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 AAR 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://pub.ist.ac.at/~schloegl/publications/