetric matrix given by [𝜔×]=[0𝜔𝑧−𝜔𝑦−𝜔𝑧0𝜔𝑥𝜔𝑦−𝜔𝑥0] .(13)The next step is to convert continuous-time model represented by (11) into a discrete-time model. Let the system sampling time be Ts, then the discrete-time model is given by
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q q&W w (11)where01 .2 [ ]Té ù-é ù = ê úë û ´ê úë ûωwW w w (12)ω = ωx ωy ωz T denotes the tri-axis gyroscope output;ω × is a 3 × 3 skew symmetric matrix given by00 .0z yz xy xw wwww wé ù-ê úé ù´ = -ê úë û ê ú-ê úë ûw (13)The next step is to convert continuous-time model repre‐sented by (11) into a discrete-time model. Let the systemsampling time be Ts, then the discrete-time model is givenby( )1 exp , 0,1,2,...
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