New Normalized LMS Algorithms Based on the Kalman Filter

Lopes, Paulo A. C.; Gerald, José A. B.

doi:10.1109/iscas.2007.378235

Cited by 23 publications

(15 citation statements)

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“…Let p(n), s(n), x(n), and y(n) be the vectors formed by grouping the corresponding scalars (with the same name) when i goes from 1 to N. Then, (3)-(6) can be written in vector notation as (20)- (26) in Table 1 with suitable values for q(n) and disregarding the max in (25), which will be discussed below.…”

Section: Fxlms Algorithmmentioning

confidence: 99%

“…It has the effect of reducing the sensitivity to measurement noise when the reference signal [x i (n) or y i (n)] takes low values (preventing division by zero). 26 In (22), the measurement noise q v in the work of Lopes and Gerald 26 is approximately upper bounded by q j (n), and the initial variance of the SP filter coefficients estimate is set to 2 w0 = 1. In the case of s(n), q(n) was selected to be sp q j (n)∕2 similarly to other works, 13,14,25 and as suggested by eq.…”

Section: Fxlms Algorithmmentioning

confidence: 99%

“…In the case of p(n), this is not very important since x H (n)x(n) = N, and q(n) is set to a small constant value only to prevent division by zero when the outputs of the oscillators are still off. 26 Note that this last approximation degrades the performance when s i takes very small or very large values but in practice, it is usually possible to choose a physical setup where the gains of the pre-amplifier and power-amplifier are chosen so that the gain of the SP is close to one. 38 in the work of Lopes and Gerald.…”

Section: Fxlms Algorithmmentioning

confidence: 99%

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A narrowband active noise control system with reference synthesis

Lopes

Gerald

2019

Adaptive Control & Signal

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Most active noise control (ANC) algorithms require a model of the secondary path (SP). If there are large changes in the SP, online SP modeling algorithms may not be able to follow the changes quickly enough to prevent divergence. In this work, the mirror-MFxLMS (MMFxLMS) is adapted to narrowband ANC, and the resulting algorithm is analyzed. The MMFxLMS is an algorithm similar to the MFxLMS and FxLMS but has online SP modeling; it is stable for any SP estimate and does not require auxiliary noise. In addition, a technique to alternate between MFxLMS and MMFxLMS is proposed, resulting in the M 3 FxLMS algorithm, which does not sacrifice performance and assures stability. However, the M 3 FxLMS requires a reference signal that is not available in feedback ANC.Feedback ANC is important in many practical cases, for instance, in ANC headphones. To solve this problem, a technique is proposed to synthesize a reference formed by a sum of sinusoids using measurements from the error sensor signal.This technique uses the fast Fourier transform to obtain estimates of the harmonic frequencies of the periodic noise components, and then refines and tracks these using a phase-locked loop (PLL). The resulting algorithm enables a stable ANC system, even under large and sudden changes in the SP. The proposed PLL is also new and has a lock-in range equal to the full band of the system. KEYWORDS active noise control (ANC), feedback, FxLMS, narrowband, PLL, stability INTRODUCTIONActive noise control (ANC) is a technique where waves (antinoise) with opposite phase to a noise signal are used to reduce the noise signal level. 1 In feedforward ANC, a signal called the reference signal is used to generate the antinoise signal, using additional information from a set of error sensors that indicates the residual noise level. In feedback ANC, the signal from a set of error sensors is used to generate the antinoise signal. In narrowband ANC, the noise to be canceled is assumed to be periodic or a sum of periodic signals. This paper addresses single-channel (one error sensor) narrowband feedback ANC, with applications, for instance, in ANC headphones.Most ANC algorithms require a secondary path (SP) model and can become unstable if that model is not sufficiently accurate. The SP model can be obtained before the start of noise canceling (offline) or during operation (online). If the SP changes significantly during noise cancelation, online SP modeling is required. However, even with online SP modeling, if there is a large and sudden change, the model may not be updated quickly enough and the algorithm may become unstable. To solve this problem, the authors have previously proposed the mirror-MFxLMS (MMFxLMS) algorithm. 2 1118

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Section: Fxlms Algorithmmentioning

confidence: 99%

Section: Fxlms Algorithmmentioning

confidence: 99%

Section: Fxlms Algorithmmentioning

confidence: 99%

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A narrowband active noise control system with reference synthesis

Lopes

Gerald

2019

Adaptive Control & Signal

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“…Some simulation based results exist (e.g., [57], [102], [103]), but the answer of which one is the best appears to depend upon the setting and regime, which are themselves often hard to characterize. Oftentimes, therefore, the choice of algorithm is domain dependent and experience driven.…”

Section: Solving the Tracking Problemmentioning

confidence: 99%

Graphical model driven methods in adaptive system identification

Yellepeddi¹

2016

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Identifying and tracking an unknown linear system from observations of its inputs and outputs is a problem at the heart of many different applications. Due to the complexity and rapid variability of modern systems, there is extensive interest in solving the problem with as little data and computation as possible.This thesis introduces the novel approach of reducing problem dimension by exploiting statistical structure on the input. By modeling the input to the system of interest as a graph-structured random process, it is shown that a large parameter identification problem can be reduced into several smaller pieces, making the overall problem considerably simpler.Algorithms that can leverage this property in order to either improve the performance or reduce the computational complexity of the estimation problem are developed. The first of these, termed the graphical expectation-maximization least squares (GEM-LS) algorithm, can utilize the reduced dimensional problems induced by the structure to improve the accuracy of the system identification problem in the low sample regime over conventional methods for linear learning with limited data, including regularized least squares methods.Next, a relaxation of the GEM-LS algorithm termed the relaxed approximate graph structured least squares (RAGS-LS) algorithm is obtained that exploits structure to perform highly efficient estimation. The RAGS-LS algorithm is then recast into a recursive framework termed the relaxed approximate graph structured recursive least squares (RAGS-RLS) algorithm, which can be used to track time-varying linear systems with low complexity while achieving tracking performance comparable to much more computationally intensive methods.The performance of the algorithms developed in the thesis in applications such as channel identification, echo cancellation and adaptive equalization demonstrate that the gains admitted by the graph framework are realizable in practice. The methods have wide applicability, and in particular show promise as the estimation and adaptation algorithms for a new breed of fast, accurate underwater acoustic modems.The contributions of the thesis illustrate the power of graphical model structure in simplifying difficult learning problems, even when the target system is not directly structured.Thesis Supervisor: James C. Preisig Title: Scientist Emeritus, Woods Hole Oceanographic Institution AcknowledgmentsPiglet noticed that even though he had a Very Small Heart, it could hold a rather large amount of Gratitude. Winnie the PoohA.A.MilneMy years at MIT have been about so much more than a degree. In the past six years you have introduced to more worlds than I ever knew existed. As this long and wonderful journey ends, I find that my heart can, too, hold so much gratitude, for everything that you have given.Of course, I haven't said who "you" is, so here goes.It is impossible to write any list of acknowledgements without having at the very top my thesis advisor Dr. James Preisig, who has truly been a wide-angle lens f...

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“…The least-mean-square (LMS) algorithm and the recursive least-squares (RLS) algorithms have established themselves as the principal tools for linear adaptive filtering. Lopes and Gerald used the LMS algorithm to get the faster convergence and a much higher noise immunity when the reference signal vector norm takes on a low value [2], while Barnawi to get much less convergence time [3]. Rosendo Macías and Expósito presented a method for self-tuning of the model error covariance to overcome the sudden changes of the input signal, so that they could properly track signal fluctuations in digital protection applications [4].…”

Section: Introductionmentioning

confidence: 99%

Melt Pressure Signature Tracking Using an Adaptive Kalman Filter in Microinjection Molding

Liu

Yung

et al. 2013

Advances in Mechanical Engineering

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In order to manufacture high quality microproducts, the precision control of injected plastic melt in the injection chamber during a microinjection process requires real-time tracking of the melt pressure when the melt passes through the nozzle. A novel type of adaptive Kalman filter algorithm based on F-distribution is proposed in this paper. This adaptive Kalman filter can switch the system between the steady state and transient state by comparing the differences of input data in F-distribution. By resetting the Kalman gain and other relevant parameters, the adaptive function guarantees the convergence of the filtered signal during the tracking process and tracks the moments which sudden changes occur in the pressure signature. The simulation experiment results show that the method can reduce the effect of measurement noise more quickly and effectively. The method is proven to be effective for microinjection molding applications.

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New Normalized LMS Algorithms Based on the Kalman Filter

Cited by 23 publications

References 5 publications

A narrowband active noise control system with reference synthesis

A narrowband active noise control system with reference synthesis

Graphical model driven methods in adaptive system identification

Melt Pressure Signature Tracking Using an Adaptive Kalman Filter in Microinjection Molding

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