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Data acquisition failures sometimes result in missing measurements
both in the input and the output signals. When you import data that
contains missing values using the MATLAB^{®} Import Wizard, these
values are automatically set to `NaN`

. `NaN`

serves
as a flag for nonexistent or undefined data. When you plot data on
a time-plot that contains missing values, gaps appear on the plot
where missing data exists.

You can use `misdata`

to estimate missing
values. This command linearly interpolates missing values to estimate
the first model. Then, it uses this model to estimate the missing
data as parameters by minimizing the output prediction errors obtained
from the reconstructed data. You can specify the model structure you
want to use in the `misdata`

argument or estimate
a default-order model using the `n4sid`

method. For
more information, see the `misdata`

reference
page.

You can only use `misdata`

on time-domain
data stored in an `iddata`

object. For more information
about creating `iddata`

objects, see Representing Time- and Frequency-Domain Data Using iddata Objects.

For example, suppose `y`

and `u`

are
output and input signals that contain `NaN`

s. This
data is sampled at `0.2`

s. The following syntax
creates a new `iddata`

object with these input and
output signals.

dat = iddata(y,u,0.2) % y and u contain NaNs % representing missing data

Apply the `misdata`

command to the new data
object. For example:

dat1 = misdata(dat); plot(dat,dat1) % Check how the missing data % was estimated on a time plot

Malfunctions can produce errors in measured values, called *outliers*.
Such outliers might be caused by signal spikes or by measurement malfunctions.
If you do not remove outliers from your data, this can adversely affect
the estimated models.

To identify the presence of outliers, perform one of the following tasks:

Before estimating a model, plot the data on a time plot and identify values that appear out of range.

After estimating a model, plot the residuals and identify unusually large values. For more information about plotting residuals, see topics on the Residual Analysis page. Evaluate the original data that is responsible for large residuals. For example, for the model

`Model`

and validation data`Data`

, you can use the following commands to plot the residuals:

% Compute the residuals E = resid(Data,Model) % Plot the residuals plot(E)

Next, try these techniques for removing or minimizing the effects of outliers:

Extract the informative data portions into segments and merge them into one multiexperiment data set (see Extract and Model Specific Data Segments). For more information about selecting and extracting data segments, see Select Subsets of Data.

### Tip

The inputs in each of the data segments must be consistently exciting the system. Splitting data into meaningful segments for steady-state data results in minimum information loss. Avoid making data segments too small.

Manually replace outliers with

`NaN`

s and then use the`misdata`

command to reconstruct flagged data. This approach treats outliers as missing data and is described in Handling Missing Data. Use this method when your data contains several inputs and outputs, and when you have difficulty finding reliable data segments in all variables.Remove outliers by prefiltering the data for high-frequency content because outliers often result from abrupt changes. For more information about filtering, see Filtering Data.

The estimation algorithm can handle outliers by assigning a
smaller weight to outlier data. A robust error criterion applies an
error penalty that is quadratic for small and moderate prediction
errors, and is linear for large prediction errors. Because outliers
produce large prediction errors, this approach gives a smaller weight
to the corresponding data points during model estimation. Set the `ErrorThreshold`

estimation
option (see `Advanced.ErrorThreshold`

in, for example, `polyestOptions`

) to a nonzero value to
activate the correction for outliers in the estimation algorithm.

To learn more about the theory of handling missing data and
outliers, see the chapter on preprocessing data in *System
Identification: Theory for the User*, Second Edition, by
Lennart Ljung, Prentice Hall PTR, 1999.

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