Showing papers on "Adaptive filter published in 2009"

Biomedical Signal Analysis: A Case-Study Approach

Abstract: Dedication. Preface. About the Author. Acknowledgments. Symbols and Abbreviations. 1 Introduction to Biomedical Signals. 1.1 The Nature of Biomedical Signals. 1.2 Examples of Biomedical Signals. 1.3 Objectives of Biomedical Signal Analysis. 1.4 Difficulties in Biomedical Signal Analysis. 1.5 Computer-aided Diagnosis. 1.6 Remarks. 1.7 Study Questions and Problems. 1.8 Laboratory Exercises and Projects. 2 Concurrent, Coupled, and Correlated Processes. 2.1 Problem Statement. 2.2 Illustration of the Problem with Case-studies. 2.3 Application: Segmentation of the PCG. 2.4 Remarks. 2.5 Study Questions and Problems. 2.6 Laboratory Exercises and Projects. 3 Filtering for Removal of Artifacts. 3.1 Problem Statement. 3.2 Illustration of the Problem with Case-studies. 3.3 Time-domain Filters. 3.4 Frequency-domain Filters. 3.5 Optimal Filtering: The Wiener Filter. 3.6 Adaptive Filters for Removal of Interference. 3.7 Selecting an Appropriate Filter. 3.8 Application: Removal of Artifacts in the ECG. 3.9 Application: Maternal - Fetal ECG. 3.10 Application: Muscle-contraction Interference. 3.11 Remarks. 3.12 Study Questions and Problems. 3.13 Laboratory Exercises and Projects. 4 Event Detection. 4.1 Problem Statement. 4.2 Illustration of the Problem with Case-studies. 4.3 Detection of Events and Waves. 4.4 Correlation Analysis of EEG channels. 4.5 Cross-spectral Techniques. 4.6 The Matched Filter. 4.7 Detection of the P Wave. 4.8 Homomorphic Filtering. 4.9 Application: ECG Rhythm Analysis. 4.10 Application: Identification of Heart Sounds. 4.11 Application: Detection of the Aortic Component of S2. 4.12 Remarks. 4.13 Study Questions and Problems. 4.14 Laboratory Exercises and Projects. 5 Waveshape and Waveform Complexity. 5.1 Problem Statement. 5.2 Illustration of the Problem with Case-studies. 5.3 Analysis of Event-related Potentials. 5.4 Morphological Analysis of ECG Waves. 5.5 Envelope Extraction and Analysis. 5.6 Analysis of Activity. 5.7 Application: Normal and Ectopic ECG Beats. 5.8 Application: Analysis of Exercise ECG. 5.9 Application: Analysis of Respiration. 5.10 Application: Correlates of Muscular Contraction. 5.11 Remarks. 5.12 Study Questions and Problems. 5.13 Laboratory Exercises and Projects. 6 Frequency-domain Characterization. 6.1 Problem Statement. 6.2 Illustration of the Problem with Case-studies. 6.3 The Fourier Spectrum. 6.4 Estimation of the Power Spectral Density Function. 6.5 Measures Derived from PSDs. 6.6 Application: Evaluation of Prosthetic Valves. 6.7 Remarks. 6.8 Study Questions and Problems. 6.9 Laboratory Exercises and Projects. 7 Modeling Biomedical Systems. 7.1 Problem Statement. 7.2 Illustration of the Problem. 7.3 Point Processes. 7.4 Parametric System Modeling. 7.5 Autoregressive or All-pole Modeling. 7.6 Pole-zero Modeling. 7.7 Electromechanical Models of Signal Generation. 7.8 Application: Heart-rate Variability. 7.9 Application: Spectral Modeling and Analysis of PCG Signals. 7.10 Application: Coronary Artery Disease. 7.11 Remarks. 7.12 Study Questions and Problems. 7.13 Laboratory Exercises and Projects. 8 Analysis of Nonstationary Signals. 8.1 Problem Statement. 8.2 Illustration of the Problem with Case-studies. 8.3 Time-variant Systems. 8.4 Fixed Segmentation. 8.5 Adaptive Segmentation. 8.6 Use of Adaptive Filters for Segmentation. 8.7 Application: Adaptive Segmentation of EEG Signals. 8.8 Application: Adaptive Segmentation of PCG Signals. 8.9 Application: Time-varying Analysis of Heart-rate Variability. 8.10 Remarks. 8.11 Study Questions and Problems. 8.12 Laboratory Exercises and Projects. 9 Pattern Classification and Diagnostic Decision. 9.1 Problem Statement. 9.2 Illustration of the Problem with Case-studies. 9.3 Pattern Classification. 9.4 Supervised Pattern Classification. 9.5 Unsupervised Pattern Classification. 9.6 Probabilistic Models and Statistical Decision. 9.7 Logistic Regression Analysis. 9.8 The Training and Test Steps. 9.9 Neural Networks. 9.10 Measures of Diagnostic Accuracy and Cost. 9.11 Reliability of Classifiers and Decisions. 9.12 Application: Normal versus Ectopic ECG Beats. 9.13 Application: Detection of Knee-joint Cartilage Pathology. 9.14 Remarks. 9.15 Study Questions and Problems. 9.16 Laboratory Exercises and Projects. References. Index.

Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations

Abstract: This article considers the application of variational Bayesian methods to joint recursive estimation of the dynamic state and the time-varying measurement noise parameters in linear state space models. The proposed adaptive Kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately. The result is a recursive algorithm, where on each step the state is estimated with Kalman filter and the sufficient statistics of the noise variances are estimated with a fixed-point iteration. The performance of the algorithm is demonstrated with simulated data.

Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models

Abstract: This book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general complex signals (circular and noncircular). It brings together adaptive filtering algorithms for feedforward (transversal) and feedback architectures and the recent developments in the statistics of complex variable, under the powerful frameworks of CR (Wirtinger) calculus and augmented complex statistics. This offers a number of theoretical performance gains, which is illustrated on both stochastic gradient algorithms, such as the augmented complex least mean square (ACLMS), and those based on Kalman filters. This work is supported by a number of simulations using synthetic and real world data, including the noncircular and intermittent radar and wind signals.

Distributed LMS for Consensus-Based In-Network Adaptive Processing

Abstract: Adaptive algorithms based on in-network processing of distributed observations are well-motivated for online parameter estimation and tracking of (non)stationary signals using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-LMS) algorithm is developed in this paper, offering simplicity and flexibility while solely requiring single-hop communications among sensors. The resultant estimator minimizes a pertinent squared-error cost by resorting to i) the alternating-direction method of multipliers so as to gain the desired degree of parallelization and ii) a stochastic approximation iteration to cope with the time-varying statistics of the process under consideration. Information is efficiently percolated across the WSN using a subset of ldquobridgerdquo sensors, which further tradeoff communication cost for robustness to sensor failures. For a linear data model and under mild assumptions aligned with those considered in the centralized LMS, stability of the novel D-LMS algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time. Interestingly, this weak stochastic stability result extends to the pragmatic setup where intersensor communications are corrupted by additive noise. In the absence of observation and communication noise, consensus is achieved almost surely as local estimates are shown exponentially convergent to the parameter of interest with probability one. Mean-square error performance of D-LMS is also assessed. Numerical simulations: i) illustrate that D-LMS outperforms existing alternatives that rely either on information diffusion among neighboring sensors, or, local sensor filtering; ii) highlight its tracking capabilities; and iii) corroborate the stability and performance analysis results.

Adaptive Reduced-Rank Processing Based on Joint and Iterative Interpolation, Decimation, and Filtering

Abstract: We present an adaptive reduced-rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems. The proposed method is based on the concept of joint and iterative interpolation, decimation and filtering. We describe an iterative least squares (LS) procedure to jointly optimize the interpolation, decimation and filtering tasks for reduced-rank adaptive filtering. In order to design the decimation unit, we present the optimal decimation scheme and also propose low-complexity decimation structures. We then develop low-complexity least-mean squares (LMS) and recursive least squares (RLS) algorithms for the proposed scheme along with automatic rank and branch adaptation techniques. An analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed. We consider the application of the proposed algorithms to interference suppression in code-division multiple-access (CDMA) systems. Simulations results show that the proposed algorithms outperform the best known reduced-rank schemes with lower complexity.

$l_{0}$ Norm Constraint LMS Algorithm for Sparse System Identification

Abstract: In order to improve the performance of least mean square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on l 0 norm-a typical metric of system sparsity, is proposed and integrated into the cost function of the LMS algorithm. This integration is equivalent to add a zero attractor in the iterations, by which the convergence rate of small coefficients, that dominate the sparse system, can be effectively improved. Moreover, using partial updating method, the computational complexity is reduced. The simulations demonstrate that the proposed algorithm can effectively improve the performance of LMS-based identification algorithms on sparse system.

Spatially and temporally varying adaptive covariance inflation for ensemble filters

Abstract: Ensemble filters are used in many data assimilation applications in geophysics. Basic implementations of ensemble filters are trivial but are susceptible to errors from many sources. Model error, sampling error and fundamental inconsistencies between the filter assumptions and reality combine to produce assimilations that are suboptimal or suffer from filter divergence. Several auxiliary algorithms have been developed to help filters tolerate these errors. For instance, covariance inflation combats the tendency of ensembles to have insufficient variance by increasing the variance during the assimilation. The amount of inflation is usually determined by trial and error. It is possible, however, to design Bayesian algorithms that determine the inflation adaptively. A spatially and temporally varying adaptive inflation algorithm is described. A normally distributed inflation random variable is associated with each element of the model state vector. Adaptive inflation is demonstrated in two low-order model experiments. In the first, the dominant error source is small ensemble sampling error. In the second, the model error is dominant. The adaptive inflation assimilations have better mean and variance estimates than other inflation methods.

k-t PCA: temporally constrained k-t BLAST reconstruction using principal component analysis.

Abstract: The k-t broad-use linear acquisition speed-up technique (BLAST) has become widespread for reducing image acquisition time in dynamic MRI. In its basic form k-t BLAST speeds up the data acquisition by undersampling k-space over time (referred to as k-t space). The resulting aliasing is resolved in the Fourier reciprocal x-f space (x = spatial position, f = temporal frequency) using an adaptive filter derived from a low-resolution estimate of the signal covariance. However, this filtering process tends to increase the reconstruction error or lower the achievable acceleration factor. This is problematic in applications exhibiting a broad range of temporal frequencies such as free-breathing myocardial perfusion imaging. We show that temporal basis functions calculated by subjecting the training data to principal component analysis (PCA) can be used to constrain the reconstruction such that the temporal resolution is improved. The presented method is called k-t PCA.

Using Correntropy as a cost function in linear adaptive filters

Abstract: Correntropy has been recently defined as a localised similarity measure between two random variables, exploiting higher order moments of the data This paper presents the use of Correntropy as a cost function for minimizing the error between the desired signal and the output of an adaptive filter, in order to train the filter weightsWe have shown that this cost function has the computational simplicity of the popular LMS algorithm, along with the robustness that is obtained by using higher order moments for error minimization We apply this technique for system identification and noise cancellation configurations The results demonstrate the advantages of the proposed cost function as compared to LMS algorithm, and the recently proposed Minimum Error Entropy (MEE) cost function

Subband Adaptive Filtering: Theory and Implementation

Abstract: Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computational complexity and improving the convergence rate of algorithms in adaptive signal processing applications. This book provides an introductory, yet extensive guide on the theory of various subband adaptive filtering techniques. For beginners, the authors discuss the basic principles that underlie the design and implementation of subband adaptive filters. For advanced readers, a comprehensive coverage of recent developments, such as multiband tapweight adaptation, delayless architectures, and filterbank design methods for reducing bandedge effects are included. Several analysis techniques and complexity evaluation are also introduced in this book to provide better understanding of subband adaptive filtering. This book bridges the gaps between the mixeddomain natures of subband adaptive filtering techniques and provides enough depth to the material augmented by many MATLAB functions and examples. Key Features: Acts as a timely introduction for researchers, graduate students and engineers who want to design and deploy subband adaptive filters in their research and applications. Bridges the gaps between two distinct domains: adaptive filter theory and multirate signal processing. Uses a practical approach through MATLAB-based source programs on the accompanying CD. Includes more than 100 M-files, allowing readers to modify the code for different algorithms and applications and to gain more insight into the theory and concepts of subband adaptive filters. Subband Adaptive Filtering is aimed primarily at practicing engineers, as well as senior undergraduate and graduate students. It will also be of interest to researchers, technical managers, and computer scientists.

An Information Theoretic Approach of Designing Sparse Kernel Adaptive Filters

Abstract: This paper discusses an information theoretic approach of designing sparse kernel adaptive filters. To determine useful data to be learned and remove redundant ones, a subjective information measure called surprise is introduced. Surprise captures the amount of information a datum contains which is transferable to a learning system. Based on this concept, we propose a systematic sparsification scheme, which can drastically reduce the time and space complexity without harming the performance of kernel adaptive filters. Nonlinear regression, short term chaotic time-series prediction, and long term time-series forecasting examples are presented.

A Fast and Accurate Synchronization Technique for Extraction of Symmetrical Components

Abstract: This paper introduces an approach for the real-time extraction of the frequency, phase angle, and symmetrical components of the grid signal, which is of great importance for many applications in power systems such as power quality and protection The proposed method is based on the concept of the adaptive notch filter that provides a fast and accurate estimation of the symmetrical components in the presence of frequency and amplitude variations In addition, the system offers a high degree of immunity and insensitivity to power system disturbances, harmonics, and other types of pollutions that exist in the grid signal The simplicity of the structure makes the method suitable for both software and hardware implementations Moreover, this very simple and very powerful tool can be used as a synchronization technique, which further simplifies the control issues currently challenging the integration of distributed energy technologies into the electricity grid Mathematical derivations are presented to describe the principles of operation, and experimental results confirm the validity of the analytical work

Noise-Driven Anisotropic Diffusion Filtering of MRI

Abstract: A new filtering method to remove Rician noise from magnetic resonance images is presented. This filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for MRI, as the speckle reducing anisotropic diffusion did for ultrasound images. The parameters of the filter are automatically chosen from the estimated noise. This property improves the convergence rate of the diffusion while preserving contours, leading to more robust and intuitive filtering. The partial derivative equation of the filter is extended to a new matrix diffusion filter which allows a coherent diffusion based on the local structure of the image and on the corresponding oriented local standard deviations. This new filter combines volumetric, planar, and linear components of the local image structure. The numerical scheme is explained and visual and quantitative results on simulated and real data sets are presented. In the experiments, the new filter leads to the best results.

Impulse Noise Removal Using Directional Difference Based Noise Detector and Adaptive Weighted Mean Filter

Abstract: A two-stage algorithm, called switching-based adaptive weighted mean filter, is proposed to remove salt-and-pepper noise from the corrupted images. First, the directional difference based noise detector is used to identify the noisy pixels by comparing the minimum absolute value of four mean differences between the current pixel and its neighbors in four directional windows with a predefined threshold. Then, the adaptive weighted mean filter is adopted to remove the detected impulses by replacing each noisy pixel with the weighted mean of its noise-free neighbors in the filtering window. Numerous simulations demonstrate that the proposed filter outperforms many other existing algorithms in terms of effectiveness in noise detection, image restoration and computational efficiency.

Adaptive Algorithms to Track the PARAFAC Decomposition of a Third-Order Tensor

Abstract: The PARAFAC decomposition of a higher-order tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines. Existing PARAFAC algorithms are computationally demanding and operate in batch mode - both serious drawbacks for on-line applications. When the data are serially acquired, or the underlying model changes with time, adaptive PARAFAC algorithms that can track the sought decomposition at low complexity would be highly desirable. This is a challenging task that has not been addressed in the literature, and the topic of this paper. Given an estimate of the PARAFAC decomposition of a tensor at instant t, we propose two adaptive algorithms to update the decomposition at instant t+1, the new tensor being obtained from the old one after appending a new slice in the 'time' dimension. The proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of state-of-art batch algorithms, at orders of magnitude lower complexity. The effectiveness of the proposed algorithms is illustrated using a MIMO radar application (tracking of directions of arrival and directions of departure) as an example.

Advanced Radar Detection Schemes Under Mismatched Signal Models

Abstract: Adaptive detection of signals embedded in correlated Gaussian noise has been an active field of research in the last decades. This topic is important in many areas of signal processing such as, just to give some examples, radar, sonar, communications, and hyperspectral imaging. Most of the existing adaptive algorithms have been designed following the lead of the derivation of Kelly's detector which assumes perfect knowledge of the target steering vector. However, in realistic scenarios, mismatches are likely to occur due to both environmental and instrumental factors. When a mismatched signal is present in the data under test, conventional algorithms may suffer severe performance degradation. The presence of strong interferers in the cell under test makes the detection task even more challenging. An effective way to cope with this scenario relies on the use of "tunable" detectors, i.e., detectors capable of changing their directivity through the tuning of proper parameters. The aim of this book is to present some recent advances in the design of tunable detectors and the focus is on the so-called two-stage detectors, i.e., adaptive algorithms obtained cascading two detectors with opposite behaviors. We derive exact closed-form expressions for the resulting probability of false alarm and the probability of detection for both matched and mismatched signals embedded in homogeneous Gaussian noise. It turns out that such solutions guarantee a wide operational range in terms of tunability while retaining, at the same time, an overall performance in presence of matched signals commensurate with Kelly's detector. Table of Contents: Introduction / Adaptive Radar Detection of Targets / Adaptive Detection Schemes for Mismatched Signals / Enhanced Adaptive Sidelobe Blanking Algorithms / Conclusions

Current Harmonic Compensation by a Single-Phase Shunt Active Power Filter Controlled by Adaptive Neural Filtering

Abstract: This paper presents a single-phase shunt active power filter (APF) for current harmonic compensation based on neural filtering. The shunt active filter, realized by a current-controlled inverter, has been used to compensate a nonlinear current load by receiving its reference from a neural adaptive notch filter. This is a recursive notch filter for the fundamental grid frequency (50 Hz) and is based on the use of a linear adaptive neuron (ADALINE). The filter's parameters are made adaptive with respect to the grid frequency fluctuations. A phase-locked loop system is used to extract the fundamental component from the coupling point voltage and to estimate the actual grid frequency. The current control of the inverter has been performed by a multiresonant controller. The estimated grid frequency is fed to the neural adaptive filter and to the multiresonant controller. In this way, the inverter creates a current equal in amplitude and opposite in sign to the load harmonic current, thus producing an almost sinusoidal grid current. An automatic tuning of the multiresonant controller is implemented, which recognizes the largest three harmonics of the load current to be compensated by the APF. The stability analysis of the proposed control system is shown. The methodology has been applied in numerical simulations and experimentally to a properly devised test setup, also in comparison with the classic sinusoidal current control based on the P-Q theory.

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

Abstract: The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bias is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.

Adaptive noise control system

Abstract: An active noise cancellation system that reduces, at a listening position, power of a noise signal radiated from a noise source to the listening position. The system includes an adaptive filter, at least one acoustic actuator and a signal processing device. The adaptive filter receives a reference signal representing the noise signal, and provides a compensation signal. The at least one acoustic actuator radiates the compensation signal to the listening position. The signal processing device evaluates and assesses the stability of the adaptive filter.

A Signal-Processing Adaptive Algorithm for Selective Current Harmonic Cancellation in Active Power Filters

Abstract: Selective harmonic cancellation has become of primary importance in a wide range of power electronics applications, for example, uninterrupted power systems, regenerative converters, and active power filters (APFs). In such applications, the primary objectives are an accurate cancellation of selected harmonics and a quick speed of response under transients. This paper provides a novel signal-processing algorithm for selective harmonic identification based on heterodyning, moving average finite-impulse response filters, and phase-locked loop (PLL). The algorithm is applied over the current of a nonlinear load in the feedforward-based control of an APF. The PLL tracks the phase and frequency of the fundamental component. Then, the fundamental phase is multiplied by the order of the selected harmonic, and two random unitary orthogonal "axis waves" are generated. These unitary waves, rotating at the harmonic frequency, are multiplied by the input load current, thereby "moving" the Fourier series coefficients of the selected harmonic to DC (heterodyning). Moving average FIR filters are used to filter the harmonics generated in the heterodyning process from the DC signal; moving average FIR filters are very suitable for most of the power quality applications, thanks to their "comb-type" frequency response and their quick transient response. Experimental results confirm good performance for steady-state harmonic cancellation and an optimal system response to load transients. The theory of the algorithm has been developed for single- and three-phase systems.

f-x adaptive seismic-trace interpolation

Abstract: We use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency-space (f-x) seismic interpolation. Adaptive prediction filters can model signals where the dominant wavenumbers vary in space. This concept leads to an f-x interpolation method that does not require windowing strategies for optimal results. In other words, adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips. The interpolation method’s performance depends on two parameters: filter length and forgetting factor. We pay particular attention to selection of the forgetting factor because it controls the algorithm’s adaptability to changes in local dip. Finally, we use synthetic- and real-data examples to illustrate the performance of the proposed adaptive f-x interpolation method.

An Investigation on the Selection of Filter Topologies for Passive Filter Applications

Abstract: Passive filters have been a very effective solution for power system harmonic mitigation. These filters have several topologies that give different frequency response characteristics. The current industry practice is to combine filters of different topologies to achieve a certain harmonic filtering goal. However, there is a lack of information on how to select different filter topologies. This decision is based on the experience of present filter designers. The goal of this paper is to investigate the filter topology selection issue. It presents our research results on the effectiveness and costs of various filter topologies for harmonic mitigation. The research results show that the association of three single-tuned filters is a very appropriate solution for most typical harmonic problems.

Prototype filter design for filter bank based multicarrier transmission

Abstract: This paper concentrates on an efficient prototype filter design in the context of filter bank based multicarrier (FBMC) transmission. An advantage of the chosen method, frequency sampling technique, is that near perfect reconstruction prototype filters can be expressed using a closed-form representation with only a few adjustable parameters. The performance of various designs are analyzed using the offset-QAM based FBMC system. Numerical results are provided to characterize different optimization criteria in terms of frequency selectivity of resulting prototype filters and total interference level of the filter bank structure. Furthermore, it is shown what kind of performance trade-offs can be obtained by adjusting those free parameters. In this sense, the presented results offer useful information to a system designer.

An effective filtering for GRACE time-variable gravity: Fan filter

Abstract: [1] Spatial low-pass filtering is necessary for processing the GRACE time-variable gravity (TVG) data which are otherwise plagued with short-wavelength noises. Here we devise a new non-isotropic filter, called the fan filter: In terms of the spherical harmonic spectrum, the fan filter is simply a 2-D double filter consisting of a low-pass along the degree n (the same as the conventional isotropic filter) simultaneously with a low-pass along the order m, whose contour projection onto the (n, m) plane is fan-shaped. It is deterministic and independent of a priori or external information, its implementation is straightforward, and the result is objective. Most importantly, we show that this simple filter performs well among its counterparts under similar conditions, in particular against the N-S striping noises prevalent in the GRACE TVG solutions. We demonstrate this with Gaussian weights at filter length and hence spatial resolution as fine as 300 km. We also deduce the fan filter's nominal amplitude-reduction factor as a function of the filter length for TVG signals that follow the Kaula rule.

Adaptive Alternating Minimization Algorithms

Abstract: The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application in many areas such as signal processing, information theory, control, and finance. A general set of sufficient conditions for the convergence and correctness of the algorithm are known when the underlying problem parameters are fixed. In many practical situations, however, the underlying problem parameters are changing over time, and the use of an adaptive algorithm is more appropriate. In this paper, we study such an adaptive version of the alternating minimization algorithm. More precisely, we consider the impact of having a slowly time-varying domain over which the minimization takes place. As a main result of this paper, we provide a general set of sufficient conditions for the convergence and correctness of the adaptive algorithm. Perhaps somewhat surprisingly, these conditions seem to be the minimal ones one would expect in such an adaptive setting. We present applications of our results to adaptive decomposition of mixtures, adaptive log-optimal portfolio selection, and adaptive filter design.

Set-Membership Adaptive Algorithms Based on Time-Varying Error Bounds for CDMA Interference Suppression

Abstract: This paper presents set-membership (SM) adaptive algorithms based on time-varying error bounds for code-division multiple-access (CDMA) interference suppression. We introduce a modified family of SM adaptive algorithms for parameter estimation with time-varying error bounds. The considered algorithms include modified versions of the SM normalized least mean square (SM-NLMS), the affine projection (SM-AP), and the bounding ellipsoidal adaptive constrained (BEACON) recursive least-square technique. The important issue of error-bound specification is addressed in a new framework that takes into account parameter estimation dependency, multiaccess, and intersymbol interference (ISI) for direct-sequence CDMA (DS-CDMA) communications. An algorithm for tracking and estimating the interference power is proposed and analyzed. This algorithm is then incorporated into the proposed time-varying error bound mechanisms. Computer simulations show that the proposed algorithms are capable of outperforming previously reported techniques with a significantly lower number of parameter updates and a reduced risk of overbounding or underbounding.

Quiet zone control system

Abstract: An active noise control system generates an anti-noise signal to drive a speaker to produce sound waves to destructively interfere with an undesired sound in a quiet zone. The anti-noise signal is generated with an adaptive filter having filter coefficients. The coefficients of the adaptive filter may be adjusted based on a first filter adjustment from a first listening region, and a second filter adjustment from a second listening region. A first weighting factor may be applied to the first filter adjustment, and a second weighting factor may be applied to the second filter adjustment. The first and second weighting factors may dictate the location and size of the quiet zone as being outside or partially within at least one of the first listening region and the second listening region.

Adaptive Combination of Proportionate Filters for Sparse Echo Cancellation

Abstract: Proportionate adaptive filters, such as those based on the improved proportionate normalized least-mean-square (IPNLMS) algorithm, have been proposed for echo cancellation as an interesting alternative to the normalized least-mean-square (NLMS) filter. Proportionate schemes offer improved performance when the echo path is sparse, but are still subject to some compromises regarding their convergence properties and steady-state error. In this paper, we study how combination schemes, where the outputs of two independent adaptive filters are adaptively mixed together, can be used to increase IPNLMS robustness to channels with different degrees of sparsity, as well as to alleviate the rate of convergence versus steady-state misadjustment tradeoff imposed by the selection of the step size. We also introduce a new block-based combination scheme which is specifically designed to further exploit the characteristics of the IPNLMS filter. The advantages of these combined filters are justified theoretically and illustrated in several echo cancellation scenarios.

The Bin-Occupancy Filter and Its Connection to the PHD Filters

Abstract: An algorithm that is capable not only of tracking multiple targets but also of ldquotrack managementrdquo-meaning that it does not need to know the number of targets as a user input-is of considerable interest. In this paper we devise a recursive track-managed filter via a quantized state-space (ldquobinrdquo) model. In the limit, as the discretization implied by the bins becomes as refined as possible (infinitesimal bins) we find that the filter equations are identical to Mahler's probability hypothesis density (PHD) filter, a novel track-managed filtering scheme that is attracting increasing attention. Thus, one contribution of this paper is an interpretation of, if not the PHD itself, at least what the PHD is doing. This does offer some intuitive appeal, but has some practical use as well: with this model it is possible to identify the PHD's ldquotarget-deathrdquo problem, and also the statistical inference structures of the PHD filters. To obviate the target death problem, PHD originator Mahler developed a new ldquocardinalizedrdquo version of PHD (CPHD). The second contribution of this paper is to extend the ldquobin-occupancyrdquo model such that the resulting recursive filter is identical to the cardinalized PHD filter.