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Input-Output Polynomial Models

ARX, ARMAX, BJ and OE models


System IdentificationIdentify models of dynamic systems from measured data


arxEstimate parameters of ARX or AR model using least squares
armaxEstimate parameters of ARMAX model using time-domain data
bjEstimate Box-Jenkins polynomial model using time domain data
iv4ARX model estimation using four-stage instrumental variable method
ivxARX model estimation using instrumental variable method with arbitrary instruments
oeEstimate Output-Error polynomial model using time or frequency domain data
polyestEstimate polynomial model using time- or frequency-domain data
idpolyPolynomial model with identifiable parameters
pemPrediction error estimate for linear and nonlinear model
arxstrucCompute loss functions for single-output ARX models
ivstrucCompute loss functions for sets of ARX model structures using instrumental variable method
selstrucSelect model order for single-output ARX models
strucGenerate model-order combinations for single-output ARX model estimation
arxRegulDetermine regularization constants for ARX model estimation
delayestEstimate time delay (dead time) from data
initSet or randomize initial parameter values
polydataAccess polynomial coefficients and uncertainties of identified model
getpvecModel parameters and associated uncertainty data
setpvecModify value of model parameters
getparObtain attributes such as values and bounds of linear model parameters
setparSet attributes such as values and bounds of linear model parameters
setPolyFormatSpecify format for B and F polynomials of multi-input polynomial model
armaxOptionsOption set for armax
arxOptionsOption set for arx
arxRegulOptionsOption set for arxRegul
bjOptionsOption set for bj
iv4OptionsOption set for iv4
oeOptionsOption set for oe
polyestOptionsOption 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.


What Are Polynomial Models?

Polynomial model structures including ARX, ARMAX, ourput-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.

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