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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/REC-html40/loose.dtd"><html><head> <title>Description of aar</title> <meta name="keywords" content="aar"> <meta name="description" content="Calculates adaptive autoregressive (AAR) and adaptive autoregressive moving average estimates (AARMA)"> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="generator" content="m2html © 2003 Guillaume Flandin"> <meta name="robots" content="index, follow"> <link type="text/css" rel="stylesheet" href="../m2html.css"></head><body><a name="_top"></a><div><a href="../index.html">Home</a> > <a href="index.html">tsa</a> > aar.m</div><!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td><td align="right"><a href="index.html">Index for tsa <img alt=">" border="0" src="../right.png"></a></td></tr></table>--><h1>aar</h1><h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="box"><strong>Calculates adaptive autoregressive (AAR) and adaptive autoregressive moving average estimates (AARMA)</strong></div><h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="box"><strong>function [a,e,REV,TOC,CPUTIME,ESU] = aar(y, Mode, arg3, arg4, arg5, arg6, arg7, arg8, arg9); </strong></div><h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="fragment"><pre class="comment"> Calculates adaptive autoregressive (AAR) and adaptive autoregressive moving average estimates (AARMA) of real-valued data series using Kalman filter algorithm. [a,e,REV] = aar(y, mode, MOP, UC, a0, A, W, V); The AAR process is described as following y(k) - a(k,1)*y(t-1) -...- a(k,p)*y(t-p) = e(k); The AARMA process is described as following y(k) - a(k,1)*y(t-1) -...- a(k,p)*y(t-p) = e(k) + b(k,1)*e(t-1) + ... + b(k,q)*e(t-q); Input: y Signal (AR-Process) Mode is a two-element vector [aMode, vMode], aMode determines 1 (out of 12) methods for updating the co-variance matrix (see also [1]) vMode determines 1 (out of 7) methods for estimating the innovation variance (see also [1]) aMode=1, vmode=2 is the RLS algorithm as used in [2] aMode=-1, LMS algorithm (signal normalized) aMode=-2, LMS algorithm with adaptive normalization MOP model order, default [10,0] MOP=[p] AAR(p) model. p AR parameters MOP=[p,q] AARMA(p,q) model, p AR parameters and q MA coefficients UC Update Coefficient, default 0 a0 Initial <a href="aar.html" class="code" title="function [a,e,REV,TOC,CPUTIME,ESU] = aar(y, Mode, arg3, arg4, arg5, arg6, arg7, arg8, arg9);">AAR</a> parameters [a(0,1), a(0,2), ..., a(0,p),b(0,1),b(0,2), ..., b(0,q)] (row vector with p+q elements, default zeros(1,p) ) A Initial Covariance matrix (positive definite pxp-matrix, default eye(p)) W system noise (required for aMode==0) V observation noise (required for vMode==0) Output: a AAR(MA) estimates [a(k,1), a(k,2), ..., a(k,p),b(k,1),b(k,2), ..., b(k,q] e error process (Adaptively filtered process) REV relative error variance MSE/MSY Hint: The mean square (prediction) error of different variants is useful for determining the free parameters (Mode, MOP, UC) REFERENCE(S): [1] A. Schloegl (2000), The electroencephalogram and the adaptive autoregressive model: theory and applications. ISBN 3-8265-7640-3 Shaker Verlag, Aachen, Germany. More references can be found at http://www.dpmi.tu-graz.ac.at/~schloegl/publications/</pre></div><!-- crossreference --><h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>This function calls:<ul style="list-style-image:url(../matlabicon.gif)"><li><a href="detrend.html" class="code" title="function [X,T]=detrend(t,X,p)">detrend</a> DETREND removes the trend from data, NaN's are considered as missing values</li></ul>This function is called by:<ul style="list-style-image:url(../matlabicon.gif)"></ul><!-- crossreference --><hr><address>Generated on Tue 17-Aug-2004 00:13:21 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address></body></html>⌨️ 快捷键说明
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