Changeset 290 for doc/html/tut_arx.html

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Timestamp:
03/06/09 15:03:45 (15 years ago)
Author:
smidl
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correction of ARX tutorial

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  • doc/html/tut_arx.html

    r287 r290  
    22<html><head><meta http-equiv="Content-Type" content="text/html;charset=UTF-8"> 
    33<title>mixpp: Theory of ARX model estimation</title> 
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    45<link href="doxygen.css" rel="stylesheet" type="text/css"> 
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    66</head><body> 
    7 <!-- Generated by Doxygen 1.5.6 --> 
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    99<!-- 
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    8787On-line estimation</a></h2> 
    8888For online estimation with stationary parameters can be easily achieved by collecting the sufficient statistics described above recursively.<p> 
    89 Extension to non-stationaly parameters, <img class="formulaInl" alt="$ \theta_t , r_t $" src="form_106.png"> can be achieved by operation called forgetting. This is an approximation of Bayesian filtering see [Kulhavy]. The resulting algorithm is defined by manipulation of sfficient statistics: <dl> 
     89Extension to non-stationaly parameters, <img class="formulaInl" alt="$ \theta_t , r_t $" src="form_106.png"> can be achieved by operation called forgetting. This is an approximation of Bayesian filtering see [Kulhavy]. The resulting algorithm is defined by manipulation of sufficient statistics: <dl> 
    9090<dt>Information matrix </dt> 
    9191<dd>which is a sum of outer products <p class="formulaDsp"> 
    92 <img class="formulaDsp" alt="\[ V_t = V_{t-1} + \phi \left[\begin{array}{c}y_{t}\\ \psi_{t}\end{array}\right] \begin{array}{c} [y_{t}',\,\psi_{t}']\\ \\\end{array} +(1-\phi) V_0 \]" src="form_107.png"> 
     92<img class="formulaDsp" alt="\[ V_t = \phi V_{t-1} + \left[\begin{array}{c}y_{t}\\ \psi_{t}\end{array}\right] \begin{array}{c} [y_{t}',\,\psi_{t}']\\ \\\end{array} +(1-\phi) V_0 \]" src="form_121.png"> 
    9393<p> 
    9494 </dd> 
    9595<dt>"Degree of freedom" </dt> 
    9696<dd>which is an accumulator of number of data records <p class="formulaDsp"> 
    97 <img class="formulaDsp" alt="\[ \nu_t = \nu_{t-1} + \phi + (1-\phi) \nu_0 \]" src="form_108.png"> 
     97<img class="formulaDsp" alt="\[ \nu_t = \phi \nu_{t-1} + 1 + (1-\phi) \nu_0 \]" src="form_122.png"> 
    9898<p> 
    9999 </dd> 
    … …  
    123123</ul> 
    124124</div> 
    125 <hr size="1"><address style="text-align: right;"><small>Generated on Wed Mar 4 18:50:14 2009 for mixpp by&nbsp; 
     125<hr size="1"><address style="text-align: right;"><small>Generated on Fri Mar 6 15:01:37 2009 for mixpp by&nbsp; 
    126126<a href="http://www.doxygen.org/index.html"> 
    127 <img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address> 
     127<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address> 
    128128</body> 
    129129</html>