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Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Preliminary Thesis Presentation
[object Object],[object Object],[object Object],[object Object],[object Object],Overview • • • • •
•  • • • • edmundhernandez.blogspot.com
Introduction The Control-Theoretical Pilot  (1/3) •  • • • • ,[object Object],[object Object],[object Object],[object Object],Note : A Pilot controlling an Aircraft is comparable to a Driver controlling a Car. =
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
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 ,[object Object],[object Object],[object Object]
Main Challenge & Research Goals • •  • • •
What? Discovering and understanding  suitable  Human Control Behavior  Parameter Estimation Methods.  Main Challenge The What and Why • •  • • • ,[object Object],[object Object],[object Object],[object Object]
Main Challenge Pilot Model Considerations • •  • • •
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.
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Current Status What did I do up until now? •   • •  • •
Literature Research •   • •  • •
[object Object],[object Object],[object Object],Literature Research Short History of Pilot Parameter Estimation  (1/2) •   • •  • • 1980s     ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],Literature Research Short History of Pilot Parameter Estimation  (2/2) •   • •  • • ,[object Object],[object Object],[object Object]
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
Literature Research Frequency- versus Time-Domain Techniques  (2/2)  •   • •  • •
Literature Research Maximum Likelihood Estimation •   • •  • • MLE is a Statistical Method introduced by Sir Ronald Aymler Fisher in 1912  ,[object Object],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
Literature Research Maximum Likelihood Estimation •   • •  • • ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Research Approach •   • • •  •
[object Object],[object Object],Research Approach Zaal et al. (July – August 2009)  (1/2) •   • • •  •
Research Approach Zaal et al. (July – August 2009)  (2/2) •   • • •  • ,[object Object]
[object Object],[object Object],[object Object],Research Approach Zaal & Sweet (August 2011)  (1/4) •   • • •  •
[object Object],Research Approach Zaal & Sweet (August 2011)  (2/4) •   • • •  •
Research Approach Zaal & Sweet (August 2011)  (3/4) •   • • •  •
Research Approach Zaal & Sweet (August 2011)  (4/4) •   • • •  •
Research Approach Standard Model • • • •  • ,[object Object]
Research Approach Multisine Excitation • • • •  •
[object Object],Research Approach Linear Time-Varying or Linear Parameter-Varying? • • •  •  • ,[object Object]
[object Object],[object Object],[object Object],[object Object],Research Approach How do we assess the MLE Method? • • • •  •
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Future Possibilities What can be done after my Research? • • • • •
In Practice Why are we doing this? • • • • • ,[object Object],[object Object],[object Object]
• • • • • Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Discussion & Questions

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Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters

  • 1. Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Preliminary Thesis Presentation
  • 2.
  • 3. • • • • • edmundhernandez.blogspot.com
  • 4.
  • 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.
  • 7. Main Challenge & Research Goals • • • • •
  • 8.
  • 9. Main Challenge Pilot Model Considerations • • • • •
  • 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.
  • 12. Literature Research • • • • •
  • 13.
  • 14.
  • 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. Literature Research Frequency- versus Time-Domain Techniques (2/2) • • • • •
  • 17.
  • 18.
  • 19. Research Approach • • • • •
  • 20.
  • 21.
  • 22.
  • 23.
  • 24. Research Approach Zaal & Sweet (August 2011) (3/4) • • • • •
  • 25. Research Approach Zaal & Sweet (August 2011) (4/4) • • • • •
  • 26.
  • 27. Research Approach Multisine Excitation • • • • •
  • 28.
  • 29.
  • 30.
  • 31.
  • 32. • • • • • Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Discussion & Questions