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Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters
 

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.

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 Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Presentation Transcript

    • Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Preliminary Thesis Presentation
      • Introduction
      • Main Challenge | Research Goals | Current Status
      • Literature Research
      • Research Approach
      • Future Possibilities | Discussion & Questions
      Overview • • • • •
    • • • • • • edmundhernandez.blogspot.com
    • 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. =
    • 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
      • Nonparametric versus Parametric
      • Nonlinear versus Linear
      • Frequency-Domain versus Time-Domain
    • Main Challenge & Research Goals • • • • •
    • 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
    • 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.
      • 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? • • • • •
    • Literature Research • • • • •
      • 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
      • 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]
    • 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
      • 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
    • 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.
    • Research Approach • • • • •
      • MLE in LTI Multichannel Pilot Models
      • Introduces Genetic Algorithm & Gauss-Newton Algorithm
      Research Approach Zaal et al. (July – August 2009) (1/2) • • • • •
    • Research Approach Zaal et al. (July – August 2009) (2/2) • • • • •
      • Global Optimum Solution of Parameters found in 90% of the Cases
      • Estimates Time-Varying Parameters
        • Wavelets
        • MLE
      Research Approach Zaal & Sweet (August 2011) (1/4) • • • • •
      • Time-Varying Parameters
      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 • • • • •
      • Generate Own Data with Matlab Simulation
    • Research Approach Multisine Excitation • • • • •
      • Time-Varying MLE with Polynomials, e.g.
      Research Approach Linear Time-Varying or Linear Parameter-Varying? • • • • •
      • Ambiguity: LTV or LPV?
      • 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? • • • • •
      • 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? • • • • •
    • In Practice Why are we doing this? • • • • •
      • Two Examples:
      • Neuromuscular Dynamics
      • Drowsy Control Behavior
    • • • • • • Maximum Likelihood Estimation of Linear Time-Varying Pilot Model Parameters Discussion & Questions