MAE142_Lecture25

MAE142_Lecture25 - State Estimation Problem Definition GPS...

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State Estimation Problem Definition GPS Application Pseudo-Range Direct Solution Method Position Uncertainty Kalman Filtering MAE 142 Differential GPS
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2 MAE 142 State Estimation State estimation involves reconstructing the state vector using measurements that may be corrupted by noise. Applications of state estimation: Spacecraft attitude determination State feeback control law implementation Accident reconstruction Tracking systems (radar, electro-optical, acoustic, …) Localization and positioning systems (GPS, LORAN, . ..) ˙ x t = f [ x t ] y t = h [ x t ] v t State Equations Measurement Function noise Can we estimate state x(t) from measurements y(t)?
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3 MAE 142 Global Positioning System The Global Positioning System (GPS) attempts estimate user position (a state vector) from noisy range measurements. i b =∥ s i − x i = pseudo-range measurement from satellite i s i = ECEF position of satellite i b = receiver clock bias x = user ECEF position . ∥= Euclidian distance i = c t r t si  corrections i = pseudo-range measurement from satellite i t r = time received at user t si = time sent from satellite i c = speed of light c = 299.792458 × 10 6 m / s Pseudo-range measurements represent a biased distance measurement between the unknown user position and the known satellite position.
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MAE142_Lecture25 - State Estimation Problem Definition GPS...

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