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Tracking with distributed sensors Luca Schenato
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Framework Modeling Algorithms Simulations Overview
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Framework Assumptions Magnetic sensors distributed on a uniform grid Position of sensors is known Exact timestamp associated with readings Time delay to relay measurement out of the network Single moving object Goal: Predict position and velocity of moving object at an arbitrary time in the future based on raw position estimation
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Modeling Magnetic sensor measures Bx By magnetic field at their position + noise Moving object: ideal magnetic dipole: x y r B
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Modeling Evader dynamics: unknown
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x t o o oo o o o o o o o o oo oo o smoothingpredictionfiltering Algorithms How many points to use ? Variable number of points: LEAST SQUARE Discount past: ON LINE LEAST SQUARE Which parametric curve to fit ? Linear quadratic o o o
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x t o o oo o o o o o o o o oo oo o smoothingpredictionfiltering Algorithms How many points to use ? Variable number of points: LEAST SQUARE Discount past: ON LINE LEAST SQUARE Which parametric curve to fit ? Linear quadratic o o o
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x t o o oo o o o o o o o o oo oo o smoothingpredictionfiltering Algorithms How many points to use ? Variable number of points: LEAST SQUARE Discount past: ON LINE LEAST SQUARE Which parametric curve to fit ? Linear quadratic o o o
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x t o o oo o o o o o o o o oo oo o smoothingpredictionfiltering Algorithms How many points to use ? Variable number of points: LEAST SQUARE Discount past: ON LINE LEAST SQUARE Which parametric curve to fit ? Linear quadratic o o o
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x t o o oo o o o o o o o o oo oo o smoothingpredictionfiltering Algorithms How many points to use ? Variable number of points: LEAST SQUARE Discount past: ON LINE LEAST SQUARE Which parametric curve to fit ? Linear quadratic o o o
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Least square: linear fitting
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Least square: quadratic fitting
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Algorithm: ONLINE least square Discount factor Latest data
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Prediction, smoothing, filtering Time desired of prediction:
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