1. Tracking with distributed sensors Luca Schenato

2. Framework Modeling Algorithms Simulations Overview

3. 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

4. Modeling Magnetic sensor measures Bx By magnetic field at their position + noise Moving object: ideal magnetic dipole: x y r B

5. Modeling Evader dynamics: unknown

6. 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

7. 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

8. 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

9. 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

10. 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

11. Least square: linear fitting

12. Least square: quadratic fitting

13. Algorithm: ONLINE least square Discount factor Latest data

14. Prediction, smoothing, filtering Time desired of prediction: