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Kalman Filter

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Kalman Filter Program


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Version 2.3 (July 2009)



The Kalman Filter is a recursive algorithm for updating linear projections of the system comprised by of an Observation Equation and a State Equation.


Observation Equation:


Kalman Observation Equation Image

State Equation:


Kalman State Equation


The user will supply a vector of observations, coefficients of variation on observation error and scale vector (qt).  The model will estimate two parameters: the state variable at time zero (b0) and the standard error on the state variable (sw).

The model will return a vector of Filtered and Smoothed observations.

There is a technical manual available with details of equations used in the model.  


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Meinhold, R and Meinhold, N. 1983. Understanding the Kalman Filter. The American Statistician, Vol. 37, No. 2 (May, 1983), pp. 123-127


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Version History


Kalman Version 2.3 (July 2009)  Includes the following changes

  • Calculation engine version 1.1 which has been modified to eliminate message "Attempting to take the derivative of sqrt(prevariable x) at x=0" and subsequent "Run Failed" message in the GUI.

  • GUI updates to eliminate a problem with the scroll bars on the Data Observations page and to correct a "Run Failed" message in certain situations when working with a new case.

  • New 'Combined' plot showing both the Filter and Smooth series on one chart.

Kalman Version 2.1 (January 2009) was upgraded from 2.0 to support Windows Vista.  

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Older Version Changes 


Version 2.0 was upgraded from version 1.0 to support the Microsoft .Net platform.

Version 1.0, was the initial beta version.


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NOAA Fisheries Toolbox Version 3.1

website last modified May 16, 2016


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