# polyest

Estimate polynomial model using time- or frequency-domain data

## Syntax

## Description

### Estimate Polynomial Model

estimates a polynomial model `sys`

= polyest(`tt`

,[`na`

`nb`

`nc`

`nd`

`nf`

`nk`

])`sys`

using the data contained in the
variables of timetable `tt`

. The software uses the first
*Nu* variables as inputs and the next *Ny* variables
as outputs, where *Nu* and *Ny* are determined from the
specified polynomial orders.

`sys`

is of the form

$$A(q)y(t)=\frac{B(q)}{F(q)}u(t-nk)+\frac{C(q)}{D(q)}e(t).$$

*A*(*q*),
*B*(*q*), *F*(*q*),
*C*(*q*) and
*D*(*q*) are polynomial matrices.
*u*(*t*) is the input, and `nk`

is
the input delay. *y*(*t*) is the output and
*e*(*t*) is the disturbance signal.
`na`

, `nb`

, `nc`

,
`nd`

, and `nf`

are the orders of the
*A*(*q*), *B*(*q*),
*C*(*q*), *D*(*q*),
and *F*(*q*) polynomials, respectively.

To select specific input and output channels from `tt`

, use
name-value syntax to set `'InputName'`

and
`'OutputName'`

to the corresponding timetable variable names.

estimates a polynomial model with additional attributes of the estimated model structure
specified by one or more `sys`

= polyest(___,`Name,Value`

)`Name,Value`

arguments. You can use this
syntax with any of the previous input-argument combinations.

### Configure Initial Parameters

### Specify Additional Estimation Options

### Return Estimated Initial Conditions

`[`

returns the estimated initial conditions as an `sys`

,`ic`

] = polyest(___)`initialCondition`

object. Use this syntax if you plan to simulate or predict the model response using the
same estimation input data, then compare the response with the same estimation output
data. Incorporating the initial conditions yields a better match during the first part of
the simulation.

## Examples

## Input Arguments

## Output Arguments

## Tips

In most situations, all the polynomials of an identified polynomial model are not simultaneously active. Set one or more of the orders

`na`

,`nc`

,`nd`

and`nf`

to zero to simplify the model structure.For example, you can estimate an output-error (OE) model by specifying

`na`

,`nc`

and`nd`

as zero.Alternatively, you can use a dedicated estimating function for the simplified model structure. Linear polynomial estimation functions include

`oe`

,`bj`

,`arx`

and`armax`

.

## Alternatives

To estimate a polynomial model using time-series data, use

`ar`

.If the structure of the estimated polynomial model is known, that is, you know which polynomials will be active, then use the appropriate dedicated estimating function. For examples, for an ARX model, use

`arx`

. Other polynomial model estimating functions include`oe`

,`armax`

, and`bj`

.To estimate a continuous-time transfer function, use

`tfest`

. You can also use`oe`

, but only with continuous-time frequency-domain data.

## Version History

**Introduced in R2012a**