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Input-Output Polynomial Models

ARX, ARMAX, BJ and OE models

Apps

System Identification

Identify models of dynamic systems from measured data

Functions

`arx`	Estimate parameters of ARX or AR model using least squares
`armax`	Estimate parameters of ARMAX model using time-domain data
`bj`	Estimate Box-Jenkins polynomial model using time domain data
`iv4`	ARX model estimation using four-stage instrumental variable method
`ivx`	ARX model estimation using instrumental variable method with arbitrary instruments
`oe`	Estimate Output-Error polynomial model using time or frequency domain data
`polyest`	Estimate polynomial model using time- or frequency-domain data
`idpoly`	Polynomial model with identifiable parameters
`pem`	Prediction error estimate for linear and nonlinear model

`arxstruc`	Compute loss functions for single-output ARX models
`ivstruc`	Compute loss functions for sets of ARX model structures using instrumental variable method
`selstruc`	Select model order for single-output ARX models
`struc`	Generate model-order combinations for single-output ARX model estimation

`arxRegul`	Determine regularization constants for ARX model estimation
`delayest`	Estimate time delay (dead time) from data
`init`	Set or randomize initial parameter values
`polydata`	Access polynomial coefficients and uncertainties of identified model
`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
`setPolyFormat`	Specify format for B and F polynomials of multi-input polynomial model

`armaxOptions`	Option set for armax
`arxOptions`	Option set for arx
`arxRegulOptions`	Option set for arxRegul
`bjOptions`	Option set for bj
`iv4Options`	Option set for iv4
`oeOptions`	Option set for oe
`polyestOptions`	Option set for polyest

Examples and How To

Preliminary Step – Estimating Model Orders and Input Delays

To estimate polynomial models, you must provide input delays and model orders.

Estimate Polynomial Models in the App

Import data into the app, specify model orders, delays and estimation options.

Estimate Polynomial Models at the Command Line

Specify model orders, delays, and estimation options.

Polynomial Sizes and Orders of Multi-Output Polynomial Models

Size of A, B, C, D, and F polynomials for multi-output models.

Estimate Models Using armax

This example shows how to estimate a linear, polynomial model with an ARMAX structure for a three-input and single-output (MISO) system using the iterative estimation method armax.

Concepts

What Are Polynomial Models?

Polynomial model structures including ARX, ARMAX, output-error, and Box-Jenkins.

Data Supported by Polynomial Models

Use time-domain and frequency-domain data to estimate discrete-time and continuous-time models.

Specifying Initial States for Iterative Estimation Algorithms

When you use the pem or polyest to estimate ARMAX, Box-Jenkins (BJ), Output-Error (OE), you must specify how the algorithm treats initial conditions.

Polynomial Model Estimation Algorithms

Choose between the ARX and IV algorithms for ARX and AR model estimation.

Featured Examples

Spectrum Estimation Using Complex Data - Marple's Test Case

Perform spectral estimation on time series data. We use Marple's test case (The complex data in L. Marple: S.L. Marple, Jr, Digital Spectral Analysis with Applications, Prentice-Hall, Englewood Cliffs, NJ 1987.)

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