Parameter Estimation

Estimate model parameters using MATLAB and Simulink

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.

Examples and How To

Statistical Analysis

• Working with Probability Distributions 8:15 (Video)
• Fitting Custom Univariate Distributions (Example)
• Fitting an Orthogonal Regression using Principal Components Analysis (Example)

System Identification

• Estimating Transfer Functions and Process Models 2:27 (Video)
• Estimating State-Space and Polynomial Models 2:20 (Video)
• Estimating and Validating Models 1:21 (Video)
• Estimating Nonlinear Black-Box Models 4:29 (Video)

Simulink Model Parameter Estimation

• Estimating DC Motor Parameters from Test Data 8:00 (Video)
• Estimating the Parameters of a Hydraulic System 3:22 (Video)
• Engine Throttle Parameter Estimation (Example)

Software Reference

Statistical Analysis

• Distribution Fitting Functions (Documentation)
• Identifying Input-Output Polynomial Models (Documentation)
• Simulink Model Parameter Estimation (Documentation)

See also: control systems, mathematical modeling, linearization, PID control, PID Tuning