Filter Design Toolbox

adaptfilt.rls

Construct a direct-form recursive least squares (RLS) FIR adaptive filter object

Syntax

• ha = adaptfilt.rls(l,lambda,invcov,coeffs,states)
  

Description

ha = adaptfilt.rls(l,lambda,invcov,coeffs,states) constructs an FIR direct-form RLS adaptive filter ha.

Input Arguments

Entries in the following table describe the input arguments for adaptfilt.rls.

Input Argument	Description
l	Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. l defaults to 10.
lambda	RLS forgetting factor. This is a scalar and should lie in the range (0, 1]. lambda defaults to 1.
invcov	Inverse of the input signal covariance matrix. For best performance, you should initialize this matrix to be a positive definite matrix.
coeffs	Vector of initial filter coefficients. it must be a length l vector. coeffs defaults to length l vector with elements equal to zero.
states	Vector of initial filter states for the adaptive filter. It must be a length l-1 vector. states defaults to a length l-1 vector of zeros.

adaptfilt.rls Object Properties

Since your adaptfilt.rls filter is an object, it has properties that define its behavior in operation. Note that many of the properties are also input arguments for creating adaptfilt.rls objects. To show you the properties that apply, this table lists and describes each property for the filter object.

Name	Range	Description
Algorithm	None	Defines the adaptive filter algorithm the object uses during adaptation.
FilterLength	Any positive integer	Reports the length of the filter, the number of coefficients or taps. Remember that filter length is filter order + 1.
Coefficients	Vector containing l elements	Vector containing the initial filter coefficients. It must be a length l vector where l is the number of filter coefficients. coeffs defaults to length l vector of zeros when you do not provide the argument for input.
States	Double array	Vector of the adaptive filter states. states defaults to a vector of zeros which has length equal to (l + projectord - 2).
ForgettingFactor	Scalar	Forgetting factor of the adaptive filter. This is a scalar and should lie in the range (0, 1]. It defaults to 1. Setting forgetting factor = 1 denotes infinite memory while adapting to find the new filter. Note that this is the lambda input argument.
KalmanGain	Vector of size (l,1)	Empty when you construct the object, this gets populated after you run the filter.
InvCov	Matrix of size l-by-l	Upper-triangular Cholesky (square root) factor of the input covariance matrix. Initialize this matrix with a positive definite upper triangular matrix.
ResetBeforeFiltering	off or on	Determine whether the filter states get restored to their starting values for each filtering operation. The starting values are the values in place when you create the filter if you have not changed the filter since you constructed it. ResetBeforeFiltering returns to zero any state that the filter changes during processing. Defaults to 'on'.
NumSamplesProcessed	Any integer	Returns the number of samples processed during filtering. Defaults to zero.

Examples

System Identification of a 32-coefficient FIR filter over 500 adaptation iterations.

• x  = randn(1,500);     % Input to the filter
  b  = fir1(31,0.5);     % FIR system to be identified
  n  = 0.1*randn(1,500); % Observation noise signal
  d  = filter(b,1,x)+n;  % Desired signal
  P0 = 10*eye(32); % Initial sqrt correlation matrix inverse
  lam = 0.99;            % RLS forgetting factor
  ha = adaptfilt.rls(32,lam,P0);
  [y,e] = filter(ha,x,d);
  subplot(2,1,1); plot(1:500,[d;y;e]);
  title('System Identification of an FIR Filter');
  legend('Desired','Output','Error');
  xlabel('Time Index'); ylabel('Signal Value');
  subplot(2,1,2); stem([b.',ha.Coefficients.']);
  legend('Actual','Estimated'); 
  xlabel('Coefficient #'); ylabel('Coefficient valUe'); grid on;
  

See Also

adaptfilt.hrls,adaptfilt.hswrls, adaptfilt.qrdrls

adaptfilt.qrdrls

adaptfilt.sd