Showing papers on "Adaptive filter published in 2010"

Kernel Adaptive Filtering: A Comprehensive Introduction

Abstract: Online learning from a signal processing perspective There is increased interest in kernel learning algorithms in neural networks and a growing need for nonlinear adaptive algorithms in advanced signal processing, communications, and controls. Kernel Adaptive Filtering is the first book to present a comprehensive, unifying introduction to online learning algorithms in reproducing kernel Hilbert spaces. Based on research being conducted in the Computational Neuro-Engineering Laboratory at the University of Florida and in the Cognitive Systems Laboratory at McMaster University, Ontario, Canada, this unique resource elevates the adaptive filtering theory to a new level, presenting a new design methodology of nonlinear adaptive filters. Covers the kernel least mean squares algorithm, kernel affine projection algorithms, the kernel recursive least squares algorithm, the theory of Gaussian process regression, and the extended kernel recursive least squares algorithm Presents a powerful model-selection method called maximum marginal likelihood Addresses the principal bottleneck of kernel adaptive filterstheir growing structure Features twelve computer-oriented experiments to reinforce the concepts, with MATLAB codes downloadable from the authors' Web site Concludes each chapter with a summary of the state of the art and potential future directions for original research Kernel Adaptive Filtering is ideal for engineers, computer scientists, and graduate students interested in nonlinear adaptive systems for online applications (applications where the data stream arrives one sample at a time and incremental optimal solutions are desirable). It is also a useful guide for those who look for nonlinear adaptive filtering methodologies to solve practical problems.

Recursive Least Squares Dictionary Learning Algorithm

Abstract: We present the recursive least squares dictionary learning algorithm, RLS-DLA, which can be used for learning overcomplete dictionaries for sparse signal representation. Most DLAs presented earlier, for example ILS-DLA and K-SVD, update the dictionary after a batch of training vectors has been processed, usually using the whole set of training vectors as one batch. The training set is used iteratively to gradually improve the dictionary. The approach in RLS-DLA is a continuous update of the dictionary as each training vector is being processed. The core of the algorithm is compact and can be effectively implemented. The algorithm is derived very much along the same path as the recursive least squares (RLS) algorithm for adaptive filtering. Thus, as in RLS, a forgetting factor ? can be introduced and easily implemented in the algorithm. Adjusting ? in an appropriate way makes the algorithm less dependent on the initial dictionary and it improves both convergence properties of RLS-DLA as well as the representation ability of the resulting dictionary. Two sets of experiments are done to test different methods for learning dictionaries. The goal of the first set is to explore some basic properties of the algorithm in a simple setup, and for the second set it is the reconstruction of a true underlying dictionary. The first experiment confirms the conjectural properties from the derivation part, while the second demonstrates excellent performance.

Cost-Effective Condition Monitoring for Wind Turbines

Abstract: Cost-effective wind turbine (WT) condition monitoring assumes more importance as turbine sizes increase and they are placed in more remote locations, for example, offshore. Conventional condition monitoring techniques, such as vibration, lubrication oil, and generator current signal analysis, require the deployment of a variety of sensors and computationally intensive analysis techniques. This paper describes a WT condition monitoring technique that uses the generator output power and rotational speed to derive a fault detection signal. The detection algorithm uses a continuous-wavelet-transform-based adaptive filter to track the energy in the prescribed time-varying fault-related frequency bands in the power signal. The central frequency of the filter is controlled by the generator speed, and the filter bandwidth is adapted to the speed fluctuation. Using this technique, fault features can be extracted, with low calculation times, from direct- or indirect-drive fixed- or variable-speed WTs. The proposed technique has been validated experimentally on a WT drive train test rig. A synchronous or induction generator was successively installed on the test rig, and both mechanical and electrical fault like perturbations were successfully detected when applied to the test rig.

Diffusion Least-Mean Squares With Adaptive Combiners: Formulation and Performance Analysis

Abstract: This paper presents an efficient adaptive combination strategy for the distributed estimation problem over diffusion networks in order to improve robustness against the spatial variation of signal and noise statistics over the network. The concept of minimum variance unbiased estimation is used to derive the proposed adaptive combiner in a systematic way. The mean, mean-square, and steady-state performance analyses of the diffusion least-mean squares (LMS) algorithms with adaptive combiners are included and the stability of convex combination rules is proved. Simulation results show (i) that the diffusion LMS algorithm with the proposed adaptive combiners outperforms those with existing static combiners and the incremental LMS algorithm, and (ii) that the theoretical analysis provides a good approximation of practical performance.

Orientation Estimation Using a Quaternion-Based Indirect Kalman Filter With Adaptive Estimation of External Acceleration

Abstract: This paper is concerned with orientation estimation using inertial and magnetic sensors. A quaternion-based indirect Kalman filter structure is used. The magnetic sensor output is only used for yaw angle estimation using two-step measurement updates. External acceleration is estimated from the residual of the filter and compensated by increasing the measurement noise covariance. Using the direction information of external information, the proposed method prevents unnecessarily increasing the measurement noise covariance corresponding to the accelerometer output, which is not affected by external acceleration. Through numerical examples, the proposed method is verified.

Denoising Nonlinear Time Series by Adaptive Filtering and Wavelet Shrinkage: A Comparison

Abstract: Time series measured in real world is often nonlinear, even chaotic. To effectively extract desired information from measured time series, it is important to preprocess data to reduce noise. In this Letter, we propose an adaptive denoising algorithm. Using chaotic Lorenz data and calculating root-mean-square-error, Lyapunov exponent, and correlation dimension, we show that our adaptive algorithm more effectively reduces noise in the chaotic Lorenz system than wavelet denoising with three different thresholding choices. We further analyze an electroencephalogram (EEG) signal in sleep apnea and show that the adaptive algorithm again more effectively reduces the Electrocardiogram (ECG) and other types of noise contaminated in EEG than wavelet approaches.

Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing

Abstract: Next-generation optical fiber systems will employ coherent detection to improve power and spectral efficiency, and to facilitate flexible impairment compensation using digital signal processors (DSPs). In a fully digital coherent system, the electric fields at the input and the output of the channel are available to DSPs at the transmitter and the receiver, enabling the use of arbitrary impairment precompensation and postcompensation algorithms. Linear time-invariant (LTI) impairments such as chromatic dispersion and polarization-mode dispersion can be compensated by adaptive linear equalizers. Non-LTI impairments, such as laser phase noise and Kerr nonlinearity, can be compensated by channel inversion. All existing impairment compensation techniques ultimately approximate channel inversion for a subset of the channel effects. We provide a unified multiblock nonlinear model for the joint compensation of the impairments in fiber transmission. We show that commonly used techniques for overcoming different impairments, despite their different appearance, are often based on the same principles such as feedback and feedforward control, and time-versus-frequency-domain representations. We highlight equivalences between techniques, and show that the choice of algorithm depends on making tradeoffs.

SPARLS: The Sparse RLS Algorithm

Abstract: We develop a recursive L1-regularized least squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight vector output stream and produces its estimate using an expectation-maximization type algorithm. We prove the convergence of the SPARLS algorithm to a near-optimal estimate in a stationary environment and present analytical results for the steady state error. Simulation studies in the context of channel estimation, employing multipath wireless channels, show that the SPARLS algorithm has significant improvement over the conventional widely used recursive least squares (RLS) algorithm in terms of mean squared error (MSE). Moreover, these simulation studies suggest that the SPARLS algorithm (with slight modifications) can operate with lower computational requirements than the RLS algorithm, when applied to tap-weight vectors with fixed support.

Eigen-based clutter filter design for ultrasound color flow imaging: a review

Abstract: Proper suppression of tissue clutter is a prerequisite for visualizing flow accurately in ultrasound color flow imaging. Among various clutter suppression methods, the eigen- based filter has shown potential because it can theoretically adapt its stopband to the actual clutter characteristics even when tissue motion is present. This paper presents a formative review on how eigen-based filters should be designed to improve their practical efficacy in adaptively suppressing clutter without affecting the blood flow echoes. Our review is centered around a comparative assessment of two eigen-filter design considerations: 1) eigen-component estimation approach (single-ensemble vs. multi-ensemble formulations), and 2) filter order selection mechanism (eigenvalue-based vs. frequencybased algorithms). To evaluate the practical efficacy of existing eigen-filter designs, we analyzed their clutter suppression level in two in vivo scenarios with substantial tissue motion (intra-operative coronary imaging and thyroid imaging). Our analysis shows that, as compared with polynomial regression filters (with or without instantaneous clutter downmixing), eigen-filters that use a frequency-based algorithm for filter order selection generally give Doppler power images with better contrast between blood and tissue regions. Results also suggest that both multi-ensemble and single-ensemble eigen-estimation approaches have their own advantages and weaknesses in different imaging scenarios. It may be beneficial to develop an algorithmic way of defining the eigen-filter formulation so that its performance advantages can be better realized.

Memristive Adaptive Filters

Abstract: Using the memristive properties of vanadium dioxide, we experimentally demonstrate an adaptive filter by placing a memristor into an LC contour. This circuit reacts to the application of select frequency signals by sharpening the quality factor of its resonant response, and thus “learns” according to the input waveform. The proposed circuit employs only analog passive elements, and may find applications in biologically inspired processing and information storage. We also extend the learning-circuit framework mathematically to include memory-reactive elements, such as memcapacitors and meminductors, and show how this expands the functionality of adaptive memory filters.

Adaptive Kalman Filtering in Networked Systems With Random Sensor Delays, Multiple Packet Dropouts and Missing Measurements

Abstract: In this paper, adaptive filtering schemes are proposed for state estimation in sensor networks and/or networked control systems with mixed uncertainties of random measurement delays, packet dropouts and missing measurements. That is, all three uncertainties in the measurement have certain probability of occurrence in the network. The filter gains can be derived by solving a set of recursive discrete-time Riccati equations. Examples are presented to demonstrate the applicability and performances of the proposed schemes.

Reduced-Rank STAP Schemes for Airborne Radar Based on Switched Joint Interpolation, Decimation and Filtering Algorithm

Abstract: In this paper, we propose a reduced-rank space-time adaptive processing (STAP) technique for airborne phased array radar applications. The proposed STAP method performs dimensionality reduction by using a reduced-rank switched joint interpolation, decimation and filtering algorithm (RR-SJIDF). In this scheme, a multiple-processing-branch (MPB) framework, which contains a set of jointly optimized interpolation, decimation and filtering units, is proposed to adaptively process the observations and suppress jammers and clutter. The output is switched to the branch with the best performance according to the minimum variance criterion. In order to design the decimation unit, we present an optimal decimation scheme and a low-complexity decimation scheme. We also develop two adaptive implementations for the proposed scheme, one based on a recursive least squares (RLS) algorithm and the other on a constrained conjugate gradient (CCG) algorithm. The proposed adaptive algorithms are tested with simulated radar data. The simulation results show that the proposed RR-SJIDF STAP schemes with both the RLS and the CCG algorithms converge at a very fast speed and provide a considerable SINR improvement over the state-of-the-art reduced-rank schemes.

A New and Efficient Algorithm for the Removal of High Density Salt and Pepper Noise in Images and Videos

Abstract: A new and efficient algorithm for high-density salt and pepper noise removal in images and videos is proposed. The existing non-linear filter like Standard Median Filter (SMF), Adaptive Median Filter (AMF), Decision Based Algorithm (DBA) and Robust Estimation Algorithm (REA) shows better results at low and medium noise densities. At high noise densities, their performance is poor. A new algorithm to remove high-density salt and pepper noise using modified sheer sorting method is proposed. The new algorithm has lower computation time when compared to other standard algorithms. Results of the algorithm is compared with various existing algorithms and it is proved that the new method has better visual appearance and quantitative measures at higher noise densities as high as 90%.

Distributed Estimation Over an Adaptive Incremental Network Based on the Affine Projection Algorithm

Abstract: We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton's method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.

A Quaternion Widely Linear Adaptive Filter

Abstract: A quaternion widely linear (QWL) model for quaternion valued mean-square-error (MSE) estimation is proposed. The augmented statistics are first introduced into the field of quaternions, and it is demonstrated that this allows for capturing the complete second order statistics available. The QWL model is next incorporated into the quaternion least mean-square (QLMS) algorithm to yield the widely linear QLMS (WL-QLMS). This allows for a unified approach to adaptive filtering of both Q-proper and Q-improper signals, leading to improved accuracies compared to the QLMS class of algorithms. Simulations on both benchmark and real world data support the analysis.

Poisson Point Processes: Imaging, Tracking, and Sensing

Abstract: : Multitarget tracking intensity filters are closely related to imaging problems, especially PET imaging. The intensity filter is obtained by three different methods. One is a Bayesian derivation involving target prediction and information updating. The second approach is a simple, compelling, and insightful intuitive argument. The third is a straightforward application of the Shepp-Vardi algorithm. The intensity filter is developed on an augmented target state space. The PHD filter is obtained from the intensity filter by substituting assumed known target birth and measurement clutter intensities for the intensity filter's predicted target birth and clutter intensities. To accommodate heterogeneous targets and sensor measurement models, a parameterized intensity filter is developed using a marked PPP Gaussian sum model. Particle and Gaussian sum implementations of intensity filters are reviewed. Mean-shift algorithms are discussed as a way to extract target state estimates. Grenander's method of sieves is discussed for regularization of the multitarget intensity filter estimates. Sources of error in the estimated target count are discussed. Finally, the multisensor intensity filter is developed using the same PPP target models as in the single sensor filter. Both homogeneous and heterogeneous multisensor fields are discussed. Multisensor intensity filters reduce the variance of estimated target count by averaging.

A Stochastic Gradient Approach on Compressive Sensing Signal Reconstruction Based on Adaptive Filtering Framework

Abstract: Based on the methodological similarity between sparse signal reconstruction and system identification, a new approach for sparse signal reconstruction in compressive sensing (CS) is proposed in this paper. This approach employs a stochastic gradient-based adaptive filtering framework, which is commonly used in system identification, to solve the sparse signal reconstruction problem. Two typical algorithms for this problem: l 0-least mean square ( l 0-LMS) algorithm and l 0-exponentially forgetting window LMS (l 0-EFWLMS) algorithm are hence introduced here. Both the algorithms utilize a zero attraction method, which has been implemented by minimizing a continuous approximation of l 0 norm of the studied signal. To improve the performances of these proposed algorithms, an l 0-zero attraction projection (l 0 -ZAP) algorithm is also adopted, which has effectively accelerated their convergence rates, making them much faster than the other existing algorithms for this problem. Advantages of the proposed approach, such as its robustness against noise, etc., are demonstrated by numerical experiments.

Constrained Kalman filtering via density function truncation for turbofan engine health estimation

Abstract: Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This article develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the probability density function (PDF) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but also improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. It is also shown that the truncated Kalman filter may provide a more accurate way of incorporating inequality constraints than other constrained filters (e.g. the projection approach to constrained filtering).

A New Adaptive Switching Median Filter

Abstract: A new Adaptive Switching Median (ASWM) filter for removing impulse noise from corrupted images is presented. The originality of ASWM is that no a priori Threshold is needed as in the case of a classical Switching Median filter. Instead, Threshold is computed locally from image pixels intensity values in a sliding window. Results show that ASWM provides better performance in terms of PSNR and MAE than many other median filter variants for random-valued impulse noise. In addition it can preserve more image details in a high noise environment.

Motion artifact cancellation in NIR spectroscopy using discrete Kalman filtering

Abstract: Background: As a continuation of our earlier work, we present in this study a Kalman filtering based algorithm for the elimination of motion artifacts present in Near Infrared spectroscopy (NIR) measurements. Functional NIR measurements suffer from head motion especially in real world applications where movement cannot be restricted such as studies involving pilots, children, etc. Since head movement can cause fluctuations unrelated to metabolic changes in the blood due to the cognitive activity, removal of these artifacts from NIR signal is necessary for reliable assessment of cognitive activity in the brain for real life applications. Methods: Previously, we had worked on adaptive and Wiener filtering for the cancellation of motion artifacts in NIR studies. Using the same NIR data set we have collected in our previous work where different speed motion artifacts were induced on the NIR measurements we compared the results of the newly proposed Kalman filtering approach with the results of previously studied adaptive and Wiener filtering methods in terms of gains in signal to noise ratio. Here, comparisons are based on paired t-tests where data from eleven subjects are used. Results: The preliminary results in this current study revealed that the proposed Kalman filtering method provides better estimates in terms of the gain in signal to noise ratio than the classical adaptive filtering approach without the need for additional sensor measurements and results comparable to Wiener filtering but better suitable for real-time applications. Conclusions: This paper presented a novel approach based on Kalman filtering for motion artifact removal in NIR recordings. The proposed approach provides a suitable solution to the motion artifact removal problem in NIR studies by combining the advantages of the existing adaptive and Wiener filtering methods in one algorithm which allows efficient real time application with no requirement on additional sensor measurements.

A Control Strategy for Hybrid Power Filter to Compensate Four-Wires Three-Phase Systems

Abstract: A control algorithm is proposed for a three-phase hybrid power filter constituted by a series active filter and a shunt passive filter. The control strategy is based on the dual formulation of the compensation system principles. It is applied by considering a balanced and resistive load as ideal load, so that the voltage waveform injected by the active filter is able to compensate the reactive power, to eliminate harmonics of the load current and to balance asymmetrical loads. This strategy improves the passive filter compensation characteristics without depending on the system impedance, and avoiding the series/shunt resonance problems, since the set load-filter would present resistive behavior. An experimental prototype was developed and experimental results are presented.

Chromatic dispersion compensation in coherent transmission system using digital filters

Abstract: We present a comparative analysis of three popular digital filters for chromatic dispersion compensation: a time-domain least mean square adaptive filter, a time-domain fiber dispersion finite impulse response filter, and a frequency-domain blind look-up filter. The filters are applied to equalize the chromatic dispersion in a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying transmission system. The characteristics of these filters are compared by evaluating their applicability for different fiber lengths, their usability for dispersion perturbations, and their computational complexity. In addition, the phase noise tolerance of these filters is also analyzed.

Adaptive Signal Processing: Next Generation Solutions

Abstract: Preface. Contributors. Chapter 1 Complex-Valued Adaptive Signal Processing. 1.1 Introduction. 1.2 Preliminaries. 1.3 Optimization in the Complex Domain. 1.4 Widely Linear Adaptive Filtering. 1.5 Nonlinear Adaptive Filtering with Multilayer Perceptrons. 1.6 Complex Independent Component Analysis. 1.7 Summary. 1.8 Acknowledgment. 1.9 Problems. References. Chapter 2 Robust Estimation Techniques for Complex-Valued Random Vectors. 2.1 Introduction. 2.2 Statistical Characterization of Complex Random Vectors. 2.3 Complex Elliptically Symmetric (CES) Distributions. 2.4 Tools to Compare Estimators. 2.5 Scatter and Pseudo-Scatter Matrices. 2.6 Array Processing Examples. 2.7 MVDR Beamformers Based on M -Estimators. 2.8 Robust ICA. 2.9 Conclusion. 2.10 Problems. References. Chapter 3 Turbo Equalization. 3.1 Introduction. 3.2 Context. 3.3 Communication Chain. 3.4 Turbo Decoder: Overview. 3.5 Forward-Backward Algorithm. 3.6 Simplified Algorithm: Interference Canceler. 3.7 Capacity Analysis. 3.8 Blind Turbo Equalization. 3.9 Convergence. 3.10 Multichannel and Multiuser Settings. 3.11 Concluding Remarks. 3.12 Problems. References. Chapter 4 Subspace Tracking for Signal Processing. 4.1 Introduction. 4.2 Linear Algebra Review. 4.3 Observation Model and Problem Statement. 4.4 Preliminary Example: Oja s Neuron. 4.5 Subspace Tracking. 4.6 Eigenvectors Tracking. 4.7 Convergence and Performance Analysis Issues. 4.8 Illustrative Examples. 4.9 Concluding Remarks. 4.10 Problems. References. Chapter 5 Particle Filtering. 5.1 Introduction. 5.2 Motivation for Use of Particle Filtering. 5.3 The Basic Idea. 5.4 The Choice of Proposal Distribution and Resampling. 5.5 Some Particle Filtering Methods. 5.6 Handling Constant Parameters. 5.7 Rao Blackwellization. 5.8 Prediction. 5.9 Smoothing. 5.10 Convergence Issues. 5.11 Computational Issues and Hardware Implementation. 5.12 Acknowledgments. 5.13 Exercises. References. Chapter 6 Nonlinear Sequential State Estimation for Solving Pattern-Classification Problems. 6.1 Introduction. 6.2 Back-Propagation and Support Vector Machine-Learning Algorithms: Review. 6.3 Supervised Training Framework of MLPs Using Nonlinear Sequential State Estimation. 6.4 The Extended Kalman Filter. 6.5 Experimental Comparison of the Extended Kalman Filtering Algorithm with the Back-Propagation and Support Vector Machine Learning Algorithms. 6.6 Concluding Remarks. 6.7 Problems. References. Chapter 7 Bandwidth Extension of Telephony Speech. 7.1 Introduction. 7.2 Organization of the Chapter. 7.3 Nonmodel-Based Algorithms for Bandwidth Extension. 7.4 Basics. 7.5 Model-Based Algorithms for Bandwidth Extension. 7.6 Evaluation of Bandwidth Extension Algorithms. 7.7 Conclusion. 7.8 Problems. References. Index.

A Variable Step-Size Matrix Normalized Subband Adaptive Filter

Abstract: The normalized subband adaptive filter (NSAF) presented by Lee and Gan can obtain faster convergence rate than the normalized least-mean-square (NLMS) algorithm with colored input signals. However, similar to other fixed step-size adaptive filtering algorithms, the NSAF requires a tradeoff between fast convergence rate and low misadjustment. Recently, a set-membership NSAF (SM-NSAF) has been developed to address this problem. Nevertheless, in order to determine the error bound of the SM-NSAF, the power of the system noise should be known. In this paper, we propose a variable step-size matrix NSAF (VSSM-NSAF) from another point of view, i.e., recovering the powers of the subband system noises from those of the subband error signals of the adaptive filter, to further improve the performance of the NSAF. The VSSM-NSAF uses an effective system noise power estimate method, which can also be applied to the under-modeling scenario, and therefore need not know the powers of the subband system noises in advance. Besides, the steady-state mean-square behavior of the proposed algorithm is analyzed, which theoretically proves that the VSSM-NSAF can obtain a low misadjustment. Simulation results show good performance of the new algorithm as compared to other members of the NSAF family.

Sparse Adaptive Filters for Echo Cancellation

Abstract: Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ``proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellation. Besides a comprehensive review of the basic proportionate-type algorithms, we also present some of the latest developments in the field and propose some new solutions for further performance improvement, e.g., variable step-size versions and novel proportionate-type affine projection algorithms. An experimental study is also provided in order to compare many sparse adaptive filters in different echo canc...

A Non-Gaussian Ensemble Filter Update for Data Assimilation

Abstract: A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error. For the nonlinear system, the deterministic filter has increasing error as ensemble size increases because all ensemble members but one become tightly clustered. In this case, the stochastic filter performs better for sufficiently large ensembles. A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter. This filter uses the order statistics of the prior observation space ensemble to create an approximate continuous prior probability dis...

Direct Data Domain STAP using Sparse Representation of Clutter Spectrum

Abstract: Space-time adaptive processing (STAP) is an effective tool for detecting a moving target in the airborne radar system. Due to the fast-changing clutter scenario and/or non side-looking configuration, the stationarity of the training data is destroyed such that the statistical-based methods suffer performance degradation. Direct data domain (D3) methods avoid non-stationary training data and can effectively suppress the clutter within the test cell. However, this benefit comes at the cost of a reduced system degree of freedom (DOF), which results in performance loss. In this paper, by exploiting the intrinsic sparsity of the spectral distribution, a new direct data domain approach using sparse representation (D3SR) is proposed, which seeks to estimate the high-resolution space-time spectrum with only the test cell. The simulation of both side-looking and non side-looking cases has illustrated the effectiveness of the D3SR spectrum estimation using focal underdetermined system solution (FOCUSS) and norm minimization. Then the clutter covariance matrix (CCM) and the corresponding adaptive filter can be effectively obtained. Since D3SR maintains the full system DOF, it can achieve better performance of output signal-clutter-ratio (SCR) and minimum detectable velocity (MDV) than current D3 methods, e.g., direct data domain least squares (D3LS). Thus D3SR is more effective against the range-dependent clutter and interference in the non-stationary clutter scenario.

A sparse adaptive filtering using time-varying soft-thresholding techniques

Abstract: In this paper, we propose a novel adaptive filtering algorithm based on an iterative use of (i) the proximity operator and (ii) the parallel variable-metric projection. Our time-varying cost function is a weighted sum of squared distances (in a variable-metric sense) plus a possibly nonsmooth penalty term, and the proposed algorithm is derived along the idea of proximal forward-backward splitting in convex analysis. For application to sparse-system identification problems, we employ the (weighted) l 1 norm as the penalty term, leading to a time-varying soft-thresholding operator. As the simple example of the proposed algorithm, we present the variable-metric affine projection algorithm composed with the time-varying soft-thresholding operator. Numerical examples demonstrate that the proposed algorithms notably outperform their counterparts without soft-thresholding both in convergence speed and steady-state mismatch, while the extra computational complexity due to the additional soft-thresholding is negligibly low.