Techniques for Parameter Estimation - NCSU
[Pages:6]Techniques for Parameter Estimation
``Millionaires should always gamble, poor men never,'' J.M. Keynes ``If I wanted to gamble, I would buy a casino,'' P. Getty
Parameter Estimation Problem
Example: Spring model has the solution
Note: Nonlinear dependence on the parameters q = (m,c,k) Admissible Parameter Space: First-Order System with Observations:
Parameter Estimation Problem
Parameter Estimation Problem (Scalar):
Issues: ? Optimization techniques ? Accommodation of errors or noise in the model and data
MATLAB Optimization Routines
Note: There is significant documentation for the Optimization Toolbox Minimization:
? fmincon: Constrained nonlinear minimization ? fminsearch: Unconstrained nonlinear minimization (Nelder-Mead) ? fminunc: Unconstrained nonlinear minimization (gradient-based trust region) ? quadprog: Quadratic programming Equation Solving: ? fsolve: Nonlinear equation solving ? fzero: scalar nonlinear equation solving
Least Squares: ? lsqlin: Constrained linear least squares ? lsqnonlin: Nonlinear least squares ? lsqnonneg: Nonnegative linear least squares
Kelley's Routines: Available at the webpage
Tie between Optimization and Root Finding
Problem 1: Problem 2: Note:
Newton's Method (n=1):
Note: Quadratic convergence if function is sufficiently smooth and `reasonable' initial value
Tie between Optimization and Root Finding
Newton's Method (n>1): Consider
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