:orphan:

.. ****************************************************************************
.. CUI
..
.. The Advanced Framework for Simulation, Integration, and Modeling (AFSIM)
..
.. The use, dissemination or disclosure of data in this file is subject to
.. limitation or restriction. See accompanying README and LICENSE for details.
.. ****************************************************************************

WSF_ALPHA_BETA_FILTER
---------------------

.. model:: filter WSF_ALPHA_BETA_FILTER
   
.. parsed-literal::

   filter <name> :model:`WSF_ALPHA_BETA_FILTER`
      ... Commands_ ...
   end_filter
 
Overview
========

Defines an alpha-beta filter for filtering tracks.

.. block:: WSF_ALPHA_BETA_FILTER

Commands
========

.. command:: alpha <value>
   
   Defines the filter's alpha (position) parameter.
   
   Default: 0.0

.. command:: beta <value>
   
   Defines the filter's beta (velocity) parameter.
   
   Default: 0.0

.. command:: debug
   
   Writes debugging information to the standard output.

Methodology
===========

The alpha-beta filter operates using the following algorithm:

   :math:`X_f  = X'_p + \alpha \times (X_m - X'_p)`

   :math:`V_f = V'_f + \frac{\beta}{dT} \times (X_m - X'_p)`

   :math:`X_p = X_f + dT \times V_f`

Where:

   +----------------+---------------------------------------+
   | :math:`\alpha` | The value of alpha_                   |
   +----------------+---------------------------------------+
   | :math:`\beta`  | The value of beta_                    |
   +----------------+---------------------------------------+
   | :math:`X_m`    | The measured position                 |
   +----------------+---------------------------------------+
   | :math:`X_f`    | The filtered position                 |
   +----------------+---------------------------------------+
   | :math:`X_p`    | The predicted position                |
   +----------------+---------------------------------------+
   | :math:`V_f`    | The filtered velocity                 |
   +----------------+---------------------------------------+
   | :math:`dT`     | The time since the last filter update |
   +----------------+---------------------------------------+

The primed values are the filtered values from the last filter update.