A time-domain feedback analysis of filtered-error adaptive gradientalgorithms

This paper provides a time-domain feedback analysis of gradient-based adaptive schemes. A key emphasis is on the robustness performance of the adaptive filters in the presence of disturbances and modeling uncertainties (along the lines of H^∞-theory and robust filtering). The analysis is carried out in a purely deterministic framework and assumes no prior statistical information or independence conditions. It is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes. The feedback structure is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The configuration is further shown to lend itself to analysis via a so-called small gain theorem, thus leading to stability and robustness conditions that require the contractivity of certain operators. Choices for the step-size parameter in order to guarantee faster rates of convergence are also derived, and simulation results are included to demonstrate the theoretical findings. In addition, the time-domain analysis provided in this paper is shown to extend the so-called transfer function approach to a general time-variant scenario without any approximations     

A 0.5 μm Concurrent Testable Chip of a Fifth-Order g m -C Filter

In this paper, we describe a testable chip of a fifth-order g _m -C low-pass filter that has a passband from 0 to 4.5 MHz. We use a current-mode method for the error detection of this filter. By comparing the current consumed by the circuit under test (CUT) and the current converted from the voltage levels of the CUT, abnormal function of circuit components can be concurrently and efficiently detected. A test chip has been fabricated using a 0.5 m, 2P2M CMOS technology. Measurement results show that this current-mode approach has little impact on the performance of the filter and can detect faults in the filter effectively. The area overhead of the circuitry for testing in this chip is about 18%.     

Delay-Range-Dependent L 2–L ∞ Filtering for Stochastic Systems with Time-Varying Interval Delay

This paper focuses on the problem of delay-range-dependent L ₂–L _∞ filter design for stochastic systems with time-varying delay. The time delay varies in an interval. A delay-range-dependent sufficient condition is formulated in terms of linear matrix inequalities (LMIs), which guarantees the existence of a linear filter. The proposed filter ensures that the filtering error system is stochastically asymptotically stable and that its L ₂–L _∞ performance satisfies a prescribed level. The corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. This work is partially supported by the Natural Science Foundation of China (60674055, 60774047), and the Taishan Scholar Programme of Shandong Province.     

Robust Recursive <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> DOA Estimation Using Spatial Forward Linear Predictor

This letter deals with robust direction of arrival (DOA) estimation based on the recursive H _∞ algorithm for the forward linear predictor. This recursive H _∞ criterion is different from traditional H ₂ estimation criterions which minimize the squared prediction error. The forward linear predictor with recursive H _∞ algorithm is a worst case optimization approach, which minimizes the total effect of the worst disturbances on the prediction error. Some computer simulation examples are provided for illustrating the effectiveness of the proposed method.

Envelope-constrained H2 FIR filter design

In this paper, we consider an envelope-constrained (EC)H ₂ optimal finite impulse response (FIR) filtering problem. Our aim is to design a filter such that theH ₂ norm of the filtering error transfer function is minimized subject to the constraint that the filter output with a given input to the signal system is contained or bounded by a prescribed envelope. The filter design problem is formulated as a standard optimization problem with linear matrix inequality (LMI) constraints. Furthermore, by relaxing theH ₂ norm constraint, we propose a robust ECFIR filter design algorithm based on the LMI approach.     

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber (1981) function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated Gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either a contaminated Gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under Gaussian noise alone     

A Unified Family of Recursive Algorithms Using Feedback

This paper investigates a family of simple recursive algorithms based on feedback around a weight vector or matrix with a multivariable discrete integrator in the forward path. It is shown that, by using simple changes, estimates of the covariance matrix, inverse-covariance matrix and their corresponding square-root values can be found. As a special vector case of the more general matrix algorithm we show that least mean squares (LMS) can also be derived.     

Adaptive MIMO decision feedback equalization for receivers with time-varying channels

In an attempt to reduce the computational complexity of vertical Bell Labs layered space time (V-BLAST) processing with time-varying channels, an efficient adaptive receiver is developed based on the generalized decision feedback equalizer (GDFE) architecture. The proposed receiver updates the filter weight vectors and detection order using a recursive least squares (RLS)-based time- and order-update algorithm. The convergence of the algorithm is examined by analysis and simulation, and it is shown that the proposed adaptive technique is considerably simpler to implement than a V-BLAST processor with channel tracking, yet the performances are almost comparable.     

室内Wi-Fi/PDR自适应鲁棒卡尔曼滤波融合定位方法

针对室内复杂环境下信道状态信息的动态性问题,本文提出了一种面向室内Wi-Fi/行人航迹推算（Pedestrian Dead Reckoning,PDR）融合定位的自适应鲁棒卡尔曼滤波方法.该方法利用自适应鲁棒卡尔曼滤波将Wi-Fi传播模型与PDR定位信息进行多重融合,推算用户的最优估计位置.同时,基于滤波反馈机制,通过融合定位结果对加权最小二乘法中的路径损耗指数和滤波模型中的观测协方差进行动态修正,保证Wi-Fi传播模型接近于真实室内环境.实验结果表明,该方法能够有效解决室内复杂环境下单一Wi-Fi定位精度低和PDR累积误差的问题,此外,路径损耗指数和观测协方差的实时修正可以提高融合定位系统的定位精度和稳定性.     

Efficient recursive estimation of the parameters of a radar or radio astronomy target

In radar or radio astronomy we observe a signal whose covariance function depends on some target parameters of interest. We consider here the problem of estimating the values of these parameters from our observation of the signal. One possible procedure is to use the method of maximum likelihood estimation. This method has the advantage that, as the duration of the observation interval becomes long, the mean square error in the maximum likelihood estimate approaches the minimum given by the Cramér-Rao bound. However, the maximum likelihood estimate is usually difficult to compute. We present here a recursive estimation procedure which divides the observation interval up into subintervals of short length; on each subinterval the signal is processed quadratically and the resulting calculation used to improve our estimate. This method has many computational advantages and, under certain conditions, we can show that the error in the resulting sequence of estimates approaches the Cramér-Rao bound. We begin by giving brief consideration to the problem of determining the functional dependence of the covariance function of the received signal on the target parameters. We then present expressions for the terms that appear in the Cramér-Rao inequality. Lastly, we describe the recursive estimation method and state conditions under which it is applicable.     

Feedback cancellation in hearing aids: results from a computersimulation

Feedback cancellation in hearing aids involves estimating the feedback signal and subtracting it from the microphone input signal. The feedback-cancellation system described updates the estimated feedback path whenever changes are detected in the feedback behavior. When a change is detected, the normal hearing-aid processing is interrupted, a pseudorandom probe signal is injected into the system, and a set of filter coefficients is adjusted to give an estimate of the feedback path. The hearing aid is then returned to normal operation with the feedback-cancellation filter as part of the system. Two approaches are investigated for computing the filter coefficients: a least-mean square (LMS) adaptive filter and a Wiener filter. Test results are presented for a computer simulation of an in-the-ear (ITE) hearing aid. The simulation results indicate that more than 10 dB of cancellation can be obtained and that the Wiener filter is more effective in the presence of strong interference     

A unified algebraic transformation approach for parallel recursiveand adaptive filtering and SVD algorithms

In this paper, a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition (SVD) algorithms. The approach is based on the explorations of some algebraic properties of the target algorithms' representations. Several typical modern digital signal processing examples are presented to illustrate the applications of the technique. They include the cascaded orthogonal recursive digital filter, the Givens rotation-based adaptive inverse QR algorithm for channel equalization, and the QR decomposition-based SVD algorithms. All three examples exhibit similar throughput constraints. There exist long feedback loops in the algorithms' signal flow graph representation, and the critical path is proportional to the size of the problem. Applying the proposed algebraic transformation techniques, parallel architectures are obtained for all three examples. For cascade orthogonal recursive filter, retiming transformation and orthogonal matrix decompositions (or pseudo-commutativity) are applied to obtain parallel filter architectures with critical path of five Givens rotations. For adaptive inverse QR algorithm, the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four Givens rotations or three Givens rotations plus two multiply-add operations, whichever turns out to be larger. For SVD algorithms, retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight Givens rotations. The critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms. Parallelism is achieved at the expense of slight increase (or the same for the SVD case) in the algorithms' computational complexity     

Systematic optical and x-ray study of In x Ga1−x As on InP

We present a systematic study of In _x Ga_1−x As on InP grown by molecular beam epitaxy using the characterization techniques of Fourier transform photoluminescence, x-ray diffraction, micro-Raman spectroscopy, and photoreflectance spectroscopy. The four techniques were used to determine and correlate the fundamental parameters of band-gap energy, phonon frequency and composition. Comparing room temperature (293 K) PL and low temperature PL indicate the presence of a partially ionized acceptor with binding energy of about 13 meV in the unintentionally doped material. Double crystal x-ray diffraction (XRD) using a symmetric <400> and asymmetric <224> reflections was also employed. The use of two reflections gives precise lattice constants, composition, and extent of film relaxation. Micro-Raman spectroscopy was used to measure phonon frequencies in the In _x Ga_1−x As films and correlated to XRD composition. Room temperature photoreflectance (PR) was used to determine band-gap energy for both the low and intermediate field cases. Band gap energies determined at room temperature by PL and PR were in agreement within experimental error.     

Tests of sequential data assimilation for retrieving profile soilmoisture and temperature from observed L-band radiobrightness

Sequential data assimilation (Kalman filter optimal estimation) techniques are applied to the problem of retrieving near-surface soil moisture and temperature state from periodic terrestrial radiobrightness observations that update soil heat and moisture diffusion models. The retrieval procedure uses a time-explicit numerical model to continuously propagate the soil state profile, its error of estimation, and its interdepth covariances through time. The model's coupled soil moisture and heat fluxes are constrained by micrometeorology boundary conditions drawn from observations or atmospheric modeling. When radiometer data are available, the Kalman filter updates the state profile estimate by weighing the propagated state, error, and covariance estimates against an a priori estimate of radiometric measurement error. The Kalman filter compares predicted and observed radiobrightnesses directly, so no inverse algorithm relating brightness to physical parameters is required. The authors demonstrate Kalman filter model effectiveness using field observations and a simulation study. An observed 1 m soil state profile is recovered over an eight-day period from daily L-band observations following an intentionally poor initial state estimate. In a four-month simulation study, they gauge the longer term behavior of the soil state retrieval and Kalman gain through multiple rain events, soil dry-downs, and updates from radiobrightnesses     

Nanoscale analysis of YBa2Cu3O7−x/La0.67Ca0.33MnO3 interfaces

The structure of interfaces in superconducting/ferromagnetic YBa₂Cu₃O_7−x/La_0.67Ca_0.33MnO₃ superlattices has been analyzed by scanning transmission electron microscopy and high spatial resolution electron energy loss spectroscopy. Individual layers are flat over long lateral distances. The interfaces are coherent, free of defects, exhibiting no roughness, and are located at the BaO plane of the superconductor. Concerning chemical disorder, EELS measurements show the absence of measurable chemical interdiffusion within experimental error bars.     

Modular and numerically stable fast transversal filters formultichannel and multiexperiment RLS

The authors present scalar implementations of multichannel and multiexperiment fast recursive least squares algorithms in transversal filter form, known as fast transversal filter (FTF) algorithms. By processing the different channels and/or experiments one at a time, the multichannel and/or multiexperiment algorithm decomposes into a set of intertwined single-channel single-experiment algorithms. For multichannel algorithms, the general case of possibly different filter orders in different channels is handled. Geometrically, this modular decomposition approach corresponds to a Gram-Schmidt orthogonalization of multiple error vectors. Algebraically, this technique corresponds to matrix triangularization of error covariance matrices and converts matrix operations into a regular set of scalar operations. Modular algorithm structures that are amenable to VLSI implementation on arrays of parallel processors naturally follow from the present approach. Numerically, the resulting algorithm benefits from the advantages of triangularization techniques in block processing     

The effect of uncertain time-variant delays in ATM networks with explicit rate feedback: a control theoretic approach

A new, more realistic model for the available bit rate traffic class in ATM network congestion control with explicit rate feedback is introduced and analyzed. This model is based on recent results by M.M. Ekanayake ("Robust stability of discrete time nonlinear systems", Ph.D. dissertation, Univ. Miami, Coral Gables, FL, 1999) regarding discrete time models for time-variant delays. The discrete time model takes into account the effect of time-variant buffer occupancy levels of ATM switches, thus treating the case of time-variant delays between a single congested node and the connected sources. For highly dynamic situations, such a model is crucial for a valid analysis of the resulting feedback system. The new model also handles the effects of the mismatch between the resource management cell rates and the variable bit rate controller sampling rate as well as buffer and rate nonlinearities. A brief stability study shows that an equilibrium in the buffer occupancy is impossible to achieve in the presence of time-variant forward path delays. Stability conditions for the case of time-variant delays in the return path are presented. Finally, illustrative examples are provided.     

An SIMD Multiprocessor Ring Architecture for the LMS Adaptive Algorithm

A new architecture for a single instruction stream, multiple data stream (SIMD) implementation of the LMS adaptive algorithm is investigated. This is denoted as a ring architecture, due to its physical configuration, and it effectively solves the latency problem often associated with prediction error feedback in adaptive filters. The multiprocessor ring efficiently updates the filter input vector by operating as a pipeline structure, while behaving as a parallel structure in computing the filter output and applying the weight adaptation algorithm. Last, individual processor timing and capacity considerations are examined.     

Robust H ∞ Control for Stochastic Time-Delay Systems with Markovian Jump Parameters via Parameter-Dependent Lyapunov Functionals

This paper deals with the problems of robust stabilization and robust H _∞ control for time-delay stochastic systems with Markovian jump parameters and convex polytopic uncertainties. The purpose is the design of state feedback controllers such that the closed-loop system is robustly exponentially stable in the mean square and satisfies a prescribed H _∞ performance level. Sufficient conditions for the solvability of the problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that desired state feedback controllers can be designed by solving a set of linear matrix inequalities.     

A Recursive Frequency Estimator Using Linear Prediction and a Kalman-Filter-Based Iterative Algorithm

This paper proposes a new Kalman-filter-based recursive frequency estimator for discrete-time multicomponent sinusoidal signals whose frequencies may be time-varying. The frequency estimator is based on the linear prediction approach and it employs the Kalman filter to track the linear prediction coefficients (LPCs) recursively. Frequencies of the sinusoids can then be computed using the estimated LPCs. Due to the coloredness of the linear prediction error, an iterative algorithm is employed to estimate the covariance matrix of the prediction error and the LPCs alternately in the Kalman filter in order to improve the tracking performance. Simulation results show that the proposed Kalman-filter-based iterative frequency estimator can achieve better tracking results than the conventional recursive least-squares-based estimators.