Tuned feedforward LMS filter with feedback control
First Claim
1. A method of tuning an adaptive feedforward noise cancellation algorithm, comprising the acts of:
 providing a feedback active noise reduction (ANR) circuit, for providing an ANR error signal;
providing a feedforward LMS tuning algorithm including at least first and second time varying parameters wherein said feedforward LMS tuning algorithm includes the formulas;
γ
_{k}=W_{k}^{T}X_{k }W_{k+1}=λ
_{k}W_{k}+μ
_{k}X_{k}e_{k}; and
adjusting said at least first and second time varying parameters as a function of instantaneous measured acoustic noise, a weight vector length and measurement noise variance, wherein said time varying parameters include;
$\begin{array}{c}{\mathrm{\mu k=\ue89e\frac{{\mathrm{\mu o\ue89e{\mathrm{\lambda k}}_{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\left({X}_{k}+{Q}_{k}\right)}{\mathrm{\lambda k=\ue89e\frac{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\left({X}_{k}+{Q}_{k}\right)2\ue89eL\ue89e\text{\hspace{1em}\ue89e\sigma q2(Xk+Qk)T\ue89e(Xk+Qk)}}{}}}_{}}}_{}}{}}}_{}\end{array}$wherein X_{k}=X_{k}+Q_{k }is a measured reference signal;
Q_{k }is measurement noise, including electronic noise and quantization noise;
σ
_{q}^{2 }is the known or measured variance of the measurement noise;
L is the length of the LMS weight vector W_{k}; and
e_{k }is an error signal which is the net result of both the feedforward method and the feedback circuit.
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Abstract
A method to automatically and adaptively tune a leaky, normalized leastmeansquare (LNLMS) algorithm so as to maximize the stability and noise reduction performance in feedforward adaptive noise cancellation systems. The automatic tuning method provides for timevarying tuning parameters λ_{k }and μ_{k }that are functions of the instantaneous measured acoustic noise signal, weight vector length, and measurement noise variance. The method addresses situations in which signaltonoise ratio varies substantially due to nonstationary noise fields, affecting stability, convergence, and steadystate noise cancellation performance of LMS algorithms. The method has been embodied in the particular context of active noise cancellation in communication headsets. However, the method is generic, in that it is applicable to a wide range of systems subject to nonstationary, i.e., timevarying, noise fields, including sonar, radar, echo cancellation, and telephony. Further, the hybridization of the disclosed Lyapunovtuned feedforward LMS filter with a feedback controller as also disclosed herein enhances stability margins, robustness, and further enhances performance.
113 Citations
5 Claims

1. A method of tuning an adaptive feedforward noise cancellation algorithm, comprising the acts of:

providing a feedback active noise reduction (ANR) circuit, for providing an ANR error signal;
providing a feedforward LMS tuning algorithm including at least first and second time varying parameters wherein said feedforward LMS tuning algorithm includes the formulas;
γ
_{k}=W_{k}^{T}X_{k }W_{k+1}=λ
_{k}W_{k}+μ
_{k}X_{k}e_{k}; and
adjusting said at least first and second time varying parameters as a function of instantaneous measured acoustic noise, a weight vector length and measurement noise variance, wherein said time varying parameters include;
$\begin{array}{c}{\mathrm{\mu k=\ue89e\frac{{\mathrm{\mu o\ue89e{\mathrm{\lambda k}}_{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\left({X}_{k}+{Q}_{k}\right)}{\mathrm{\lambda k=\ue89e\frac{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\left({X}_{k}+{Q}_{k}\right)2\ue89eL\ue89e\text{\hspace{1em}\ue89e\sigma q2(Xk+Qk)T\ue89e(Xk+Qk)}}{}}}_{}}}_{}}{}}}_{}\end{array}$ wherein X_{k}=X_{k}+Q_{k }is a measured reference signal;
Q_{k }is measurement noise, including electronic noise and quantization noise;
σ
_{q}^{2 }is the known or measured variance of the measurement noise;
L is the length of the LMS weight vector W_{k}; and
e_{k }is an error signal which is the net result of both the feedforward method and the feedback circuit.  View Dependent Claims (2, 3)


4. A method of tuning an algorithm for providing noise cancellation, comprising the acts of:

receiving a measured reference signal, the measured reference signal including a measurement noise component having a measurement noise value of known variance; and
generating an acoustic noise cancellation signal according to the formulas;
γ
_{k}=W_{k}^{T}X_{k }W_{k+1}=λ
_{k}W_{k}+μ
_{k}X_{k}e_{k }wherein time varying parameters λ
_{k }and μ
_{k }are determined according to the formulas;
$\begin{array}{c}{\mathrm{\mu k=\ue89e\frac{{\mathrm{\mu o\ue89e{\mathrm{\lambda k}}_{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\left({X}_{k}+{Q}_{k}\right)}{\mathrm{\lambda k=\ue89e\frac{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\left({X}_{k}+{Q}_{k}\right)2\ue89eL\ue89e\text{\hspace{1em}\ue89e\sigma q2(Xk+Qk)T\ue89e(Xk+Qk)}}{}}}_{}}}_{}}{}}}_{}\end{array}$ wherein X_{k}=X_{k}+Q_{k }is a measured reference signal;
Q_{k }is electronic noise and quantization;
σ
_{q}^{2 }is a known variance of the measurement noise;
L is the length of weight vector W_{k}; and
e_{k }is an error signal which is the net result of both a feedforward tuning method and a feedback active noise reduction method.


5. A method of tuning a least mean square (LMS) filter comprising the acts of:

providing a feedback active noise reduction (ANR) circuit, for providing an ANR error signal;
formulating a Lyapunov function of a LMS filter weight vector, a reference input signal, a measurement noise on the measured reference input signal, a time varying leakage parameter λ
_{k}, and a step size parameter μ
_{k};
using the resultant Lyapunov function to identify formulas for computing the time varying leakage parameter λ
_{k }and step size parameter μ
_{k }that maximize stability and performance of the resultant LMS filter weight vector update equationW_{k+1}=λ
_{k}W_{k}+μ
_{k}e_{k}X_{k }wherein said time varying parameters determined are ${\mathrm{\mu k=\frac{{\mathrm{\mu o\ue89e{\mathrm{\lambda k}}_{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\text{\hspace{1em}\ue89e(Xk+Qk)}}}}_{}}{}}}_{}$${\mathrm{\lambda k=\frac{{\left({X}_{k}+{Q}_{k}\right)}^{T}\ue89e\text{\hspace{1em}\ue89e(Xk+Qk)2\ue89eL\ue89e\hspace{1em}\ue89e\sigma q2(Xk+Qk)T\ue89e\hspace{1em}\ue89e(Xk+Qk).}}{}}}_{}$ wherein X_{k}=X_{k}+Q_{k }is a measured reference signal;
Q_{k }is electronic noise and quantization;
σ
_{q}^{2 }is a known variance of the measurement noise;
L is the length of weight vector W_{k}; and
e_{k}is an error signal which is the net result of both the ANR circuit and the LMS filter.

1 Specification