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Showing papers on "Recursive least squares filter published in 2001"


Journal ArticleDOI
TL;DR: A selective-partial-update normalized least-mean-square (NLMS) algorithm is developed, and its stability is analyzed using the traditional independence assumptions and error-energy bounds, and the new algorithms appear to have good convergence performance.
Abstract: In some applications of adaptive filtering such as active noise reduction, and network and acoustic echo cancellation, the adaptive filter may be required to have a large number of coefficients in order to model the unknown physical medium with sufficient accuracy. The computational complexity of adaptation algorithms is proportional to the number of filter coefficients. This implies that, for long adaptive filters, the adaptation task can become prohibitively expensive, ruling out cost-effective implementation on digital signal processors. The purpose of partial coefficient updates is to reduce the computational complexity of an adaptive filter by adapting a block of the filter coefficients rather than the entire filter at every iteration. In this paper, we develop a selective-partial-update normalized least-mean-square (NLMS) algorithm, and analyze its stability using the traditional independence assumptions and error-energy bounds. Selective partial updating is also extended to the affine projection (AP) algorithm by introducing multiple constraints. The new algorithms appear to have good convergence performance as attested to by computer simulations with real speech signals.

196 citations


Proceedings ArticleDOI
29 Aug 2001
TL;DR: Experimental results on mechanical test lungs show a large improvement in uniform tracking by the adaptive controller over classical PID control methods currently used throughout the ventilator industry.
Abstract: For the control of critical care ventilators, the problem of tracking a desired pressure trajectory within a patient connecting circuit is solved using indirect adaptive control. This control uses an inverse model of patient lung mechanics and the ventilator connecting circuit. Online estimates of physical parameters are provided using standard recursive least squares with forgetting factor. The indirect method achieves robust performance over a wide range of patient conditions, and also since physical estimates of respiratory parameters are available, they can be applied to diagnostics and/or additional control measures for ventilation. This control method has been applied to NPB 840 ventilator hardware in the loop using the real time simulation software, VisSim. Experimental results on mechanical test lungs show a large improvement in uniform tracking by the adaptive controller over classical PID control methods currently used throughout the ventilator industry.

162 citations


Journal ArticleDOI
TL;DR: An efficient algorithm for the fitting of multivariate autoregressive models (MVAR) with time-dependent parameters to multidimensional signals with a particular advantage is that it requires only a low computation effort in comparison to well known procedures applied to single trials.

145 citations


Journal ArticleDOI
TL;DR: Simulations under different scenarios demonstrate that this technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating has better interference suppression than both the RLS beamformer with no quadRatic constraint and the R LS beamformer using the scaled projection technique, as well as faster convergence than LMS beamformers.
Abstract: Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. We propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, where the amount of loading has a closed-form solution. Simulations under different scenarios demonstrate that this algorithm has better interference suppression than both the RLS beamformer with no quadratic constraint and the RLS beamformer using the scaled projection technique, as well as faster convergence than LMS beamformers.

135 citations


Journal ArticleDOI
TL;DR: This work deals with interference suppression in asynchronous direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation and derives a new family of minimum mean-square-error detectors, which differ from their conventional counterparts in that they minimize a modified cost function.
Abstract: We deal with interference suppression in asynchronous direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation. Such an interference may arise from other users of the network, from external low-rate systems, as well as from a CDMA network coexisting with the primary network to form a dual-rate network. We derive, for all of these cases, a new family of minimum mean-square-error detectors, which differ from their conventional counterparts in that they minimize a modified cost function. Since the resulting structure is not implementable with acceptable complexity, we also propose some suboptimum systems. The statistical analysis reveals that both the optimum and the suboptimum receivers are near-far resistant, not only with respect to the other users, but also with respect to the external interference. We also present a blind and a recursive least squares-based, decision-directed implementation of the receivers wherein only the signature and the timing of the user to be decoded and the signaling time and the frequency offset of the external interferer are assumed known. Finally, computer simulations show that the proposed adaptive algorithm outperforms the classical decision-directed RLS algorithm.

87 citations


Journal ArticleDOI
28 Jun 2001
TL;DR: This paper generalizes the Kalman filter to one that approximates the fixed point of an operator that is known to be a Euclidean norm contraction, and establishes convergence of the algorithm and explores efficiency gains through computational experiments involving optimal stopping and queueing problems.
Abstract: The traditional Kalman filter can be viewed as a recursive stochastic algorithm that approximates an unknown function via a linear combination of prespecified basis functions given a sequence of noisy samples. In this paper, we generalize the algorithm to one that approximates the fixed point of an operator that is known to be a Euclidean norm contraction. Instead of noisy samples of the desired fixed point, the algorithm updates parameters based on noisy samples of functions generated by application of the operator, in the spirit of Robbins---Monro stochastic approximation. The algorithm is motivated by temporal-difference learning, and our developments lead to a possibly more efficient variant of temporal-difference learning. We establish convergence of the algorithm and explore efficiency gains through computational experiments involving optimal stopping and queueing problems.

81 citations


Journal ArticleDOI
TL;DR: In this paper, an adaptive-predictive control algorithm is developed for a class of SISO nonlinear discrete-time systems based on a generalized predictive control (GPC) approach, which is model-free, based directly on pseudo-partial derivative derived on-line from the input and output information of the system using a recursive least squares type of identification algorithm.
Abstract: In this paper, an adaptive-predictive control algorithm is developed for a class of SISO nonlinear discrete-time systems based on a generalized predictive control (GPC) approach. The design is model-free, based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using a recursive least squares type of identification algorithm. The proposed control is especially useful for nonlinear systems with vaguely known dynamics. Robust stability of the closed-loop system is analyzed and proven in the paper. Simulation and real-time application examples are provided for real nonlinear systems which are known to be difficult to model and control.

80 citations


Journal ArticleDOI
TL;DR: This work represents part of a suite of tools which will partially automate security and safety assessments, allow some assessments to be done remotely, and provide additional sensor modalities with which to make assessments.

80 citations


Reference BookDOI
20 Jul 2001
TL;DR: In this paper, the intricate relationship between adaptive filtering and signal analysis is discussed, highlighting stochastic processes, signal representations and properties, analytical tools, and implementation methods, as well as practical applications in information, estimation, and circuit theories.
Abstract: This text emphasizes the intricate relationship between adaptive filtering and signal analysis - highlighting stochastic processes, signal representations and properties, analytical tools, and implementation methods. This second edition includes new chapters on adaptive techniques in communications and rotation-based algorithms. It provides practical applications in information, estimation, and circuit theories.

75 citations


Journal ArticleDOI
TL;DR: The analysis shows that the limiting estimate of the feedback for feedback cancellation schemes that apply some recursive prediction error method with a quadratic norm may be biased if there is an error in the used model of the input signal to the hearing aid, and that the system is not identifiable unless a second input signal is added to the output of the hearing aids.
Abstract: The undesired effects of acoustic feedback of hearing aids can be reduced with an internal feedback path that is an estimate of the external feedback path. This paper analyzes the limiting estimate of the feedback for feedback cancellation schemes that apply some recursive prediction error method with a quadratic norm, e.g., least mean square (LMS) and recursive least squares (RLS), to the output and input signals of the hearing aid to identify the feedback path. The data used for identification are then collected in a closed loop and the estimate used in one recursion will affect the data used in succeeding recursions. These properties have to be considered in the analysis. The analysis shows that the limiting estimate may be biased if there is an error in the used model of the input signal to the hearing aid, and that the system is not identifiable unless a second input signal to the system is added to the output of the hearing aid or the signal processing of the hearing aid used to modify the signal to the impaired ear is nonlinear. The limiting estimate is presented as the solution to an optimization problem in the frequency domain. An analytical expression of the limiting estimate is presented for a special case. For other cases an algorithm is presented that can be used to find a numerical solution. The results can be useful when the model structure used with the recursive identification is chosen.

74 citations


Journal ArticleDOI
TL;DR: A simple recursive algorithm for bounded, uniformly distributed noise estimation problems from over complete linear expansions with subtractive dithered quantization that is faster than the O(1/n) MSE obtained by standard recursive least squares estimation and is optimal to within a constant factor.
Abstract: Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such bounded-noise estimation problems. The mean-square error (MSE) of the algorithm is "almost" O(1/n/sup 2/), where n is the number of samples. This rate is faster than the O(1/n) MSE obtained by standard recursive least squares estimation and is optimal to within a constant factor.

Proceedings ArticleDOI
25 Jul 2001
TL;DR: An online approach for rule-base evolution by recursive adaptation of rule structure and parameters is described, to maximise the model transparency by simplifying the fuzzy linguistic descriptions of the input variables and minimising the reliance on the use of computationally expensive techniques.
Abstract: An online approach for rule-base evolution by recursive adaptation of rule structure and parameters is described . An integral part of the procedure is to maximise the model transparency by simplifying the fuzzy linguistic descriptions of the input variables. The rule base evolves over time, utilising direct calculation approaches and hence minimising the reliance on the use of computationally expensive techniques, such as genetic algorithms. An online version of subtractive clustering recently introduced by the authors (P.P. Angelov and R.A. Buswell) is used for determination of the antecedent part of the fuzzy rules. Recursive least squares estimation is employed to determine the parameters of the consequent part of each rule. The use of these efficient non-iterative techniques is the key to the low computational demands of the algorithm. The application of similarity measures improves the interpretability and compactness of the resulting eR model, with no significant detriment to the model precision. A time series prediction problem on data from a real indoor climate control (ICC) system has been considered to test and validate the proposed model simplification method.

Journal ArticleDOI
TL;DR: It is proposed that neural networks are first trained by the RLS algorithm and then some unimportant weights are removed based on the approximate Hessian matrix, which shows that the approach is an effective training and pruning method for neural networks.

Journal ArticleDOI
TL;DR: A new cyclic blind recursive least squares (RLS)-based algorithm is introduced, capable of tracking the periodically time-varying receiver structure, and allowing adaptive interference cancellation with a moderate complexity increase.
Abstract: In this work, the problem of joint suppression of multiple-access and narrow-band interference (NBI) for an asynchronous direct-sequence code-division multiple-access (CDMA) system operating on a frequency-selective fading channel is addressed. The receiver structure we consider can be deemed as a two-stage one: the first stage consists of a bank of minimum mean-square-error (MMSE) filters, each keyed to a given replica of the useful signal, and aimed at suppressing the overall interference; the second stage, assuming knowledge of the fading channel coefficients realizations, combines the MMSE filters outputs according to a maximal-ratio combining rule. Due to the presence of the NBI, the resulting structure is in general time-varying, and becomes periodically time-varying if the NBI bit-rate has a rational ratio to that of the CDMA system. Moreover, enlarging the observation window beyond the signaling interval and oversampling the signal space may yield a noticeable performance improvement. For the relevant case that the said ratio is rational, a new cyclic blind recursive least squares (RLS)-based algorithm is introduced, capable of tracking the periodically time-varying receiver structure, and allowing adaptive interference cancellation with a moderate complexity increase. We also come up with a closed-form expression for the conditional bit-error rate (BER), which is useful both to evaluate semi-analytical methods to assess the unconditional BER and to derive bounds on the system near-far resistance. The results indicate that the receiver achieves very satisfactory performance in comparison to previously known structures. Computer simulations also demonstrate that the cyclic blind RLS algorithm exhibits quite fast convergence dynamics.

Journal ArticleDOI
TL;DR: An heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches, which produce a better convergence performance than previously published algorithms.
Abstract: In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

Journal ArticleDOI
TL;DR: Adapt step-size blind LMS algorithms and adaptive forgetting factor blind RLS algorithms for code-aided suppression of multiple access interference (MAI) and narrowband interference (NBI) in DS/CDMA systems are developed.
Abstract: This paper develops adaptive step-size blind LMS algorithms and adaptive forgetting factor blind RLS algorithms for code-aided suppression of multiple access interference (MAI) and narrowband interference (NBI) in DS/CDMA systems. These algorithms optimally adapt both the step size (forgetting factor) and the weight vector of the blind linear multiuser detector using the received measurements. Simulations are provided to compare the proposed algorithms with previously studied blind RLS and blind LMS algorithms. They show that the adaptive step-size blind LMS algorithm and adaptive forgetting factor blind RLS algorithm field significant improvements over the standard blind LMS algorithm and blind RLS algorithm in dynamic environments where the number of interferers are time-varying.

Journal ArticleDOI
TL;DR: Two modified RLS algorithms are derived by requiring robustness in its prediction performance to input perturbations to tackle the problem of diminishing weight decay effect as training progresses.
Abstract: Recursive least squares (RLS)-based algorithms are a class of fast online training algorithms for feedforward multilayered neural networks (FMNNs). Though the standard RLS algorithm has an implicit weight decay term in its energy function, the weight decay effect decreases linearly as the number of learning epochs increases, thus rendering a diminishing weight decay effect as training progresses. In this paper, we derive two modified RLS algorithms to tackle this problem. In the first algorithm, namely, the true weight decay RLS (TWDRLS) algorithm, we consider a modified energy function whereby the weight decay effect remains constant, irrespective of the number of learning epochs. The second version, the input perturbation RLS (IPRLS) algorithm, is derived by requiring robustness in its prediction performance to input perturbations. Simulation results show that both algorithms improve the generalization capability of the trained network.

Journal ArticleDOI
01 Aug 2001
TL;DR: An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed in this article, where instead of using the conventional least-square cost function, a new cost function based on an Mestimator is used to suppress the effect of impulse noise on the filter weights.
Abstract: An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either contaminated gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under gaussian noise alone.

Journal ArticleDOI
TL;DR: In this article, a wideband stereophonic acoustic echo cancellation (SAEC) algorithm based on a fast recursive least squares (FRLS) algorithm in a subband structure, with equidistant frequency bands, is presented.
Abstract: Teleconferencing systems employ acoustic echo cancelers to reduce echoes that result from the coupling between loudspeaker and microphone. To enhance the sound realism, two-channel audio is necessary. However, stereophonic acoustic echo cancellation (SAEC) is more difficult to solve because of the necessity to uniquely identify two acoustic paths, which becomes problematic since the two excitation signals are highly correlated. In this paper, a wideband stereophonic acoustic echo canceler is presented. The fundamental difficulty of stereophonic acoustic echo cancellation is described and an echo canceler based on a fast recursive least squares (FRLS) algorithm in a subband structure, with equidistant frequency bands, is proposed. The structure has been used in a real-time implementation, with which experiments have been performed. In this paper, simulation results of this implementation on real life recordings, with 8 kHz bandwidth, are studied. The results clearly verify that the theoretic fundamental problem of SAEC also applies in real-life situations. They also show that more sophisticated adaptive algorithms are needed in the lower frequency regions than in the higher regions.

Journal ArticleDOI
TL;DR: An asynchronous direct-sequence code division multiple access (DS/CDMA) system wherein users are allowed to transmit their symbols at one out of two available data rates is considered, and it is shown that detection of the users transmitting at the higher rate requires a periodically time-varying processing of the observables.
Abstract: In this paper, the authors consider an asynchronous direct-sequence code division multiple access (DS/CDMA) system wherein users are allowed to transmit their symbols at one out of two available data rates. Three possible access schemes are considered, namely, the variable spreading length (VSL), the variable chip rate (VCR), and the variable chip rate with frequency shift (VCRFS) formats. Their performance is compared for the case that a linear one-shot multiuser receiver is employed. It is also shown that detection of the users transmitting at the higher rate requires a periodically time-varying processing of the observables. Moreover, the problem of blind adaptive receiver implementation is studied, and a cyclic blind recursive-least-squares (RLS) algorithm is provided which is capable of converging to the periodically time-varying high-rate users detection structure. Numerical results show that the proposed receivers are near-far resistant, and that the VCRFS access technique achieves the best performance. Finally as to the adaptive blind receiver implementation, computer simulations have revealed that the cyclic RLS algorithm for blind adaptive high-rate users demodulation outperforms the conventional RLS algorithm in most cases of primary importance.

Journal ArticleDOI
TL;DR: The local approach for detection of abrupt changes is adopted as a computational engine for the change detection and the effectiveness and robustness of the proposed algorithm in fault detection and isolation are demonstrated through Monte Carlo simulations.
Abstract: This paper deals with detection of parameter changes of total least squares and generalized total least squares models and its application in fault detection and isolation. Total least squares and generalized total least squares are frequently used to model processes when all measured process variables are corrupted by disturbances. It is therefore of practical interest to monitor processes and detect faults using the total least squares and generalized total least squares as well. The local approach for detection of abrupt changes is adopted as a computational engine for the change detection. The effectiveness and robustness of the proposed algorithm in fault detection and isolation are demonstrated through Monte Carlo simulations: a pilot-scale experiment and sensor validation of an industrial distillation column.

Journal ArticleDOI
TL;DR: An adaptive multiuser recursive least squares (RLS) algorithm is presented which determines the MMSE adjusted filter coefficients with less complexity than individual adaptation for each user in linear and nonlinear space-time minimum mean-square-error networks.
Abstract: We investigate linear and nonlinear space-time minimum mean-square-error (MMSE) multiuser detectors for high data rate wireless code-division multiple-access (CDMA) networks. The centralized reverse-link detectors comprise a space-time feedforward filter and a multiuser feedback filter which processes the previously detected symbols of all in-sector users. The feedforward filter processes chip-rate samples from a bank of chip-matched filters which operate on the baseband outputs from an array of antennas. We present an adaptive multiuser recursive least squares (RLS) algorithm which determines the MMSE adjusted filter coefficients with less complexity than individual adaptation for each user. We calculate the outage probabilities and isolate the effects of antenna, diversity, and interference suppression gains for linear and nonlinear filtering and for CDMA systems with varying levels of system control (e.g., timing control, code assignment, cell layout). For eight users transmitting uncoded 2-Mb/s quadrature phase-shift keying with a spreading gain of eight chips per symbol over a fading channel with a multipath delay spread of 1.25 /spl mu/s, the performance of a three-antenna feedforward/feedback detector was within 1 dB (in signal-to-noise ratio per antenna) of ideal detection in the absence of interference. By training for 10% of a 5-ms frame, RLS adaptation enabled the same detector to suffer less than a 0.5-dB penalty due to the combined effects of imperfect coefficients and error propagation. The advantage of nonlinear feedforward/feedback detection over linear feedforward detection was shown to be significantly larger for a CDMA system with enhanced system control.

Patent
20 Feb 2001
TL;DR: In this paper, the authors proposed a channel tracking mechanism based on the weighted recursive least squares algorithm and implemented the estimation process by recursively updating channel model parameters upon the arrival of new sample data.
Abstract: A novel and useful channel tracking mechanism operative to generate channel estimate updates on blocks of samples during reception of a message. The tracking mechanism is based on the weighted recursive least squares algorithm and implements the estimation process by recursively updating channel model parameters upon the arrival of new sample data. The mechanism is operative to update channel estimate information once per sample block. An interblock exponential weighting factor is also applied. The block length is chosen short enough to enable good tracking performance while being sufficiently long enough to minimize the overhead of generating preliminary decisions and of updating precalculated tables in the equalizer. The method of the invention can be performed in either hardware or software. A computer comprising a processor, memory, etc. is operative to execute software adapted to perform the channel tracking method of the present invention.

Journal ArticleDOI
TL;DR: The results of performance evaluation indicate that the proposed hierarchical LMS algorithm can speed up convergence rate and reduce the excess mean squared error (MSE) of the standard L MS algorithm.
Abstract: We propose a hierarchical least mean square (LMS) algorithm where the taps of a filter are organized into a hierarchy, and the minimization process is performed repeatedly from the bottom level to the top level. The results of performance evaluation indicate that the proposed hierarchical LMS algorithm can speed up convergence rate and reduce the excess mean squared error (MSE) of the standard LMS algorithm.

Journal ArticleDOI
TL;DR: It is shown that a second round of averaging leads to the recursive least‐squares algorithm with a forgetting factor, which means that in case the true parameters are changing as a random walk, accelerated convergence does not, typically, give optimal tracking properties.
Abstract: The so-called accelerated convergence is an ingenuous idea to improve the asymptotic accuracy in stochastic approximation (gradient based) algorithms. The estimates obtained from the basic algorith ...

Journal ArticleDOI
TL;DR: It is shown, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures, and that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally based models.
Abstract: The existing derivations of conventional fast RLS adaptive filters are intrinsically dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. We show, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures. We show that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally based models. One of the benefits of working with orthonormal bases is that fewer parameters can be used to model long impulse responses.

Journal ArticleDOI
TL;DR: In this article, a nonlinear model-based controller is developed to regulate the cell biomass exit concentration of a continuous-flow bioreactor by manipulating the dilution rate, which is shown to be nominally stable over the manipulated variable range [0.941, 0.999]h -1 using the structured singular value.
Abstract: Nonlinear model-based controllers are developed to regulate the cell biomass exit concentration of a continuous-flow bioreactor by manipulating the dilution rate. Plant-friendly input sequences are used to identify a second-order Volterra series model from a virtual plant. A Volterra-Laguerre model is produced by projection onto the orthonormal Laguerre basis functions. A partitioned nonlinear inverse (PNLI) controller is synthesized and is shown to be nominally stable over the manipulated variable range [0.941, 0.999]h -1 using the structured singular value. A referenced-based switching algorithm is incorporated to improve the robustness and stability characteristics of the closed-loop system. Nonlinear model predictive control (NMPC) alleviates the need for the switching controller, and an analytical NMPC solution incorporating recursive least squares avoids entrapment in local objective function minima. This controller offers optimum tracking for unreachable setpoints as well as tracking of the constrained local minimum for input-magnitude-constrained problems modeled by second-order Volterra-Laguerre systems.

Journal ArticleDOI
TL;DR: This paper presents a method for adaptively optimizing the reconstructor of a closed-loop AO system in real time that relies on recursive least squares techniques to track the temporal and spatial correlations of the turbulent wave-front.

Patent
10 Sep 2001
TL;DR: In this article, a method for combining a direct sequence spread spectrum signal comprising signal components that each may be characterized with a space variable and a time variable comprising the steps of: despreading said signal components; and determining a set of combining coefficients from said signal component using a minimum mean square error combining method that considers said space and time variables of the signal components in parallel.
Abstract: One aspect of the present invention is a method for combining a direct sequence spread spectrum signal comprising signal components that each may be characterized with a space variable and a time variable comprising the steps of: despreading said signal components; and determining a set of combining coefficients from said signal components using a Minimum Mean Square Error combining method that considers said space and time variables of the signal components in parallel. The Minimum Mean Square Error combining methods may utilize iterative methods such as the Least Mean Squares method or the Recursive Least Squares method.

Proceedings ArticleDOI
07 May 2001
TL;DR: The feedback-type active noise control (ANC) system uses only one microphone to provide necessary signals for adjusting the adaptive filter and the local convergence condition is derived, a counterpart of the well-known 90/spl deg/ condition for the feedforward-type ANC.
Abstract: The feedback-type active noise control (ANC) system uses only one microphone to provide necessary signals for adjusting the adaptive filter. Due to the complicated nature of the whole adaptive filter structure there have been no theoretical results about its convergence properties. First a stationary point of the adaptive filter using the filtered-X LMS algorithm is obtained by the averaging method combined with the frequency domain technique. Then the local convergence condition is derived. This is a counterpart of the well-known 90/spl deg/ condition for the feedforward-type ANC. Finally, the convergence condition is explicitly given for a simple example and its validity is shown by some simulations.