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Model And Filter

Model And Filter. Name: 韩 瑜 Email ： hanyu@sjtu.edu.cn. Background. Black Box Signal evolution Noise Input Output. Model. Why choose Differential Equations. Realization Circuit (time-delay) Analysis ODE Fourier. Approximation in theory. Curve Fitting

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Model And Filter

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  1. Model And Filter Name: 韩 瑜 Email：hanyu@sjtu.edu.cn

  2. Background • Black Box • Signal evolution • Noise • Input • Output

  3. Model

  4. Why choose Differential Equations • Realization • Circuit (time-delay) • Analysis • ODE • Fourier

  5. Approximation in theory • Curve Fitting Find original formula of system • Function Approximation Simplify system (has known system precisely)

  6. Curve Fitting Usually Solve this problem

  7. For instance

  8. Least square error

  9. Classic Filter Theory Review • Signal Process

  10. Modern Filter • Wiener Filter • Karlman Filter • Adaptive Filter • Wavelet Filter

  11. Method in H2 Space • LMS • Fitting and Approximation are same (Mention that approximation use Hilbert polynomial)

  12. Defect • It’s difficult to compute by tradition matrix algorithm in actual fact • Some information are same between each generation, but not used, and do same work again

  13. Kalman’s method • Model • Iteration equation

  14. Variant dimension

  15. Kalman Filter

  16. How to understand P(t|t)&P(t+1|t) Many t and t+1, like: X(t+1|t), X(t|t) P(t+1|t), P(t+1|t) How to understand these?

  17. Relation with Kalman

  18. Recursive method • Kalman recursive method • RLS recursive method

  19. Adaptive Filter • Back to model • if model is change Equal to dimension change or Dimension increasing • Iteration equation

  20. Variant dimension

  21. Identification

  22. Model • Widely Accept • Rewrite • Evolution • Observation

  23. Iteration filter • Add some condition • Iteration • Some equation

  24. Wavelet Filter 1.Wavelet decomposition 2.Coefficients restrain 3.Reconstruction

  25. Wavelet Filter Result

  26. Method in H-inf Space • Fitting And Approximation are not same • Approximation: • 2nd Chebyshev polynomial • Fitting • model

  27. Linear programming For H-inf • linear programming method • Mention:

  28. Future of Filters • Filter of H2 • Research may be useless now for low dimension data • Computer and computation • Filter of H-inf • Linear programming • LMI (?) • H2&Hinf filter (?)

  29. Thank You! Question?

  30. Homework

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