Adaptive Filtering: Applications and Implementation

How Good is Your Predictor? Expanding Confidence Intervals To Define Probability Densities On Adaptive Parameters

Authors:

Mark Dzwonczyk,
Teresa H.Y. Meng,

Page (NA) Paper number 2160

Abstract:

A method is proposed to measure the performance of linear predictors as they track non-stationary stochastic processes. Classical linear regression techniques are combined with a novel use of instantaneous error to define the likelihood that the coefficients of a linear predictor adequately capture a system's state. The resultant probability measure serves as a metric of predictor performance: a probability near unity indicates that the predictor is performing well, while a probability near zero indicates the state of the system is poorly captured by the coefficients. The approach is extended to trace coefficients, weighted by these probabilities, as they move about in a space of possible states. The probability measure provides an instantaneous confidence measure of the route that the system proceeds upon within that space: a likelihood roadmap of the state of the system through time. Specifically, the method is applied to the important problem of predicting the vibration signature of rotorcraft gearboxes as they mechanically fail. Actual data from US Navy drivetrain teststands are used to validate the method and underlying assumptions.

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Fast QR Based IIR Adaptive Filtering Algorithm

Authors:

Mounir Bhouri,

Page (NA) Paper number 2476

Abstract:

In this paper, we present a new QR based algorithm for IIR adaptive filtering. This algorithm achieves a reduction of complexity with regard to the IIR-QR algorithm by using a block reduction transformation. Moreover, this new approach make it possible to directly transform fast FIR algorithm into fast O(N) versions of the IIR algorithm. Therefore, we derive a fast version of the algorithm from the rotation-based lattice algorithm (QR-LSL). Simulations, have proven the fast convergence and the good numerical properties of both algorithms for systems satisfying the strictly positive real (SPR) condition.

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Cone Constrained Adaptive Algorithms and Multiple Access Interference Cancellation

Authors:

Milos I Doroslovacki,
Branimir R Vojcić,

Page (NA) Paper number 2256

Abstract:

A parameterization of the cone around a given vector in N-dimensional vector space is derived. Vectors obtained by changing the parameter values can not escape the cone. The constraint is useful when it is known that an optimal vector of filter coefficients is close in direction with the given vector. Adaptive filtering algorithms that use the steepest descent method and stochastic gradient approximation are developed for the case of filter coefficients constrained in the cone. There is no need for monitoring the constraint since it is always satisfied by the construction. Two optimization criteria are explicitly considered: the least mean square and constant modulus. The cone constrained constant modulus algorithm (CMA) is applied to the problem of user detection in a synchronous direct sequence code division multiple access system. Its convergence is compared with the plain CMA and back projection CMA. Under severe conditions the cone constrained CMA is the only one who locks to the desired user.

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Theoretical Aspects of Power Reduction for Adaptive Filters

Authors:

Robby Gupta,
Alfred O Hero,

Page (NA) Paper number 2010

Abstract:

Adaptive filters are used in a number of applications, many of which can benefit from a reduction in power. In this paper we present derivations of the approximate expressions for the increase in mean square error of the LMS adaptive algorithm when the total processing power is decreased.

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A Fast Weighted Subband Adaptive Algorithm

Authors:

Khaled A Mayyas,
T. Aboulnasr, School of Information Technology and Engineering, Faculty of Engineering, University of Ottawa, Ottawa, Canada, K1N 6N5 (Canada)

Page (NA) Paper number 1949

Abstract:

The block algorithm in [1] has illustrated significant improvement in performance over the NLMS algorithm. However, it is known that block processing algorithms have lower tracking capabilities than their sample-by-sample counterparts. The Fast Affine Projection (FAP) algorithm [2] also outperforms the NLMS with a slight increase in complexity, but involves the fast calculation of the inverse of a covariance matrix of the input data that could undermine the performance of the algorithm. In this paper, we present a sample-by-sample version of the algorithm in [1] and develop a low complexity implementation of this algorithm using a similar approach to that in [2]. The new fast algorithm does not require matrix inversion thus alleviating the drawbacks of the FAP algorithm. A variable step size version of the proposed algorithm is also presented.

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A Tree-Systolic Array of DLMS Adaptive Filter

Authors:

Lan-Da Van, National Taiwan University, Dept. of Electrical Engr, Ph. D. Student (Taiwan)
Shing Tenqchen,
Chia-Hsun Chang,
Wu-Shiung Feng, Professor, Dept. of Electrical Engineering, National Taiwan University (Taiwan)

Page (NA) Paper number 1860

Abstract:

In this work, we develop an optimized binary tree-level rule for the design of systolic array structure of Delay LMS (DLMS) adaptive filter. Using our developed method, higher convergence rate can be obtained without sacrificing the properties of expanding systolic array structure. Also, based on our optimized tree rule, user can easily design any even-number tap adaptive system with minimum delay and high regularity under the constraints of maximum driving and the total number of taps.

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Computationally Efficient Version of the Decision Feedback Equalizer

Authors:

Rajarshi Gupta,
Mantu Kiran,
Edward A Lee,

Page (NA) Paper number 1811

Abstract:

We propose a computationally efficient version of the Decision Feedback Equalizer (DFE) and compare its performance with the conventional DFE. The proposed equalizer requires fewer taps than the conventional one. This reduces the computational load proportionally and leads to faster adaptation. Identical performance of the two structures in terms of probability of error is also demonstrated using both theoretical and simulation results.

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Spectral Line RLS Adaptive Filtering Algorithm

Authors:

Dinko Begusić, University of Split, Split, Croatia. (Croatia)
Darel Linebarger, University of Texas at Dallas, Richardson, Texas, USA. (USA)
Eric M. Dowling,
Balaji B Raghothaman,

Page (NA) Paper number 1751

Abstract:

A family of adaptive filtering algorithms for processing signals which have energy concentrated in a relatively small number of component subspaces in the spectral domain is introduced. The approach is based on transform domain signal decomposition and linear least squares filtering of the selected subset of transform domain signal components. The derivation is based on the linear least squares adaptive filtering framework introduced in our previous work. Fast convergence and computational efficiency are the main characteristics of the resulting algorithms. The method is applied to the problem of adaptive line enhancement comb filtering and DFT is used as a transform method. It is also shown that the resulting adaptive structure is capable of handling the case of non-coinciding frequencies. The performance of the algorithm is evaluated through a series of simulation experiments.

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Recursive Cost Function Adaptation for Echo Cancellation

Authors:

Corneliu Rusu, Tampere University of Technology, Finland (Finland)
Colin F.N. Cowan, The Queen's University of Belfast, U.K. (U.K.)

Page (NA) Paper number 1534

Abstract:

The goal of this paper is to introduce the RCFA (Recursive Cost Function Adaptation) algorithm. The derivation of the new algorithm does not use an estimator of the instantaneous error as the previous CFA (Cost Function Adaptation) algorithms did. In the RCFA case, the new error power is computing from the previous error power using an usual LMS recursive equation. The proposed method improves the sensitivity of the error power with respect to the noisy error, while the other benefits of the CFA algorithms in terms of the convergence speed and residual error remain. The properties of the new algorithm will be compared, using computer simulations, to standard LMS and LMF. The effect of the parameters involved in the design of the error power adaptive subsystem is also discussed.

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A Non Stationary RLS Algorithm for Adaptive Tracking of Markov Time Varying Channel

Authors:

Monia Turki-Hadaj Alouane,
Meriem Jaidane-Saidane,

Page (NA) Paper number 1213

Abstract:

In this paper we propose a new adaptive algorithm designed to track system presented by a filter that has markovian time evolution. As the Non Stationary LMS (NSLMS) algorithm the Non Stationary RLS (NSRLS) algorithm performs better than the LMS and is able to identify the unknown order and parameters of the markov model. However in the case of the NSRLS algorithm, the convergence speed of the markovian parameter is very high compared to that of the NSLMS algorithm. Moreover, the NSRLS algorithm has a better tracking capacity than the NSLMS, especially when the filter poles that characterize time variations of the channel are close to the unit circle.

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