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Reconstructing Improper Values with Reference Data
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:doc:`/SingleStepClassifiers/CausalStep/index`

This step uses the reference data to reconstruct improper values. An improper value :math:`Y_i` at time step :math:`i` is estimated using the following formula: 

.. math::

   {\hat{Y}_i = \frac{Y_{i-1}}{Y^r_{i-1}} Y^r_i}\quad\text{,}

where :math:`\hat{Y}_i` is the reconstructed value at time step :math:`i` and :math:`Y^r_i` is the reference data value at time step :math:`i`\ .

.. rubric:: Input Parameters

1. Input data including improper values

2. Definition of improper values ('nan', 'inf', or 'null', etc.)

.. rubric:: Output Parameters

1. Output data excluding improper values

.. rubric:: Workflow

.. image:: workflow.svg


.. rubric:: References

- T.\  Bellemans, B. De Schutter, and B. De Moor, Data acquisition, interfacing and pre-processing of highway traffic data, In Proceedings of Telematics Automotive 2000, Birmingham, UK, vol. 1, pp. 4/1-4/7, Apr. 2000.