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misdata

Reconstruct missing input and output data

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Syntax

Datae = misdata(Data)
Datae = misdata(Data,Model)
Datae = misdata(Data,MaxIterations,Tol)
Datae = misdata(___,Name,Value)

Description

Datae = misdata(Data) reconstructs missing input and output time-domain data.

Data contains time-domain data, which can be in the form of a timetable, a comma-separated pair of numeric matrices, or a time-domain iddata object.

Missing data samples (both in inputs and in outputs) are expressed as NaNs. Datae, which is the same form as Data, contains the reconstructed data set where the missing data has been replaced by reasonable estimates.

Datae = misdata(Data,Model) specifies a model used for the reconstruction of missing data. Model is any linear identified model (idtf, idproc, idgrey, idpoly, idss). If no suitable model is known, it is estimated in an iterative fashion using default order state-space models.

Datae = misdata(Data,MaxIterations,Tol) specifies maximum number of iterations and tolerance. MaxIterations is the maximum number of iterations carried out (the default is 10). The iterations are terminated when the difference between two consecutive data estimates differs by less than Tol%. The default value of Tol is 1.

Datae = misdata(___,Name,Value) uses additional model options specified by one or more name-value arguments.

The available arguments consist of:

  • InputName and OutputName — Input and output channel names. Use these arguments especially when data is a timetable that has more variables than you want to use, or when there. Also use OutputName to identify the output channels when the timetable data contains more than one output variable. Otherwise, the software interprets only the last variable as an output channel.

    For example, specify the input and output signal variable names using Datae = misdata(data,'InputName',["u1","u3"],'OutputName',"y1"). You can use this syntax with any of the previous input-argument combinations.

  • Ts and TimeUnit — Sample time and time units. Use these arguments especially when you are data contains numeric matrices, which do not provide sample-time information.

Examples

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Open Live Script

Load data with missing data points.

load('missing_data.mat')

missing_data is an iddata object containing input-output data.

Plot the data.

plot(missing_data)

Figure contains 2 axes objects. Axes object 1 with title y1 contains an object of type line. This object represents missing\_data. Axes object 2 with title u1 contains an object of type line. This object represents missing\_data.

The output data contains missing data between indices 10 and 100.

To reconstruct missing data using a specified model, estimate the model using measured data that has no missing samples. In this example, estimate a transfer function model with 2 poles.

data2 = missing_data(101:end);
model = tfest(data2,2);

Reconstruct the missing data.

datae = misdata(missing_data,model);

Plot the original and reconstructed data.

plot(missing_data,'b',datae,'--r')

Figure contains 2 axes objects. Axes object 1 with title y1 contains 2 objects of type line. These objects represent missing\_data, datae. Axes object 2 with title u1 contains 2 objects of type line. These objects represent missing\_data, datae.

If you do not specify a model for reconstructing the data, the software alternates between estimating missing data and estimating models, based on the current data reconstruction.

Algorithms

For a given model, the missing data is estimated as parameters so as to minimize the output prediction errors obtained from the reconstructed data. See Section 14.2 in Ljung (1999). Treating missing outputs as parameters is not the best approach from a statistical point of view, but is a good approximation in many cases.

When no model is given, the algorithm alternates between estimating missing data and estimating models, based on the current reconstruction.

Version History

Introduced before R2006a

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See Also

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