Compute estimate of autoregressive (AR) model parameters using YuleWalker method
Estimation / Parametric Estimation
dspparest3
The YuleWalker AR Estimator block uses the YuleWalker AR method, also called the autocorrelation method, to fit an autoregressive (AR) model to the windowed input data by minimizing the forward prediction error in the least squares sense. This formulation leads to the YuleWalker equations, which are solved by the LevinsonDurbin recursion. Block outputs are always nonsingular.
The YuleWalker AR Estimator block can output the AR model coefficients as polynomial coefficients, reflection coefficients, or both. The input can be a row vector, a column vector, or an unoriented vector which is assumed to be the output of an AR system driven by white noise. The block accepts matrices, and treats each column of the matrix as a channel. If the input is a row vector of length N, the input is treated as N different channels. If the input is an unoriented vector, the input is treated as a single channel. The block computes the normalized estimate of the AR system parameters, A(z), independently for each successive input frame.
$$H\left(z\right)=\frac{\sqrt{G}}{A\left(z\right)}=\frac{\sqrt{G}}{1+a(2){z}^{1}+\dots +a\left(p+1\right){z}^{p}}$$
When you select Inherit estimation order from input dimensions, the order p of the allpole model is one less than the length of each input channel. Otherwise, the order is the value specified by the Estimation order parameter. To guarantee a valid output, you must set the Estimation order parameter to be a scalar less than or equal to half the input channel length. The YuleWalker AR Estimator and Burg AR Estimator blocks return similar results for large frame sizes.
When Output(s) is set to A
, port A is enabled.
For each channel, port A outputs a column of length p+1 that contains
the normalized estimate of the AR model coefficients in descending powers of
z
[1 a(2) ... a(p+1)]
When Output(s) is set to K
, port K is enabled.
For each channel, port K outputs a lengthp column whose elements are
the AR model reflection coefficients. When Output(s) is set to
A and K
, both port A and K are enabled, and each port outputs the
respective AR model coefficients for each channel.
The square of the model gain, G, is provided at port G. G is a scalar for each channel.
See the Burg AR Estimator block reference page for a comparison of the Burg AR Estimator, Covariance AR Estimator, Modified Covariance AR Estimator, and YuleWalker AR Estimator blocks.
The type of AR model coefficients output by the block. The block can
output polynomial coefficients (A
), reflection
coefficients (K
), or both (A and
K
).
When selected, sets the estimation order p to one less than the length of each input channel.
The order of the AR model, p. This parameter is enabled when you do not select Inherit estimation order from input dimensions.
Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: PrenticeHall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood Cliffs, NJ: PrenticeHall, 1987.
Port  Supported Data Types 

Input 

A 

K 

G 

Burg AR Estimator  DSP System Toolbox 
Covariance AR Estimator  DSP System Toolbox 
Modified Covariance AR Estimator  DSP System Toolbox 
YuleWalker Method  DSP System Toolbox 
aryule  Signal Processing Toolbox 