Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters
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The document presents a preliminary thesis on maximum likelihood estimation (MLE) of parameters for a linear time-varying pilot model, highlighting the challenges of quantifying human manual control behavior. It discusses system identification methodologies, historical literature, and ongoing research approaches, aiming to enhance the understanding of pilot model dynamics with reduced experimental data. Future possibilities include applications in neuromuscular dynamics and drowsy control behavior.
![Contemporary Research LTV / LPV Systems Wavelets Linear Least Squares (LS) / Autoregressive Moving Average (ARMA) MLE Literature Research Short History of Pilot Parameter Estimation (2/2) • • • • • 1990s-2000s Significant System Identification Contributions: Lennart Ljung [Sweden] Johan Schoukens & Rik Pintelon [Belgium]](https://image.slidesharecdn.com/preliminarypresentationslideshare-111001081610-phpapp02/85/Maximum-Likelihood-Estimation-of-Linear-Time-Varying-Pilot-Model-Parameters-14-320.jpg)
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. Introduction Main Challenge | Research Goals | Current Status Literature Research Research Approach Future Possibilities | Discussion & Questions Overview • • • • •
- 3. • • • • • edmundhernandez.blogspot.com
- 4. Introduction The Control-Theoretical Pilot (1/3) • • • • • Human Manual Vehicle Control Behavior is Nonlinear Time-Varying Closed-Loop Process Note : A Pilot controlling an Aircraft is comparable to a Driver controlling a Car. =
- 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. 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 Nonparametric versus Parametric Nonlinear versus Linear Frequency-Domain versus Time-Domain
- 7. Main Challenge & Research Goals • • • • •
- 8. What? Discovering and understanding suitable Human Control Behavior Parameter Estimation Methods. Main Challenge The What and Why • • • • • Why? To further quantify Human Time-Varying Manual Control . This is useful for: Design of Advanced Manual Control Systems Enhanced Tuning of Simulators
- 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. Literature Research System Identification Methods Maximum Likelihood Estimation (MLE) System Classes Linear Parameter-Varying (LPV) Systems Linear Time-Varying (LTV) Systems Analyzed and Compared Possible Model Options Structure and Inputs Future Options Refined Scope of the Research Setup Initial Simulation Structure in Matlab Current Status What did I do up until now? • • • • •
- 12. Literature Research • • • • •
- 13. 1960s-1970s McRuer’s Quasi-Linear Pilot Models Single/Multi-Loop Identification Methods in Frequency- and Time-Domains Literature Research Short History of Pilot Parameter Estimation (1/2) • • • • • 1980s 1990s-2000s Neuromuscular Pilot Model Validation Generalized Identification Approach with Fourier Coefficients Linear Time-Invariant (LTI) Models
- 14. Contemporary Research LTV / LPV Systems Wavelets Linear Least Squares (LS) / Autoregressive Moving Average (ARMA) MLE Literature Research Short History of Pilot Parameter Estimation (2/2) • • • • • 1990s-2000s Significant System Identification Contributions: Lennart Ljung [Sweden] Johan Schoukens & Rik Pintelon [Belgium]
- 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. Literature Research Maximum Likelihood Estimation • • • • • MLE is a Statistical Method introduced by Sir Ronald Aymler Fisher in 1912 Parameter Vector 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. Literature Research Maximum Likelihood Estimation • • • • • Main Reasons for MLE: Consistent and Efficient Statistical Properties Best Possible Estimator for Dynamical Systems Errors between Simulated Output u and Measured Output u m have an Unbiased Gaussian Distribution , which makes it possible to use the Mean Square Error Matrix. However, for Advanced Time-Varying Systems, Time-Varying Kalman Filters might be needed, which makes everything more complex.
- 19. Research Approach • • • • •
- 20. MLE in LTI Multichannel Pilot Models Introduces Genetic Algorithm & Gauss-Newton Algorithm Research Approach Zaal et al. (July – August 2009) (1/2) • • • • •
- 21. Research Approach Zaal et al. (July – August 2009) (2/2) • • • • • Global Optimum Solution of Parameters found in 90% of the Cases
- 22. Estimates Time-Varying Parameters Wavelets MLE Research Approach Zaal & Sweet (August 2011) (1/4) • • • • •
- 23. Time-Varying Parameters Research Approach Zaal & Sweet (August 2011) (2/4) • • • • •
- 24. Research Approach Zaal & Sweet (August 2011) (3/4) • • • • •
- 25. Research Approach Zaal & Sweet (August 2011) (4/4) • • • • •
- 26. Research Approach Standard Model • • • • • Generate Own Data with Matlab Simulation
- 27. Research Approach Multisine Excitation • • • • •
- 28. Time-Varying MLE with Polynomials, e.g. Research Approach Linear Time-Varying or Linear Parameter-Varying? • • • • • Ambiguity: LTV or LPV?
- 29. Cramér-Rao Inequality Assess the Quality of an Estimator by its Mean-Square Error Matrix Good Estimators make P small (Cramér-Rao Lower Bound) M is the Fisher Information Matrix Research Approach How do we assess the MLE Method? • • • • •
- 30. Increase Complexity of the Matlab Model Augment with other Methods, e.g. Linear Parameter-Varying Methods Neural Networks B-Splines Expand to Online Simulations Research the Effect of different Forcing Functions Future Possibilities What can be done after my Research? • • • • •
- 31. In Practice Why are we doing this? • • • • • Two Examples: Neuromuscular Dynamics Drowsy Control Behavior
- 32. • • • • • Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Discussion & Questions