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Showing papers on "Recursive least squares filter published in 2011"


Journal ArticleDOI
TL;DR: This paper derives a least squares-based and a gradient-based iterative identification algorithms for Wiener nonlinear systems, estimating directly the parameters of Wiener systems without re-parameterization to generate redundant estimates.

226 citations


Journal ArticleDOI
TL;DR: In this paper, an efficient implementation of an iteratively reweighted least square algorithm for recovering a matrix from a small number of linear measurements is presented and analyzed, which is designed for the simultaneous promotion of both a minimal nuclear norm and an approximately low rank solution.
Abstract: We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a minimal nuclear norm and an approximately low-rank solution. Under the assumption that the linear measurements fulfill a suitable generalization of the null space property known in the context of compressed sensing, the algorithm is guaranteed to recover iteratively any matrix with an error of the order of the best $k$-rank approximation. In certain relevant cases, for instance, for the matrix completion problem, our version of this algorithm can take advantage of the Woodbury matrix identity, which allows us to expedite the solution of the least squares problems required at each iteration. We present numerical experiments which confirm the robustness of the algorithm for the solution of matrix completion problems, and we demonstrate its competitiveness with respect to other techniques proposed recently in the literature.

225 citations


Journal ArticleDOI
TL;DR: A hierarchical least squares (HLS) identification algorithm is presented to estimate the parameters of the dual-rate ARMAX models and the performance analysis and simulation results confirm that the estimation accuracy of the proposed algorithms are close to that of the RLS algorithm, but the proposed algorithm retains much less computational burden.
Abstract: This technical note studies identification problems for dual-rate sampled-data linear systems with noises. A hierarchical least squares (HLS) identification algorithm is presented to estimate the parameters of the dual-rate ARMAX models. The basic idea is to decompose the identification model of a dual-rate system into several sub-identification models with smaller dimensions and fewer parameters. The proposed algorithm is more computationally efficient than the recursive least squares (RLS) algorithm since the RLS algorithm requires computing the covariance matrix of large sizes, while the HLS algorithm deals with the covariance matrix of small sizes. Compared with our previous work, a detailed study of the HLS algorithm is conducted in this technical note. The performance analysis and simulation results confirm that the estimation accuracy of the proposed algorithm are close to that of the RLS algorithm, but the proposed algorithm retains much less computational burden.

208 citations


Journal ArticleDOI
TL;DR: Simulations show that the proposed equalization algorithms outperform the existing reduced- and full- algorithms while requiring a comparable computational cost.
Abstract: This paper presents a novel adaptive reduced-rank multiple-input-multiple-output (MIMO) equalization scheme and algorithms based on alternating optimization design techniques for MIMO spatial multiplexing systems. The proposed reduced-rank equalization structure consists of a joint iterative optimization of the following two equalization stages: 1) a transformation matrix that performs dimensionality reduction and 2) a reduced-rank estimator that retrieves the desired transmitted symbol. The proposed reduced-rank architecture is incorporated into an equalization structure that allows both decision feedback and linear schemes to mitigate the interantenna (IAI) and intersymbol interference (ISI). We develop alternating least squares (LS) expressions for the design of the transformation matrix and the reduced-rank estimator along with computationally efficient alternating recursive least squares (RLS) adaptive estimation algorithms. We then present an algorithm that automatically adjusts the model order of the proposed scheme. An analysis of the LS algorithms is carried out along with sufficient conditions for convergence and a proof of convergence of the proposed algorithms to the reduced-rank Wiener filter. Simulations show that the proposed equalization algorithms outperform the existing reduced- and full- algorithms while requiring a comparable computational cost.

181 citations


Journal ArticleDOI
TL;DR: With the LS-SVMAF, the least squares support vector machines adaptive filter, this paper can model and predict the hand tremor more effectively and improve the precision and reliability in the master–slave robotic system for microsurgery.
Abstract: One of the main problems for effective control of a minimally invasive surgery (MIS) is the imprecision that caused by hand tremor. In this paper, a novel adaptive filter, the least squares support vector machines adaptive filter (LS-SVMAF), is proposed to overcome this problem. Compared with traditional methods like multi layer perceptron (MLP), LS-SVM shows a superior performance of nonlinear modeling with small scale of data set or high dimensional input space. With the LS-SVMAF, we can model and predict the hand tremor more effectively and improve the precision and reliability in the master–slave robotic system for microsurgery. Simulation results demonstrate the effectiveness of the proposed filter and its superior performance over its competing rivals.

155 citations


Journal ArticleDOI
Dongqing Wang1
TL;DR: In this article, a filtering and auxiliary model-based recursive least squares (F-AM-RLS) identification algorithm was proposed for parameter estimation of output error moving average (OEMA) systems.
Abstract: For parameter estimation of output error moving average (OEMA) systems, this study combines the auxiliary model identification idea with the filtering theory, transforms an OEMA system into two identification models and presents a filtering and auxiliary model-based recursive least squares (F-AM-RLS) identification algorithm. Compared with the auxiliary model-based recursive extended least squares algorithm, the proposed F-AM-RLS algorithm has a high computational efficiency. Moreover, a filtering and auxiliary model-based least squares iterative (F-AM-LSI) identification algorithm is derived for OEMA systems with finite measurement input-output data. Compared with the F-AM-RLS approach, the proposed F-AM-LSI algorithm updates the parameter estimation using all the available data at each iteration, and thus can generate highly accurate parameter estimates.

150 citations


Journal ArticleDOI
TL;DR: A sequential averaging filter is developed that adaptively varies the number of complexes included in the averaging based on the characteristics of the ECG signal, which demonstrates that, without using a priori knowledge on signal characteristics, the Filter with adaptive noise estimation performs similar to the filter with optimized fixed noise covariance.
Abstract: The ongoing trend of ECG monitoring techniques to become more ambulatory and less obtrusive generally comes at the expense of decreased signal quality. To enhance this quality, consecutive ECG complexes can be averaged triggered on the heartbeat, exploiting the quasi-periodicity of the ECG. However, this averaging constitutes a tradeoff between improvement of the SNR and loss of clinically relevant physiological signal dynamics. Using a Bayesian framework, in this paper, a sequential averaging filter is developed that, in essence, adaptively varies the number of complexes included in the averaging based on the characteristics of the ECG signal. The filter has the form of an adaptive Kalman filter. The adaptive estimation of the process and measurement noise covariances is performed by maximizing the Bayesian evidence function of the sequential ECG estimation and by exploiting the spatial correlation between several simultaneously recorded ECG signals, respectively. The noise covariance estimates thus obtained render the filter capable of ascribing more weight to newly arriving data when these data contain morphological variability, and of reducing this weight in cases of no morphological variability. The filter is evaluated by applying it to a variety of ECG signals. To gauge the relevance of the adaptive noise-covariance estimation, the performance of the filter is compared to that of a Kalman filter with fixed, (a posteriori) optimized noise covariance. This comparison demonstrates that, without using a priori knowledge on signal characteristics, the filter with adaptive noise estimation performs similar to the filter with optimized fixed noise covariance, favoring the adaptive filter in cases where no a priori information is available or where signal characteristics are expected to fluctuate.

146 citations


Journal ArticleDOI
TL;DR: In this article, a model-based supervisory and optimal control strategy for central chiller plants is presented to enhance their energy efficiency and control performance. And the optimal strategy is formulated using simplified models of major components and the genetic algorithm (GA).

146 citations


Journal ArticleDOI
TL;DR: It is shown that the convex regularized RLS algorithm performs as well as, and possibly better than, the regular RLS when there is a constraint on the value of the conveX function evaluated at the true weight vector.
Abstract: In this letter, the RLS adaptive algorithm is considered in the system identification setting. The RLS algorithm is regularized using a general convex function of the system impulse response estimate. The normal equations corresponding to the convex regularized cost function are derived, and a recursive algorithm for the update of the tap estimates is established. We also introduce a closed-form expression for selecting the regularization parameter. With this selection of the regularization parameter, we show that the convex regularized RLS algorithm performs as well as, and possibly better than, the regular RLS when there is a constraint on the value of the convex function evaluated at the true weight vector. Simulations demonstrate the superiority of the convex regularized RLS with automatic parameter selection over regular RLS for the sparse system identification setting.

125 citations


Journal ArticleDOI
TL;DR: In this paper, a bias compensation based recursive least squares identification algorithm was proposed for ARX-like systems by means of the prefilter idea and bias compensation principle, which can give the unbiased estimates of the system model parameters in the presence of colored noises and can be on-line implemented.

116 citations


Journal ArticleDOI
TL;DR: This paper presents a recursive least squares (RLS) identification algorithm based on bias compensation technique for multi-input single-output (MISO) systems with colored noises to obtain unbiased recursive estimates of the systems.

Journal ArticleDOI
TL;DR: The results show that the proposed algorithms outperform the best known reduced-rank schemes, while requiring lower complexity.
Abstract: This work proposes a blind adaptive reduced-rank scheme and constrained constant-modulus (CCM) adaptive algorithms for interference suppression in wireless communications systems. The proposed scheme and algorithms are based on a two-stage processing framework that consists of a transformation matrix that performs dimensionality reduction followed by a reduced-rank estimator. The complex structure of the transformation matrix of existing methods motivates the development of a blind adaptive reduced-rank constrained (BARC) scheme along with a low-complexity reduced-rank decomposition. The proposed BARC scheme and a reduced-rank decomposition based on the concept of joint interpolation, switched decimation and reduced-rank estimation subject to a set of constraints are then detailed. The proposed set of constraints ensures that the multipath components of the channel are combined prior to dimensionality reduction. We develop low-complexity joint interpolation and decimation techniques, stochastic gradient, and recursive least squares reduced-rank estimation algorithms. A model-order selection algorithm for adjusting the length of the estimators is devised along with techniques for determining the required number of switching branches to attain a predefined performance. An analysis of the convergence properties and issues of the proposed optimization and algorithms is carried out, and the key features of the optimization problem are discussed. We consider the application of the proposed algorithms to interference suppression in DS-CDMA systems. The results show that the proposed algorithms outperform the best known reduced-rank schemes, while requiring lower complexity.

Journal ArticleDOI
TL;DR: Two new adaptive model predictive control algorithms, both consisting of an on-line process identification part and a predictive control part, applied to the temperature control of a fluidized bed furnace reactor and the auto-pilot control of an F-16 aircraft.
Abstract: This paper presents two new adaptive model predictive control algorithms, both consisting of an on-line process identification part and a predictive control part. Both parts are executed at each sampling instant. The predictive control part of the first algorithm is the Nonlinear Model Predictive Control strategy and the control part of the second algorithm is the Generalized Predictive Control strategy. In the identification parts of both algorithms the process model is approximated by a series-parallel neural network structure which is trained by a recursive least squares (ARLS) method. The two control algorithms have been applied to: 1) the temperature control of a fluidized bed furnace reactor (FBFR) of a pilot plant and 2) the auto-pilot control of an F-16 aircraft. The training and validation data of the neural network are obtained from the open-loop simulation of the FBFR and the nonlinear F-16 aircraft models. The identification and control simulation results show that the first algorithm outperforms the second one at the expense of extra computation time.

Journal ArticleDOI
TL;DR: In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented and the method is used to develop an adaptive fuzzy predictive functional controller for a pH process.
Abstract: In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented. The presented method combines a recursive Gustafson–Kessel clustering algorithm and the fuzzy recursive least squares method. The on-line Gustafson–Kessel clustering method is derived. The recursive equations for fuzzy covariance matrix, its inverse and cluster centers are given. The use of the method is presented on two examples. First example demonstrates the use of the method for monitoring of the waste water treatment process and in the second example the method is used to develop an adaptive fuzzy predictive functional controller for a pH process. The results for the Mackey–Glass time series prediction are also given.

Journal ArticleDOI
TL;DR: In this paper, the adaptive notch filter was used to improve the transient response time of harmonic detection using adaptive filters applied to shunt active power filters and the synchronization of the adaptive filter orthogonal input signals was achieved automatically without the need of a phase-locked loop.
Abstract: This paper describes new strategies to improve the transient response time of harmonic detection using adaptive filters applied to shunt active power filters. Two cases are presented and discussed, both using an adaptive notch filter, but one uses the least mean square algorithm to adjust the coefficients and the other uses the recursive least squares algorithm. The synchronization of the adaptive notch filter orthogonal input signals, which are generated by the Clarke transformation of the load currents, is achieved automatically without the need of a phase-locked loop. This procedure significantly reduces the real-time computation burden. Simulations using Matlab/Simulink are presented to clarify the algorithm, and practical implementation is performed using the DSP Texas Instruments TMS320F2812. The experimental results are presented and discussed.

Journal ArticleDOI
TL;DR: It has been observed that by appropriately choosing the data assignment criterion, the proposed on-line method can be extended to deal also with the identification of piecewise affine models and is tested through some computer simulations and the modeling of an open channel system.

Journal ArticleDOI
TL;DR: This paper presents and incorporates an error bound function into the two channel estimation methods, which can automatically adjust the error bound with the update of the channel estimates, and shows good performance of the proposed algorithms in terms of convergence speed, steady-state mean square error, and bit error rate.
Abstract: In this paper, we consider a general cooperative wireless sensor network (WSN) with multiple hops and the problem of channel estimation. Two matrix-based set-membership (SM) algorithms are developed for the estimation of complex matrix channel parameters. The main goal is to significantly reduce the computational complexity, compared with existing channel estimators, and extend the lifetime of the WSN by reducing its power consumption. The first proposed algorithm is the SM normalized least mean squares (SM-NLMS) algorithm. The second is the SM recursive least squares (RLS) algorithm called BEACON. Then, we present and incorporate an error bound function into the two channel estimation methods, which can automatically adjust the error bound with the update of the channel estimates. Steady-state analysis in the output mean-square error (MSE) is presented, and closed-form formulas for the excess MSE and the probability of update in each recursion are provided. Computer simulations show good performance of our proposed algorithms in terms of convergence speed, steady-state mean square error, and bit error rate (BER) and demonstrate reduced complexity and robustness against time-varying environments and different signal-to-noise ratio (SNR) values.

Journal ArticleDOI
TL;DR: Application of the proposed approach to a real mechanical system indicates better tracking capability of the multi-wavelet basis function algorithm compared with the normalized least squares or recursive least squares routines.
Abstract: This brief introduces a new parametric modelling and identification method for linear time-varying systems using a block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be applied to track rapidly or even sharply varying processes and is developed by combining wavelet approximation theory with a block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstationary processes. Application of the proposed approach to a real mechanical system indicates better tracking capability of the multi-wavelet basis function algorithm compared with the normalized least squares or recursive least squares routines.

Proceedings ArticleDOI
09 May 2011
TL;DR: Two ways to estimate the interaction force at the end-effector of a robot by combining filtered dynamic equations with a recursive least squares estimation algorithm to provide a smoothened force signal are discussed.
Abstract: This paper discusses two ways to estimate the interaction force at the end-effector of a robot. The first approach that is presented combines filtered dynamic equations with a recursive least squares estimation algorithm to provide a smoothened force signal, which is useful in the (common) case of noisy torque measurements.

Journal ArticleDOI
TL;DR: It is shown that the developed algorithm gives a comparable degree of accuracy to other algorithms, and can be used in a number of fields, including adaptive nonlinear control, model predictive control, fault detection, diagnostics and robotics.
Abstract: In this paper we propose a new approach to on-line Takagi-Sugeno fuzzy model identification. It combines a recursive fuzzy c-means algorithm and recursive least squares. First the method is derived and than it is tested and compared on a benchmark problem of the Mackey-Glass time series with other established on-line identification methods. We showed that the developed algorithm gives a comparable degree of accuracy to other algorithms. The proposed algorithm can be used in a number of fields, including adaptive nonlinear control, model predictive control, fault detection, diagnostics and robotics. An example of identification based on a real data of the waste-water treatment process is also presented.

Journal ArticleDOI
TL;DR: A theorem is stated and proven which guarantees uniform stability of a general discrete-time system and the backpropagation (BP) algorithm with a new time-varying rate is uniformly stable for online identification and the identification error converges to a small zone bounded by the uncertainty.
Abstract: Neural networks (NNs) have numerous applications to online processes, but the problem of stability is rarely discussed. This is an extremely important issue because, if the stability of a solution is not guaranteed, the equipment that is being used can be damaged, which can also cause serious accidents. It is true that in some research papers this problem has been considered, but this concerns continuous-time NN only. At the same time, there are many systems that are better described in the discrete time domain such as population of animals, the annual expenses in an industry, the interest earned by a bank, or the prediction of the distribution of loads stored every hour in a warehouse. Therefore, it is of paramount importance to consider the stability of the discrete-time NN. This paper makes several important contributions. 1) A theorem is stated and proven which guarantees uniform stability of a general discrete-time system. 2) It is proven that the backpropagation (BP) algorithm with a new time-varying rate is uniformly stable for online identification and the identification error converges to a small zone bounded by the uncertainty. 3) It is proven that the weights' error is bounded by the initial weights' error, i.e., overfitting is eliminated in the proposed algorithm. 4) The BP algorithm is applied to predict the distribution of loads that a transelevator receives from a trailer and places in the deposits in a warehouse every hour, so that the deposits in the warehouse are reserved in advance using the prediction results. 5) The BP algorithm is compared with the recursive least square (RLS) algorithm and with the Takagi-Sugeno type fuzzy inference system in the problem of predicting the distribution of loads in a warehouse, giving that the first and the second are stable and the third is unstable. 6) The BP algorithm is compared with the RLS algorithm and with the Kalman filter algorithm in a synthetic example.

Proceedings ArticleDOI
18 Aug 2011
TL;DR: In this article, a battery model that is suitable for real-time state-of-charge (SOC) estimation of a Lithium-Ion battery is presented, where the battery open circuit voltage (OCV) as a function of SOC is described by an adaptation of the Nernst equation.
Abstract: A battery model that is suitable for real-time State-of-Charge (SOC) estimation of a Lithium-Ion battery is presented in this paper. The battery open circuit voltage (OCV) as a function of SOC is described by an adaptation of the Nernst equation. The analytical representation can facilitate Kalman filtering or observer-based SOC estimation methods. A zero-state hysteresis correction term is used to depict the hysteresis effect of the battery. A parallel resistance-capacitance (RC) network is used to depict the relaxation effect of the battery. A linear discrete-time formulation of the battery model is derived. A recursive least squares algorithm with forgetting is applied to implement the online parameter calibration. Validation results show that the calibrated model can accurately simulate the dynamic voltage behavior of the Lithium-Ion battery for two different experimental data sets.

Journal ArticleDOI
TL;DR: The simulation results reveal that the authors' scheme successfully mitigates the error propagation and approaches the performance of the optimal ML detector, while requiring a significantly lower complexity than the ML and sphere decoder detectors.
Abstract: In this study, the authors propose a novel successive interference cancellation (SIC) strategy for multiple-input multiple-output spatial multiplexing systems based on a structure with multiple interference cancellation branches. The proposed multi-branch SIC (MB-SIC) structure employs multiple SIC schemes in parallel and each branch detects the signal according to its respective ordering pattern. By selecting the branch which yields the estimates with the best performance according to the selection rule, the MB-SIC detector, therefore, achieves higher detection diversity. The authors consider three selection rules for the proposed detector, namely, the maximum likelihood (ML), the minimum mean square error and the constant modulus criteria. An efficient adaptive receiver is developed to update the filter weight vectors and estimate the channel using the recursive least squares algorithm. Furthermore a bit error probability performance analysis is carried out. The simulation results reveal that the authors' scheme successfully mitigates the error propagation and approaches the performance of the optimal ML detector, while requiring a significantly lower complexity than the ML and sphere decoder detectors.

Journal ArticleDOI
TL;DR: Detailed simulation analysis and experimental validation on a prototype synchronous dc-dc buck converter is presented, showing the superior dynamic performance and voltage regulation compared to conventional PID and adaptive LMS control schemes, with only a modest increase in the computational burden to the microprocessor.
Abstract: This paper presents an alternative technique for the adaptive control of power electronic converter circuits. Specific attention is given to the adaptive control of a dc-dc converter. The proposed technique is based on a simple adaptive filter method and uses a one-tap finite impulse response (FIR) prediction error filter (PEF). The method is computationally efficient and based around a dichotomous coordinate descent (DCD) algorithm. The DCD-recursive least squares (RLS) algorithm has been employed as the adaptive PEF to reduce the computational complexity of existing RLS algorithms for efficient hardware implementation. Results show that the DCD-RLS is able to improve the dynamic performance and convergence rate of the adaptive gains (filter taps) within the controller. In turn, this yields a significant improvement in the overall dynamic performance of the closed-loop control system, particularly in the event of abrupt parameter changes. The proposed controller uses an adaptive proportional-derivative+integral (PD +I) structure which, alongside the DCD algorithm, offers an effective substitute to a conventional proportional-integral-derivative (PID) controller. The nonadaptive integral controller (+I), introduced in the feedback loop, increases the excitation of the filter tap weight and ensures good regulation. The approach results in a fast adaptive controller with self-loop compensation. This is required to minimize the prediction error signal and, in turn, minimize the voltage error signal in the loop by automatically calculating the optimal pole locations. The prediction error signal is further minimized through a second-stage FIR filter (adaptation gain stage). This ensures that the adaptive gains converge to their optimal value. This paper presents detailed simulation analysis and experimental validation on a prototype synchronous dc-dc buck converter. The experimental results clearly demonstrate the superior dynamic performance and voltage regulation compared to conventional PID and adaptive LMS control schemes, with only a modest increase in the computational burden to the microprocessor.

Journal ArticleDOI
TL;DR: The given illustrative example indicates that the proposed algorithm can generate more accurate parameter estimates compared with the auxiliary model based recursive generalized extended least squares algorithm.

Journal ArticleDOI
TL;DR: An overview of the current state of the art in adaptive equalization techniques has been presented.
Abstract: The recent digital transmission systems impose the application of channel equalizers with short training time and high tracking rate. Equalization techniques compensate for the time dispersion introduced by communication channels and combat the resulting inter-symbol interference (ISI) effect. Given a channel of unknown impulse response, the purpose of an adaptive equalizer is to operate on the channel output such that the cascade connection of the channel and the equalizer provides an approximation to an ideal transmission medium. Typically, adaptive equalizers used in digital communications require an initial training period, during which a known data sequence is transmitted. A replica of this sequence is made available at the receiver in proper synchronism with the transmitter, thereby making it possible for adjustments to be made to the equalizer coefficients in accordance with the adaptive filtering algorithm employed in the equalizer design. In this paper, an overview of the current state of the art in adaptive equalization techniques has been presented.

Proceedings ArticleDOI
18 Nov 2011
TL;DR: It is shown that the sampling period could be substantially reduced by using carry-save accumulation instead of shift-accumulation for DA-based inner-product implementation for the computation of filter output.
Abstract: In this paper, we propose an efficient pipelined architecture for high-speed adaptive filter based on distributed arithmetic (DA). We have shown that the sampling period could be substantially reduced by using carry-save accumulation instead of shift-accumulation for DA-based inner-product implementation for the computation of filter output. Unlike the existing design, the proposed design does not involve any lookup table (LUT). It involves half the number of registers compared to the existing DA-based design to store the sum of different combinations of input samples. The proposed design involves nearly 17% more hardware but offers nearly 7 times throughput and nearly 14 times less energy per sample, in average for filter orders N = 8, 16 and 32 over the existing DA-based design for adaptive filter.

Journal ArticleDOI
TL;DR: A new robust recursive least-squares adaptive filtering algorithm that uses a priori error-dependent weights that offers improved robustness as well as better tracking compared to the conventional RLS andursive least-M estimate adaptation algorithms.
Abstract: A new robust recursive least-squares (RLS) adaptive filtering algorithm that uses a priori error-dependent weights is proposed. Robustness against impulsive noise is achieved by choosing the weights on the basis of the L1 norms of the crosscorrelation vector and the input-signal autocorrelation matrix. The proposed algorithm also uses a variable forgetting factor that leads to fast tracking. Simulation results show that the proposed algorithm offers improved robustness as well as better tracking compared to the conventional RLS and recursive least-M estimate adaptation algorithms.

Journal ArticleDOI
TL;DR: In this paper, a sparsity inducing weighted l.............. 1.............. norm penalty was added to the RLS cost function to improve the adaptive identification of sparse systems, which achieved faster convergence than standard RLS when the system under consideration is sparse.
Abstract: The authors propose a new approach for the adaptive identification of sparse systems. This approach improves on the recursive least squares (RLS) algorithm by adding a sparsity inducing weighted l 1 norm penalty to the RLS cost function. Subgradient analysis is utilised to develop the recursive update equations for the calculation of the optimum system estimate, which minimises the regularised cost function. Two new algorithms are introduced by considering two different weighting scenarios for the l 1 norm penalty. These new l 1 relaxation-based RLS algorithms emphasise sparsity during the adaptive filtering process, and they allow for faster convergence than standard RLS when the system under consideration is sparse. The authors test the performance of the novel algorithms and compare it with standard RLS and other adaptive algorithms for sparse system identification.

Journal ArticleDOI
TL;DR: A new FIR adaptive filtering algorithm based on the Quasi-Newton (QN) optimization algorithm that uses a variable step-size in the coefficient update equation that leads to an improved performance.