Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters

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Preliminary MSc. Thesis Presentation 'Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters' by Martin Kers.

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Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters

  1. 1. Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Preliminary Thesis Presentation
  2. 2. <ul><li>Introduction </li></ul><ul><li>Main Challenge | Research Goals | Current Status </li></ul><ul><li>Literature Research </li></ul><ul><li>Research Approach </li></ul><ul><li>Future Possibilities | Discussion & Questions </li></ul>Overview • • • • •
  3. 3. • • • • • edmundhernandez.blogspot.com
  4. 4. Introduction The Control-Theoretical Pilot (1/3) • • • • • <ul><li>Human Manual Vehicle Control Behavior is </li></ul><ul><ul><li>Nonlinear </li></ul></ul><ul><ul><li>Time-Varying </li></ul></ul><ul><ul><li>Closed-Loop Process </li></ul></ul>Note : A Pilot controlling an Aircraft is comparable to a Driver controlling a Car. =
  5. 5. Introduction The Control-Theoretical Pilot (2/3) • • • • • System Identification since 1960s to estimate Pilot Model Parameters (e.g. gain K , damping constant ζ nm , natural frequency ω nm ) Input Time
  6. 6. Introduction The Control-Theoretical Pilot (3/3) • • • • • System Identification since 1960s to estimate Pilot Model Parameters (e.g. gain K , damping constant ζ nm , natural frequency ω nm ) Input Time <ul><li>Nonparametric versus Parametric </li></ul><ul><li>Nonlinear versus Linear </li></ul><ul><li>Frequency-Domain versus Time-Domain </li></ul>
  7. 7. Main Challenge & Research Goals • • • • •
  8. 8. What? Discovering and understanding suitable Human Control Behavior Parameter Estimation Methods. Main Challenge The What and Why • • • • • <ul><li>Why? </li></ul><ul><li>To further quantify Human Time-Varying Manual Control . This is useful for: </li></ul><ul><ul><ul><li>Design of Advanced Manual Control Systems </li></ul></ul></ul><ul><ul><ul><li>Enhanced Tuning of Simulators </li></ul></ul></ul>
  9. 9. Main Challenge Pilot Model Considerations • • • • •
  10. 10. Primary Goal Advanced Understanding of Time-Varying Pilot Model Parameter Estimation with Maximum Likelihood Estimation to further quantify Time-Varying Human Control Behavior. Research Goals • • • • • Secondary Goal Shorten the Amount of Experimental Data needed for Qualitatively Equivalent Parameter Estimation of Multichannel Pilot Models.
  11. 11. <ul><li>Literature Research </li></ul><ul><ul><li>System Identification Methods </li></ul></ul><ul><ul><ul><li>Maximum Likelihood Estimation (MLE) </li></ul></ul></ul><ul><ul><li>System Classes </li></ul></ul><ul><ul><ul><li>Linear Parameter-Varying (LPV) Systems </li></ul></ul></ul><ul><ul><ul><li>Linear Time-Varying (LTV) Systems </li></ul></ul></ul><ul><li>Analyzed and Compared Possible Model Options </li></ul><ul><ul><li>Structure and Inputs </li></ul></ul><ul><ul><li>Future Options </li></ul></ul><ul><li>Refined Scope of the Research </li></ul><ul><li>Setup Initial Simulation Structure in Matlab </li></ul>Current Status What did I do up until now? • • • • •
  12. 12. Literature Research • • • • •
  13. 13. <ul><li>1960s-1970s </li></ul><ul><ul><li>McRuer’s Quasi-Linear Pilot Models </li></ul></ul><ul><ul><li>Single/Multi-Loop Identification Methods in Frequency- and Time-Domains </li></ul></ul>Literature Research Short History of Pilot Parameter Estimation (1/2) • • • • • 1980s  <ul><li>1990s-2000s </li></ul><ul><ul><li>Neuromuscular Pilot Model Validation </li></ul></ul><ul><ul><li>Generalized Identification Approach with Fourier Coefficients </li></ul></ul><ul><ul><li>Linear Time-Invariant (LTI) Models </li></ul></ul>
  14. 14. <ul><li>Contemporary Research </li></ul><ul><ul><li>LTV / LPV Systems </li></ul></ul><ul><ul><li>Wavelets </li></ul></ul><ul><ul><li>Linear Least Squares (LS) / Autoregressive Moving Average (ARMA) </li></ul></ul><ul><ul><li>MLE </li></ul></ul>Literature Research Short History of Pilot Parameter Estimation (2/2) • • • • • <ul><li>1990s-2000s Significant System Identification Contributions: </li></ul><ul><ul><li>Lennart Ljung [Sweden] </li></ul></ul><ul><ul><li>Johan Schoukens & Rik Pintelon [Belgium] </li></ul></ul>
  15. 15. Literature Research Frequency- versus Time-Domain Techniques (1/2) • • • • • Frequency-Domain Time-Domain Continuous-Time Data Discrete-Time Data No A Priori Information necessary A Priori Information necessary Fast Computation Slower Computation Limited to LTI Systems Time-Varying Systems Limited Methods available Variety of Methods available
  16. 16. Literature Research Frequency- versus Time-Domain Techniques (2/2) • • • • •
  17. 17. Literature Research Maximum Likelihood Estimation • • • • • MLE is a Statistical Method introduced by Sir Ronald Aymler Fisher in 1912 <ul><li>Parameter Vector </li></ul>2. Find Estimate to maximize Likelihood Function: 3. Conditional Probability Density Function (PDF) of one Measurement : 4. Minimize Negative Log-Likelihood to find Maximum Likelihood Estimate
  18. 18. Literature Research Maximum Likelihood Estimation • • • • • <ul><li>Main Reasons for MLE: </li></ul><ul><li>Consistent and Efficient Statistical Properties </li></ul><ul><li>Best Possible Estimator for Dynamical Systems </li></ul><ul><li>Errors between Simulated Output u and </li></ul><ul><li>Measured Output u m have an Unbiased Gaussian Distribution , which </li></ul><ul><li>makes it possible to use the Mean Square Error Matrix. </li></ul><ul><li>However, for Advanced Time-Varying Systems, Time-Varying Kalman Filters might be needed, which makes everything more complex. </li></ul>
  19. 19. Research Approach • • • • •
  20. 20. <ul><li>MLE in LTI Multichannel Pilot Models </li></ul><ul><li>Introduces Genetic Algorithm & Gauss-Newton Algorithm </li></ul>Research Approach Zaal et al. (July – August 2009) (1/2) • • • • •
  21. 21. Research Approach Zaal et al. (July – August 2009) (2/2) • • • • • <ul><li>Global Optimum Solution of Parameters found in 90% of the Cases </li></ul>
  22. 22. <ul><li>Estimates Time-Varying Parameters </li></ul><ul><ul><li>Wavelets </li></ul></ul><ul><ul><li>MLE </li></ul></ul>Research Approach Zaal & Sweet (August 2011) (1/4) • • • • •
  23. 23. <ul><li>Time-Varying Parameters </li></ul>Research Approach Zaal & Sweet (August 2011) (2/4) • • • • •
  24. 24. Research Approach Zaal & Sweet (August 2011) (3/4) • • • • •
  25. 25. Research Approach Zaal & Sweet (August 2011) (4/4) • • • • •
  26. 26. Research Approach Standard Model • • • • • <ul><li>Generate Own Data with Matlab Simulation </li></ul>
  27. 27. Research Approach Multisine Excitation • • • • •
  28. 28. <ul><li>Time-Varying MLE with Polynomials, e.g. </li></ul>Research Approach Linear Time-Varying or Linear Parameter-Varying? • • • • • <ul><li>Ambiguity: LTV or LPV? </li></ul>
  29. 29. <ul><li>Cramér-Rao Inequality </li></ul><ul><ul><li>Assess the Quality of an Estimator by its Mean-Square Error Matrix </li></ul></ul><ul><ul><li>Good Estimators make P small (Cramér-Rao Lower Bound) </li></ul></ul><ul><ul><li>M is the Fisher Information Matrix </li></ul></ul>Research Approach How do we assess the MLE Method? • • • • •
  30. 30. <ul><li>Increase Complexity of the Matlab Model </li></ul><ul><li>Augment with other Methods, e.g. </li></ul><ul><ul><li>Linear Parameter-Varying Methods </li></ul></ul><ul><ul><li>Neural Networks </li></ul></ul><ul><ul><li>B-Splines </li></ul></ul><ul><li>Expand to Online Simulations </li></ul><ul><li>Research the Effect of different Forcing Functions </li></ul>Future Possibilities What can be done after my Research? • • • • •
  31. 31. In Practice Why are we doing this? • • • • • <ul><li>Two Examples: </li></ul><ul><li>Neuromuscular Dynamics </li></ul><ul><li>Drowsy Control Behavior </li></ul>
  32. 32. • • • • • Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Discussion & Questions

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