Showing papers on "Recursive least squares filter published in 2000"
TL;DR: A receiver to perform coherent communication over Doppler spread channels is presented in this first paper of two, which treats theoretical aspects whereas the second part presents implementation issues and results.
Abstract: Scattering functions from several experiments demonstrate that acoustic underwater channels are doubly spread. Receivers used on these channels to date have difficulty with large Doppler spreads. A receiver to perform coherent communication over Doppler spread channels is presented in this first paper of two. The receiver contains a channel tracker and a linear decoder. The tracker operates by means of a modified recursive least squares algorithm which makes use of frequency-domain filters called Doppler lines. The decoder makes use of the channel tracker coefficients in order to perform minimum mean square error decoding. This first paper treats theoretical aspects whereas the second part presents implementation issues and results.
182 citations
TL;DR: The new fast nonlinear adaptive filtering algorithms called the least mean M-estimate (LMM) and transform domain LMM (TLMM) algorithms are derived and Simulation results show that they are robust to impulsive noise in the desired and input signals with an arithmetic complexity of order O(N).
Abstract: This paper proposes two gradient-based adaptive algorithms, called the least mean M estimate and the transform domain least mean M-estimate (TLMM) algorithms, for robust adaptive filtering in impulse noise. A robust M-estimator is used as the objective function to suppress the adverse effects of impulse noise on the filter weights. They have a computational complexity of order O(N) and can be viewed, respectively, as the generalization of the least mean square and the transform-domain least mean square algorithms. A robust method fur estimating the required thresholds in the M-estimator is also given. Simulation results show that the TLMM algorithm, in particular, is more robust and effective than other commonly used algorithms in suppressing the adverse effects of the impulses.
171 citations
TL;DR: In this paper, an experimental comparison between the weighted least squares (WLS) estimation and the extended Kalman filtering (EKF) methods for robot dynamic identification is presented.
141 citations
TL;DR: An adaptive finite-duration impulse response filter, based on a least-mean-square algorithm, has been developed to derive a relatively noise-free time series from the continuous Global Positioning System (CGPS) results as mentioned in this paper.
Abstract: Though state-of-the-art dual-frequency receivers are employed in the continuous Global Positioning System (CGPS) arrays, the CGPS coordinate time series are typically very noisy due to the effects of atmospheric biases, multipath, receiver noise, and so on, with multipath generally being considered the major noise contributor. An adaptive finite-duration impulse response filter, based on a least-mean-square algorithm, has been developed to derive a relatively noise-free time series from the CGPS results. Furthermore, this algorithm is suitable for real-time applications. Numerical simulation studies indicate that the adaptive filters is a powerful signal decomposer, which can significantly mitigate multipath effects. By applying the filter to both pseudorange and carrier phase multipath sequences derived from some experimental GPS data, multipath models have been reliably derived. It is found that the best multipath mitigation strategy is forward filtering using data on two adjacent days, which reduces the standard deviations of the pseudorange multipath time series to about one fourth its magnitude before correction and to about half in the case of carrier phase. The filter has been successfully applied to the pseudorange multipath sequences derived from CGPS data. The benefit of this techniques is that the affected observable sequences can be corrected, and then these corrected observables can be used to improve the quality of the GPS coordinate results. © 2000 John Wiley & Sons, Inc.
118 citations
TL;DR: Simulation results showed that the RLM algorithm performs better than the conventional RLS, NRLS, and the OSFKF algorithms when the desired and input signals are corrupted by impulses.
Abstract: This paper proposes a recursive least M-estimate (RLM) algorithm for robust adaptive filtering in impulse noise. It employs an M-estimate cost function, which is able to suppress the effect of impulses on the filter weights. Simulation results showed that the RLM algorithm performs better than the conventional RLS, NRLS, and the OSFKF algorithms when the desired and input signals are corrupted by impulses. Its initial convergence, steady-state error, computational complexity, and robustness to sudden system change are comparable to the conventional RLS algorithm in the presence of Gaussian noise alone.
104 citations
TL;DR: The binormalized data-reusing least mean squares (BNDR-LMS) algorithm is analyzed, which corresponds to the affine projection algorithm for the case of two projections, and compares favorably with other normalized LMS-like algorithms when the input signal is correlated.
Abstract: Normalized least mean squares algorithms for FIR adaptive filtering with or without the reuse of past information are known to converge often faster than the conventional least mean squares (LMS) algorithm. This correspondence analyzes an LMS-like algorithm: the binormalized data-reusing least mean squares (BNDR-LMS) algorithm. This algorithm, which corresponds to the affine projection algorithm for the case of two projections, compares favorably with other normalized LMS-like algorithms when the input signal is correlated. Convergence analyses in the mean and in the mean-squared are presented, and a closed-form formula for the mean squared error is provided for white input signals as well as its extension to the case of a colored input signal. A simple model for the input-signal vector that imparts simplicity and tractability to the analysis of second-order statistics is fully described. The methodology is readily applicable to other adaptation algorithms of difficult analysis. Simulation results validate the analysis and ensuing assumptions.
91 citations
TL;DR: In this paper, the Gauss-Newton variable forgetting factor recursive least squares (GN-VFF-RLS) algorithm is presented, which can be used to improve the tracking capability in time varying parameter estimation.
Abstract: The Gauss-Newton variable forgetting factor recursive least squares (GN-VFF-RLS) algorithm is presented, which can be used to improve the tracking capability in time varying parameter estimation. Compared to the existing algorithm, the exponentially windowed recursive least squares (EW-RLS) algorithm with optimal forgetting factor, the presented method leads to a significant improvement in fast time varying parameter estimation. The effects of signal to noise ratio and nonstationarity have been tested using computer simulations with the given parameter model. An assessment of the performance of each algorithm is presented in terms of the mean-square-deviation (MSD).
86 citations
TL;DR: A fast algorithm for the basic deconvolution problem is developed due to the low displacement rank of the involved matrices and the sparsity of the generators and Monte-Carlo simulations indicate the superior statistical performance of the structured total least squares estimator compared to other estimators such as the ordinary total least square estimator.
Abstract: In this paper we develop a fast algorithm for the basic deconvolution problem. First we show that the kernel problem to be solved in the basic deconvolution problem is a so-called structured total least squares problem. Due to the low displacement rank of the involved matrices and the sparsity of the generators, we are able to develop a fast algorithm. We apply the new algorithm on a deconvolution problem arising in a medical application in renography. By means of this example, we show the increased computational performance of our algorithm as compared to other algorithms for solving this type of structured total least squares problem. In addition, Monte-Carlo simulations indicate the superior statistical performance of the structured total least squares estimator compared to other estimators such as the ordinary total least squares estimator.
68 citations
TL;DR: This proposed linear prediction-based decision-feedback differential detection scheme for M-ary differential phase-shift keying signals transmitted over Ricean fading channels can improve conventional DD significantly for a multitude of frequency-nonselective channels, as shown analytically and by computer simulations.
Abstract: In this paper, linear prediction-based decision-feedback differential detection (DF-DD) for M-ary differential phase-shift keying (MDPSK) signals transmitted over Ricean fading channels is proposed. This scheme can improve conventional DD significantly for a multitude of frequency-nonselective channels, as shown analytically and by computer simulations. Prediction-based DF-DD is particularly well suited for application in mobile communications since the predictor coefficients may be updated regularly using the recursive least squares (RLS) algorithm. Here, adaptation can start blind, i.e., no training sequence and no a prior knowledge about the channel statistics are required. A further important characteristic of the proposed detection scheme is that no degradation occurs under frequency offset. The bit error rate (BER) performance of QDPSK with genie-aided prediction-based DF-DD is analyzed, and it is shown under which conditions the irreducible error floor of conventional DD can be removed entirely. In addition, the influence of Doppler shift is discussed. Last, the proposed scheme is compared with a second DF-DD scheme, which is based on multiple-symbol detection.
67 citations
05 Jun 2000
TL;DR: It is shown that the obtained algorithm is complex to implement, and to reduce the complexity the authors need to remove a constraint resulting in the unconstrained frequency-domain LMS (UFLMS) algorithm.
Abstract: We derive a new frequency-domain adaptive algorithm by using a frequency-domain recursive least squares criterion, minimizing an error signal in the frequency-domain. We then derive an exact adaptive algorithm from the so-called normal equation. It is shown that the obtained algorithm is complex to implement, and to reduce the complexity we need to remove a constraint resulting in the unconstrained frequency-domain LMS (UFLMS) algorithm. Most importantly, we generalize all this to the multi-channel case, thereby exploiting the cross-power spectra among all the channels which is very important (for a fast convergence rate) in multichannel acoustic echo cancellation (AEC), where the input signals are highly correlated.
56 citations
TL;DR: It is proved that BAG has identical convergence and tracking properties to recursive least squares (LMS) but has a computational cost similar to the least mean squares ( LMS) algorithm-i.e., an order of magnitude lower computational cost than RLS.
Abstract: In this paper, we present a blind adaptive gradient (BAG) algorithm for code-aided suppression of multiple-access interference (MAI) and narrow-band interference (NBI) in direct-sequence/code-division multiple-access (DS/CDMA) systems. This BAG algorithm is based on the concept of accelerating the convergence of a stochastic gradient algorithm by averaging. This ingenious concept of averaging was invented by Polyak and Juditsky (1992)-this paper examines its application to blind multiuser detection and NBI suppression in DS/CDMA systems. We prove that BAG has identical convergence and tracking properties to recursive least squares (LMS) but has a computational cost similar to the least mean squares (LMS) algorithm-i.e., an order of magnitude lower computational cost than RLS. Simulations are used to compare our averaged gradient algorithm with the blind LMS and LMS schemes.
TL;DR: In this paper, a method for adaptive and recursive estimation in a class of non-linear autoregressive models with external input is proposed, which is a combination of recursive least squares with exponential forgetting and local polynomial regression.
Abstract: SUMMARY A method for adaptive and recursive estimation in a class of non-linear autoregressive models with external input is proposed. The model class considered is conditionally parametric ARX-models (CPARX-models), which is conventional ARX-models in which the parameters are replaced by smooth, but otherwise unknown, functions of a low-dimensional input process. These coe$cient functions are estimated adaptively and recursively without specifying a global parametric form, i.e. the method allows for on-line tracking of the coe$cient functions. Essentially, in its most simple form, the method is a combination of recursive least squares with exponential forgetting and local polynomial regression. It is argued, that it is appropriate to let the forgetting factor vary with the value of the external signal which is the argument of the coe$cient functions. Some of the key properties of the modi"ed method are studied by simulation. Copyright ( 2000 John Wiley & Sons, Ltd.
TL;DR: In this article, robust schemes in regression are adapted to mean and covariance structure analysis, providing an iteratively reweighted least squares approach to robust structural equation modeling, which reduces to a standard distribution-free methodology if all cases are equally weighted.
Abstract: Robust schemes in regression are adapted to mean and covariance structure analysis, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is properly weighted according to its distance, based on first and second order moments, from the structural model. A simple weighting function is adopted because of its flexibility with changing dimensions. The weight matrix is obtained from an adaptive way of using residuals. Test statistic and standard error estimators are given, based on iteratively reweighted least squares. The method reduces to a standard distribution-free methodology if all cases are equally weighted. Examples demonstrate the value of the robust procedure.
TL;DR: A sliding window adaptive RLS-like algorithm for filtering alpha-stable noise that behaves much like the RLS algorithm in terms of convergence speed and computational complexity compared to previously introduced stochastic gradient-based algorithms, which behave like the LMS algorithm.
Abstract: We introduce a sliding window adaptive RLS-like algorithm for filtering alpha-stable noise. Unlike previously introduced stochastic gradient-type algorithms, the new adaptation algorithm minimizes the L/sub p/ norm of the error exactly in a sliding window of fixed size. Therefore, it behaves much like the RLS algorithm in terms of convergence speed and computational complexity compared to previously introduced stochastic gradient-based algorithms, which behave like the LMS algorithm. It is shown that the new algorithm achieves superior convergence rate at the expense of increased computational complexity.
TL;DR: The NNGD algorithm outperforms a gradient based algorithm for use in a neural adaptive filter, as well as the standard least mean squares (LMS) and normalised LMS algorithms.
Abstract: A novel normalised nonlinear gradient descent (NNGD) algorithm for training neural adaptive feedforward filters is presented. The algorithm is based on minimisation of the instantaneous prediction error for contractive activation functions of a neuron, and provides an adaptive learning rate. Normalisation is performed via calculation of the product of the tap input power to the filter and the squared first derivative of the activation function of a neuron. The NNGD algorithm outperforms a gradient based algorithm for use in a neural adaptive filter, as well as the standard least mean squares (LMS) and normalised LMS algorithms. To support the analysis, simulation results on real speech are provided.
TL;DR: A characterization process is described that uses a recursive least squares (RLS) algorithm by which an equation-based model can be automatically built that can be used to estimate the power consumed in the circuit for any given input/output signal statistics.
Abstract: In this paper, we propose a modeling technique that captures the dependence of the power dissipation of a (combinational or sequential) logic circuit on its input/output signal switching statistics. The resulting power macromodel consists of a quadratic or cubic equation in four variables, that can be used to estimate the power consumed in the circuit for any given input/output signal statistics. Given a low-level (typically gate-level) description of the circuit, we describe a characterization process that uses a recursive least squares (RLS) algorithm by which such an equation-based model can be automatically built. This approach has been implemented and models have been built and tested for many combinational and sequential benchmark circuits.
TL;DR: In this article, an improved least squares (ILS) objective function is used to reduce the estimation bias caused by measurement noise, and a novel adaptive filter is developed to track a time-varying polynomial system.
Abstract: This paper studies the nonlinear system identification problem in a noisy environment using an adaptive algorithm. In particular, nonlinear systems of the polynomial type are considered here. An improved least squares (ILS) objective function is used to reduce the estimation bias caused by measurement noise. Based on this ILS criterion, a novel adaptive filter is developed to track a time-varying polynomial system. Numerical simulations showed that the proposed adaptive algorithm was superior to the conventional identification technique. We applied this new adaptive filter to demodulate the signals of transmission in a chaotic multiuser spread spectrum (SS) communication system. It was observed that the new approach was effective in demodulating a SS signal, even at low signal-to-noise ratios (SNR's).
TL;DR: In this article, the shape restrictions are translated into linear inequality conditions on spline coefficients and the basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist.
Abstract: Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.
24 Apr 2000
TL;DR: Two methods for robot dynamic identification which include the weighted least squares estimation and the extended Kalman filtering are presented which are compared for a SCARA robot.
Abstract: This paper presents a comparison of two methods for robot dynamic identification which include the weighted least squares estimation and the extended Kalman filtering. Comparative experimental results and discussion are presented for a SCARA robot.
01 Sep 2000
TL;DR: It is shown, throw computer experiments, that a large reduction in the residual noise can be achieved in non-stationary environments, compared with the LMS and RLS based algorithms, especially when on-line secondary path modeling is used.
Abstract: Most Active Noise Control (ANC) systems use some form of the LMS [5] [9] algorithm due to its reduced computational complexity However, the problems associated with it are well-known, namely slow convergence and high sensitivity to the eigenvalue spread [3] [9] To overcome these problems the RLS algorithm is often used, but it is now widely known, that the RLS loses many of its good properties for a forgetting factor lower than one Namely, it has been shown that in some applications the LMS algorithm is actually better in tracking non-stationary systems than the RLS algorithm [2] [3] One approach, which works well with non-stationary systems, is to use some specialized form of the Kalman filter, which can be interpreted as a generalization of the RLS algorithm [1][3][4] The Kalman filter has a high computational complexity, similar to that of the RLS algorithm, which can make it costly for some applications Nevertheless, for narrow-band ANC, the number of taps is not very large [9], and the application of the Kalman filter in ANC may be easily handled by today DSP's In this paper, a specialized version of the Kalman filter fitted to ANC is developed; both control filter adaptation and secondary path modeling It is shown, throw computer experiments, that a large reduction in the residual noise can be achieved in non-stationary environments, compared with the LMS and RLS based algorithms, especially when on-line secondary path modeling is used
Journal Article•
TL;DR: This paper proposes a local method where, for each query, different model candidates are first generated, then assessed and finally selected, and introduces in the context of local learning the recursive least squares algorithm as an efficient way to generate local models.
Abstract: Local learning techniques, for each query, extract a prediction interpolating locally the neighboring examples which are considered relevant according to a distance measure. As other learning approaches, the local learning procedure can be conveniently decomposed into a parametric identification and a structural identification. While parametric identification is reduced to a linear regression, structural identification requires that the designer perform a certain number of choices. In this paper we focus on an automatic queryby-query selection of the bandwidth, a structural parameter which plays a major role in the final performance. We propose a local method where, for each query, different model candidates are first generated, then assessed and finally selected. We introduce in the context of local learning the recursive least squares algorithm as an efficient way to generate local models. Moreover, local cross-validation is used as an economic way to validate different alternatives. As far as model selection is concerned, the winner-takes-all strategy and a local combination of the most promising models are explored. The method proposed is tested on six different datasets and compared with state-of-the-art approaches.
TL;DR: In this article, the design and performance of nonlinear minimum mean square error multiuser detectors for direct sequence code-division multiple-access (CDMA) networks are considered, where the cyclostationarity of the MAI and ISI is exploited through a feedforward filter (FFF) which processes samples at the output of parallel chip-matched filters, and a feedback filter (FBF), which processes detected symbols.
Abstract: We consider the design and performance of nonlinear minimum mean-square-error multiuser detectors for direct sequence code-division multiple-access (CDMA) networks. With multiple users transmitting asynchronously at high data rates over multipath fading channels, the detectors contend with both multiple-access interference (MAI) and intersymbol interference (ISI). The cyclostationarity of the MAI and ISI is exploited through a feedforward filter (FFF), which processes samples at the output of parallel chip-matched filters, and a feedback filter (FBF), which processes detected symbols. By altering the connectivity of the FFF and FBF, we define four architectures based on fully connected (FC) and nonconnected (NC) filters. Increased connectivity of the FFF gives each user access to more samples of the received signal, while increased connectivity of the FBF provides each user access to previous decisions of other users. We consider three methods for specifying the FFF sampling and propose a nonuniform FFF sampling scheme based on multipath ray tracking that can offer improved performance relative to uniform FFF sampling. For the FC architecture, we capitalize on the sharing of filter contents among users by deriving a multiuser recursive least squares (RLS) algorithm and direct matrix inversion approach, which determine the coefficients more efficiently than single-user algorithms. We estimate the uncoded bit-error rate (BER) of the feedforward/feedback detectors for CDMA systems with varying levels of power control and timing control for multipath channels with quasi-static Rayleigh fading. Simulations of packet-based QPSK transmission validate the theoretical BER analysis and demonstrate that the multiuser RLS adapted detectors train in several hundred symbols and avoid severe error propagation during data transmission mode.
TL;DR: Experimental results for a 12/8 motor demonstrate that estimation is possible over the full range of operating conditions, including the field-weakening region, with a typical accuracy of better than two mechanical degrees.
Abstract: This paper describes a new algorithm for the estimation of rotor position in a switched reluctance motor. It is based on a recursive least-squares estimator deducing both position and speed. A particular advantage of the algorithm is its ability to extract information about rotor position at very low speeds (one electrical cycle per minute) from voltage and current waveforms sampled only at the converter switching frequency. Experimental results for a 12/8 motor demonstrate that estimation is possible over the full range of operating conditions, including the field-weakening region, with a typical accuracy of better than two mechanical degrees. The paper also illustrates the performance of the algorithm by showing it operating within a sensorless position controller.
TL;DR: Analysis of a convolutionally coded code-division multiple-access system, which employs a linear, minimum mean-square error (MMSE) receiver for interference suppression, shows that the MMSE receiver with coding can provide a substantial gain over the matched-filter receiver in a rapidly varying, Rayleigh fading channel.
Abstract: This paper analyzes the performance of a convolutionally coded code-division multiple-access system, which employs a linear, minimum mean-square error (MMSE) receiver for interference suppression. A flat, Rayleigh fading channel is considered, where convolutional encoding and interleaving are employed in order to combat the effects of the fading. Theoretical results are derived for the average bit-error probability of the MMSE receiver, where the optimum tap weights for the adaptive filter are determined by the solution of the Wiener-Hopf equations. Simulation results showing the average bit-error rate of the MMSE receiver are also presented, which incorporate the effects of recursive least squares adaptation, channel estimation using pilot symbol-assisted modulation, and finite interleaving. Results show that the MMSE receiver with coding can provide a substantial gain over the matched-filter receiver in a rapidly varying, Rayleigh fading channel. The results also reiterate the fact that lower rate codes are not necessarily the best choice when used with the MMSE receiver.
TL;DR: In this article, variable gain least mean-square (LMS) and weighted recursive least-squares (WRLS) algorithms have been proposed based on the setmembership identification.
TL;DR: In this paper, generalized least squares methods are proposed to estimate potential mean structure parameters and evaluate whether the given model can be successfully augmented with a mean structure, and a simulation evaluates the performance of some alternative tests.
Abstract: The vast majority of structural equation models contains no mean structure, that is, the population means are estimated at the sample means and then eliminated from modeling consideration. Generalized least squares methods are proposed to estimate potential mean structure parameters and to evaluate whether the given model can be successfully augmented with a mean structure. A simulation evaluates the performance of some alternative tests. A method that takes variability due to the estimation of covariance structure parameters into account in the mean structure estimator, as well as in the weight matrix of the generalized least squares function, performs best. In small samples, the F test and Yuan-Bentler adjusted chi-square test perform best. For example, if there is interest in modeling whether arithmetic skills or vocabulary levels are increasing across time, as one would expect in school, an analysis of means is an essential modeling component.
TL;DR: In this paper, the authors compared various coherent space-time processing methods for a condition of a marginally overspread channel operating at 50 kHz and found that a suboptimal approach consisting of the adaptive beamformer followed by RLS equalization reduced reverberation and transmission errors.
Abstract: Achieving reliable underwater communication in shallow water is a difficult task because of the random time-varying nature of multipath propagation. When the product of Doppler-related signal bandwidth spread and multipath-related time spread of the channel is larger than one, some types of adaptive signal processing may not work very well. In this paper, various methods of coherent space-time processing are compared for a condition of a marginally overspread channel operating at 50 kHz. Various combinations of suboptimal spatially adaptive and time adaptive methods are considered. The coherent path beamformer (CPB) and recursive least squares (RLS) adaptive beamformer, both in combination with RLS time filtering, are analyzed. Also considered in the analysis is the combined RLS space-time optimal adaptive processor. Many experiments using broad-band phase-shift-keyed transmissions in shallow water have been conducted to provide data for testing these various processing methods. Because of the rapid time variation of the multipath, the product of bandwidth spread and time spread at this test site approached unity. In this environment, a suboptimal approach consisting of the adaptive beamformer followed by RLS equalization reduced reverberation and transmission errors.
TL;DR: A novel noncoherent receiver for M-ary differential phase-shift keying signals transmitted over intersymbol interference channels is presented, and the performance of the proposed receiver approaches that of a coherent linear minimum mean-squared-error equalizer.
Abstract: A novel noncoherent receiver for M-ary differential phase-shift keying signals transmitted over intersymbol interference channels is presented. The noncoherent receiver consists of a linear equalizer and a decision-feedback differential detector. A significant performance gain over a previously proposed noncoherent receiver can be observed. For an infinite number of feedback symbols, the optimum equalizer coefficients can be calculated analytically, and the performance of the proposed receiver approaches that of a coherent linear minimum mean-squared-error equalizer. Moreover, a modified least mean square and a modified recursive least squares algorithm for adaptation of the equalizer coefficients are discussed.
01 Dec 2000
TL;DR: It is shown in this paper that, based on an invariant formulation of the problem at hand, a solution is possible that relies on recursive linear least squares that lends itself to an online implementation, as demonstrated here with experimental results.
Abstract: The hand-eye problem consists in determining the relative pose between two coordinate frames fixed to the same rigid body from measurements of the poses attained by these two frames, as the body moves. In robotics this problem arises when two frames are attached to the end-effector (EE), one of these at the gripper, the other to a sensor such as a camera or a laser range-finder. Various procedures have been proposed to solve this problem when perfect pose measurements are available at a pair of EE poses, the treatment of noisy measurements being a current research topic. Solutions proposed for the case of perfect measurements require an iterative procedure based on the singular-value decomposition, which itself relies on iterative procedures. The treatment of noisy measurements has led to offline least-square solutions. It is shown in this paper that, based on an invariant formulation of the problem at hand, a solution is possible that relies on recursive linear least squares. Thus, the procedure lends itself to an online implementation, as demonstrated here with experimental results. A major difference between the proposed procedure and those reported in the literature is that the latter are iterative; ours is recursive.
01 Sep 2000
TL;DR: The new fast nonlinear adaptive filtering algorithms called the least mean M-estimate (LMM) and transform domain LMM (TLMM) algorithms are derived and Simulation results show that they are robust to impulsive noise in the desired and input signals with an arithmetic complexity of order O(N).
Abstract: Adaptive filters with suitable nonlinear devices are very effective in suppressing the adverse effect due to impulse noise. In a previous work, the authors have proposed a new class of nonlinear adaptive filters using the concept of robust statistics [1,2]. The robust M-estimator is used as the objective function, instead of the mean square errors, to suppress the impulse noise. The optimal coefficient vector for such nonlinear filter is governed by a normal equation which can be solved by a recursive least squares like algorithm with O(N2) arithmetic complexity, where N is the length of the adaptive filter. In this paper, we generalize the robust statistic concept to least mean square (LMS) and transform domain LMS algorithms. The new fast nonlinear adaptive filtering algorithms called the least mean M-estimate (LMM) and transform domain LMM (TLMM) algorithms are derived. Simulation results show that they are robust to impulsive noise in the desired and input signals with an arithmetic complexity of order O(N).