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# rplr

Estimate general input-output models using recursive pseudolinear regression method

## Syntax

```thm = rplr(z,nn,adm,adg)
[thm,yhat,P,phi] = rplr(z,nn,adm,adg,th0,P0,phi0)
```

## Description

`rplr` is not compatible with MATLAB® Coder™ or MATLAB Compiler™.

This is a direct alternative to `rpem` and has essentially the same syntax. See `rpem` for an explanation of the input and output arguments.

`rplr` differs from `rpem` in that it uses another gradient approximation. See Section 11.5 in Ljung (1999). Several of the special cases are well-known algorithms.

When applied to ARMAX models, (`nn = [na nb nc 0 0 nk]`), `rplr` gives the extended least squares (ELS) method. When applied to the output-error structure (`nn = [0 nb 0 0 nf nk]`), the method is known as HARF in the `adm = 'ff'` case and SHARF in the `adm = 'ng'` case.

`rplr` can also be applied to the time-series case in which an ARMA model is estimated with:

```z = y nn = [na nc] ```

## Examples

### Estimate Output-Error Model Parameters Using Recursive Pseudolinear Regression

Specify the order and delays of an Output-Error model structure.

```na = 0; nb = 2; nc = 0; nd = 0; nf = 2; nk = 1;```

Load the estimation data.

`load iddata1 z1`

Estimate the parameters using forgetting factor algorithm, with forgetting factor 0.99.

`EstimatedParameters = rplr(z1,[na nb nc nd nf nk],'ff',0.99);`

## References

For more information about HARF and SHARF, see Chapter 11 in Ljung (1999).

## See Also

### Topics

Introduced before R2006a

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