# Linear Grey-Box Models

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

## Functions

 `greyest` Linear grey-box model estimation `idgrey` Linear ODE (grey-box model) with identifiable parameters `pem` Prediction error estimate for linear and nonlinear model
 `findstates` Estimate initial states of model `init` Set or randomize initial parameter values `getpvec` Model parameters and associated uncertainty data `setpvec` Modify value of model parameters `getpar` Obtain attributes such as values and bounds of linear model parameters `setpar` Set attributes such as values and bounds of linear model parameters
 `findstatesOptions` Option set for `findstates` `greyestOptions` Option set for `greyest`

## 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 State-Space Models with Structured Parameterization

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

Estimate Coefficients of ODEs to Fit Given Solution

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.

## 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.

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