# Grey-Box Model Estimation

Estimate coefficients of linear and nonlinear differential, difference and state-space equations

## Functions

 `greyest` Linear grey-box model estimation `nlgreyest` Estimate nonlinear grey-box model parameters `idgrey` Linear ODE (grey-box model) with identifiable parameters `idnlgrey` Nonlinear grey-box model `pem` Prediction error estimate for linear and nonlinear model
 `findstates` Estimate initial states of model `init` Set or randomize initial parameter values `getinit` Values of `idnlgrey` model initial states `setinit` Set initial states of `idnlgrey` model object `getpar` Parameter values and properties of `idnlgrey` model parameters `setpar` Set initial parameter values of `idnlgrey` model object `getpvec` Model parameters and associated uncertainty data `setpvec` Modify value of model parameters `sim` Simulate response of identified model
 `greyestOptions` Option set for `greyest` `nlgreyestOptions` Option set for `nlgreyest` `findstatesOptions` Option set for `findstates` `simOptions` Option set for `sim`

## Examples and How To

Estimate Linear Grey-Box Models

How to define and estimate linear grey-box models at the command line.

Estimate Continuous-Time Grey-Box Model for Heat Diffusion

This example shows how to estimate the heat conductivity and the heat-transfer coefficient of a continuous-time grey-box model for a heated-rod system.

Estimate Discrete-Time Grey-Box Model with Parameterized Disturbance

This example shows how to create a single-input and single-output grey-box model structure when you know the variance of the measurement noise.

Estimate Coefficients of ODEs to Fit Given Solution

This example shows how to estimate model parameters using linear and nonlinear grey-box modeling.

Estimate Model Using Zero/Pole/Gain Parameters

This example shows how to estimate a model that is parameterized by poles, zeros, and gains.

Estimate Nonlinear Grey-Box Models

How to define and estimate nonlinear grey-box models at the command line.

Creating IDNLGREY Model Files

This example shows how to write ODE files for nonlinear grey-box models as MATLAB and C MEX files.

Estimate State-Space Models with Structured Parameterization

Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values.

## Concepts

Supported Grey-Box Models

Types of supported grey-box models.

Data Supported by Grey-Box Models

Types of supported data for estimating grey-box models.

Choosing idgrey or idnlgrey Model Object

Difference between `idgrey` and `idnlgrey` model objects for representing grey-box model objects.

Identifying State-Space Models with Separate Process and Measurement Noise Descriptions

An identified linear model is used to simulate and predict system outputs for given input and noise signals.

Loss Function and Model Quality Metrics

Configure the loss function that is minimized during parameter estimation. After estimation, use model quality metrics to assess the quality of identified models.

Estimation Report

The estimation report contains information about the results and options used for a model estimation.

Regularized Estimates of Model Parameters

Regularization is the technique for specifying constraints on the flexibility of a model, thereby reducing uncertainty in the estimated parameter values.

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