16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde Example: Discrete time system(typical servo structure) 1 The input u(n) is any known command signal The noise n(n) is a wideband noise approximated as white with power density n The measurements are of y and are processed at intervals At with discrete measurement variance Rk Form the approximating continuous Kalman filter R=R2△ x1=x2 i2=KF(u-x1)-K(2+ .- =Ax+Gu+ Bn The continuous approximation measurement z is16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 7 of 9 Example: Discrete time system (typical servo structure) The input u t( ) is any known command signal. The noise n t( ) is a wideband noise approximated as white with power density N . The measurements are of y and are processed at intervals ∆t with discrete measurement variance Rk . Form the approximating continuous Kalman filter: R = ∆ R t k ( )( ) 1 2 2 12 01 0 0 F R FR F R x x x Kux Kx n x xu n KK K K Ax Gu Bn = = −− + ⎡ ⎤ ⎡⎤ ⎡ ⎤ = ++ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎣ ⎦ ⎣⎦ ⎣ ⎦ −− − =++    The continuous approximation measurement z is