Parameter Estimation

Parameter estimation plays a critical role in accurately describing system behavior through mathematical models. Model examples include statistical probability distribution functions, parametric dynamic models, and data-based Simulink models. MathWorks products provide a broad range of parameter estimation capabilities.

Improving the accuracy of statistical models can involve estimating:

• Parameters of a probability distribution, such as the mean and standard deviation of a normal distribution
• Regression coefficients of a regression model, such as y = a'x  

Statistics Toolbox™supports these and similar parameter estimation tasks with more than 30 different probability distributions, including Normal, Weibull, Gamma, Generalized Pareto, and Poisson. The toolbox also supports linear and nonlinear regression.

Creating accurate parametric dynamic models can involve estimating:

• Coefficients of transfer functions, including ARX, ARMAX, Box-Jenkins, and Output-Error
• Entries of state-space matrices
• Coefficients of ODEs or well-structured systems with parameter constraints (grey-box system identification)
• Regression coefficients, saturation levels, or dead-zone limits for nonlinear dynamic systems, including nonlinear ARX and Hammerstein-Wiener

System Identification Toolbox™ supports these tasks by providing parameter estimation capabilities for linear and nonlinear parametric dynamic models.

Common tasks for parameter estimation of Simulink models include:

• Importing and processing input-output test data, such as the voltage input and rotor speed output of a DC motor
• Specifying which model parameters and initial conditions to estimate, such as motor resistance and inertia

Simulink Design Optimization™supports these parameter estimation tasks with a Control and Estimation Tools Manager GUI that helps you configure, manipulate, and run your Simulink optimization problem.

Introduction to Simulink Design Optimization (Webinar)