基于声矢量水听器阵列误差的自校正算法

对声矢量水听器阵列的各类误差进行了分类,推导了各类误差对阵列信号模型的影响因子,通过Monte Carlo实验分析对比了各类误差对阵列DOA估计性能的影响,然后将方向性误差和位置误差归结为幅度误差和相位误差,在传统声压阵列误差校正模型和算法的基础上,得到矢量阵列误差自校正的优化模型及自校正算法,最后,通过仿真实验和外场实验的数据处理表明,自校正算法具有良好的参数估计性能,具有一定的工程实用性.     

Antenna calibration technique based on channel prediction in time-varying TDD-MIMO system

The traditional antenna calibration for time division duplex multiple input multiple output (TDD-MIMO) systems assume that free-space channel keeps constant during calibration, which is unreasonable under the high-speed rail and other time-varying channel scenarios for time variability can cause calibration error. This paper analyzes the performance of traditional antenna calibration methods, and then proposes an antenna calibration method based on Wiener channel prediction for time-varying TDD-MIMO system. Through theoretical derivation, we get the capacity formula of the TDD-MIMO system using traditional antenna calibration and antenna calibration based on channel prediction. The theoretical analysis and simulation results both indicate that the performance degradation of antenna calibration can be caused by time-varying channel and the prediction algorithm proposed in the paper can well compensate for the performance loss and significantly improve the antenna calibration performance for time-varying TDD-MIMO system.     

Memetic Algorithms for Multiple Interference Cancellations of Linear Array Based on Phase-Amplitude Perturbations

A novel method based on the memetic algorithm for the design of multiple interference cancellations of a linear array antenna by phase-amplitude perturbations is proposed. The adaptive array antenna is capable of sensing the presence of interference sources and suppressing the interferences in the interfering directions. This technique can increase the signal-to-interference ratio. The memetic algorithm is applied to find the weighting vector which makes the pattern nulling optimization of the proposed adaptive antenna. This technique is also able to do the cancellation of multiple interferences for different incident directions.     

Optimal complex exponentials BEM and channel estimation in doubly selective channel

Over doubly selective channel, the optimal complex exponentials BEM (CE-BEM) is required to characterize the transmission in transform domain in order to reducing the huge number of the estimated parameters during directly estimating the impulse response in time domain. This paper proposed an improved CE-BEM to alleviating the high frequency sampling error caused by conventional CE-BEM. On the one hand, exploiting the improved CE-BEM, we achieve the sampling point is in the Doppler spread spectrum and the maximum sampling frequency is equal to the maximum Doppler shift. On the other hand we optimize the function and dimension of basis in CE-BEM respectively ,and obtain the closed solution of the EM based channel estimation differential operator by exploiting the above optimal BEM. Finally, the numerical results and theoretic analysis show that the dimension of basis is mainly depend on the maximum Doppler shift and signal-to-noise ratio (SNR), and if fixing the number of the pilot symbol, the dimension of basis is higher, the modeling error is smaller, while the accuracy of the parameter estimation is reduced, which implies that we need to achieve a tradeoff between the modeling error and the accuracy of the parameter estimation and the basis function influences the accuracy of describing the Doppler spread spectrum after identifying the dimension of the basis.     

Synthesis of a unidirectional systolic array for matrix–vector multiplication

In this paper we present a procedure, based on data dependencies and space–time transformations of index space, to design a unidirectional linear systolic array (ULSA) for computing a matrix–vector product. The obtained array is optimal with respect to the number of processing elements (PEs) for a given problem size. The execution time of the array is the minimal possible for that number of PEs. To achieve this, we first derive an appropriate systolic algorithm for ULSA synthesis. In order to design a ULSA with the optimal number of PEs we then perform an accommodation of the index space to the projection direction vector. The performance of the synthesized array is discussed and compared with the bidirectional linear SA. Finally, we demonstrate how this array can be used to compute the correlation of two given sequences.     

An EM-Like Algorithm for Semi- and Nonparametric Estimation in Multivariate Mixtures

We propose an algorithm for nonparametric estimation for finite mixtures of multivariate random vectors that strongly resembles a true EM algorithm. The vectors are assumed to have independent coordinates conditional upon knowing from which mixture component they come, but otherwise their density functions are completely unspecified. Sometimes, the density functions may be partially specified by Euclidean parameters, a case we call semiparametric. Our algorithm is much more flexible and easily applicable than existing algorithms in the literature; it can be extended to any number of mixture components and any number of vector coordinates of the multivariate observations. Thus it may be applied even in situations where the model is not identifiable, so care is called for when using it in situations for which identifiability is difficult to establish conclusively. Our algorithm yields much smaller mean integrated squared errors than an alternative algorithm in a simulation study. In another example using a real dataset, it provides new insights that extend previous analyses. Finally, we present two different variations of our algorithm, one stochastic and one deterministic, and find anecdotal evidence that there is not a great deal of difference between the performance of these two variants. The computer code and data used in this article are available online.     

On the LASSO and its Dual

Abstract

Proposed by Tibshirani, the least absolute shrinkage and selection operator (LASSO) estimates a vector of regression coefficients by minimizing the residual sum of squares subject to a constraint on the l ¹-norm of the coefficient vector. The LASSO estimator typically has one or more zero elements and thus shares characteristics of both shrinkage estimation and variable selection. In this article we treat the LASSO as a convex programming problem and derive its dual. Consideration of the primal and dual problems together leads to important new insights into the characteristics of the LASSO estimator and to an improved method for estimating its covariance matrix. Using these results we also develop an efficient algorithm for computing LASSO estimates which is usable even in cases where the number of regressors exceeds the number of observations. An S-Plus library based on this algorithm is available from StatLib.     

Genetic algorithm and M-estimator based robust sequential estimation of parameters of nonlinear sinusoidal signals

Estimation of parameters of nonlinear superimposed sinusoidal signals is an important problem in digital signal processing. In this paper, we consider the problem of estimation of parameters of real valued sinusoidal signals. We propose a real-coded genetic algorithm based robust sequential estimation procedure for estimation of signal parameters. The proposed sequential method is based on elitist generational genetic algorithm and robust M-estimation techniques. The method is particularly useful when there is a large number of superimposed sinusoidal components present in the observed signal and is robust with respect to presence of outliers in the data and impulsive heavy tail noise distributions. Simulations studies and real life signal analysis are performed to ascertain the performance of the proposed sequential procedure. It is observed that the proposed methods perform better than the usual non-robust methods of estimation.     

A wavelet-based nested iteration–inexact conjugate gradient algorithm for adaptively solving elliptic PDEs

In Cohen et al. (Math Comput 70:27–75, 2001), a new paradigm for the adaptive solution of linear elliptic partial differential equations (PDEs) was proposed, based on wavelet discretizations. Starting from a well-conditioned representation of the linear operator equation in infinite wavelet coordinates, one performs perturbed gradient iterations involving approximate matrix–vector multiplications of finite portions of the operator. In a bootstrap-type fashion, increasingly smaller tolerances guarantee convergence of the adaptive method. In addition, coarsening performed on the iterates allow one to prove asymptotically optimal complexity results when compared to the wavelet best N-term approximation. In the present paper, we study adaptive wavelet schemes for symmetric operators employing inexact conjugate gradient routines. Inspired by fast schemes on uniform grids, we incorporate coarsening and the adaptive application of the elliptic operator into a nested iteration algorithm. Our numerical results demonstrate that the runtime of the algorithm is linear in the number of unknowns and substantial savings in memory can be achieved in two and three space dimensions.     

Cooley-Tukey FFT在高维的算法

A new fast algorithm is presented for multidimensional DFT in this paper. This algorithm is derived based on an interesting coding technique for multidimensional integral point, named the technique vector coding. And called the algorithm VCFFT (vector coding fast Fourier transform). Since the VC-FFT is the extension of Cooley-Tukey algorithm from one-dimensional to multidimensional, its structure of program is simple as Cooley-Tukey FFT, and significantly reduces multiplications and recursive stages.     

A Euclidean Algorithm for Normal Bases

Inversion in finite fields is a critical operation for many applications. A well-known representation basis, i.e., normal basis, provides an efficient squaring operation realized as a simple rotation of the operand coefficients. Inversion in normal basis is computed using methods derived from Fermat’s Little theorem, e.g., the Itoh–Tsujii algorithm or with the aid of basis conversion algorithms using the Extended Euclidean algorithm. In this paper we present alternative normal basis inversion algorithm derived from the polynomial version of the extended Euclidean algorithm. The normal basis Euclidean algorithm has (roughly) the same complexity as the polynomial version of the Euclidean algorithm. The proposed algorithm requires on average a linear number of multiplications. We also present a modification to our algorithm which delays the multiplications to the very end of the computation and thereby gives opportunity for recursive computation using only a logarithmic number of multiplications.This work was supported by the National Science Foundation ITR Awards # 0112889 and CAREER Award # 0133297.     

Similar basis function algorithm for numerical estimation of Fourier integrals

The methodological difficulties of estimating Fourier integrals using the fast Fourier transform (FFT) algorithm have intensified the interest in an alternative approach based on the Filon’s method of computing the trigonometric integrals. Following this approach, we introduce in this paper a similar basis function (SBF) algorithm that decomposes the function to be transformed into the sum of finite elements termed “similar basis functions”. Due to a simple analytical form of SBF, the reassignment of the SBFs’ similarity relationships into the transformation domain reduces the estimation of the Fourier integrals to a number of standard computational procedures. The SBF algorithm is capable to deal with both uniform and non-uniform samples of the function under analysis. Using this opportunity, we extend a general SBF algorithm by a fast SBF algorithm which deals with exponentially increasing sampling intervals. The efficiency and the accuracy of the method are illustrated by computer experiments with frequency characteristics and transient responses of a typical dynamic system.     

Scaling by Binormalization

We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices.     

Backfitting neural networks

Summary  Regression and classification problems can be viewed as special cases of the problem of function estimation. It is rather well known that a two-layer perceptron with sigmoidal transformation functions can approximate any continuous function on the compact subsets ofRP if there are sufficient number of hidden nodes. In this paper, we present an algorithm for fitting perceptron models, which is quite different from the usual backpropagation or Levenberg-Marquardt algorithm. This new algorithm based on backfitting ensures a better convergence than backpropagation. We have also used resampling techniques to select an ideal number of hidden nodes automatically using the training data itself. This resampling technique helps to avoid the problem of overfitting that one faces for the usual perceptron learning algorithms without any model selection scheme. Case studies and simulation results are presented to illustrate the performance of this proposed algorithm.     

Support vector quantile regression with varying coefficients

Quantile regression has received a great deal of attention as an important tool for modeling statistical quantities of interest other than the conditional mean. Varying coefficient models are widely used to explore dynamic patterns among popular models available to avoid the curse of dimensionality. We propose a support vector quantile regression model with varying coefficients and its two estimation methods. One uses the quadratic programming, and the other uses the iteratively reweighted least squares procedure. The proposed method can be applied easily and effectively to estimating the nonlinear regression quantiles depending on the high-dimensional vector of smoothing variables. We also present the model selection method that employs generalized cross validation and generalized approximate cross validation techniques for choosing the hyperparameters, which affect the performance of the proposed model. Numerical studies are conducted to illustrate the performance of the proposed model.     

A simple inequality for the variance of the number of zeros of a differentiable Gaussian stationary process

The variance of the number of zeros of a Gaussian differentiable stationary process in a finite time interval can be represented by a single integral of a sophisticated function having singularities in the vicinity of zero, which complicates computer calculations. In this paper, for a wide class of correlation functions, an inequality estimating this variance in simpler terms is proved. Two of three considered examples demonstrate the limits of the effectiveness of the obtained inequality by comparison with special processes earlier established by the author for which the variance is calculated by formulas without integrals. In the two subsequent cases, the inequality is used for the asymptotic estimation of the variance of the number of zeros in a small time interval and, in the last one, in addition to this asymptotics, the upper and lower bounds for the most widely used analytic process in all time intervals.     

A multiple template approach for robust tracking of fast motion target

Target tracking is very important in computer vision and related areas. It is usually difficult to accurately track fast motion target with appearance variations. Sometimes the tracking algorithms fail for heavy appearance variations. A multiple template method to track fast motion target with appearance changes is presented under the framework of appearance model with Kalman filter. Firstly, we construct a multiple template appearance model, which includes both the original template and templates affinely transformed from original one. Generally speaking, appearance variations of fast motion target can be covered by affine transformation. Therefore, the affine transform-enhanced templates match the target of appearance variations better than conventional models. Secondly, we present an improved Kalman filter for approximate estimating the motion trail of the target and a modified similarity evaluation function for exact matching. The estimation approach can reduce time complexity of the algorithm and keep accuracy in the meantime. Thirdly, we propose an adaptive scheme for updating template set to alleviate the drift problem. The scheme considers the following differences: the weight differences in two successive frames; different types of affine transformation applied to templates. Finally, experiments demonstrate that the proposed algorithm is robust to appearance variation of fast motion target and achieves real-time performance on middle/low-range computing platform.     

A new method for computing the matrix exponential operation based on vector valued rational approximations

In this paper a new method for computing the action of the matrix exponential on a vector e^Atb, where A is a complex matrix and t is a positive real number, is proposed. Our approach is based on vector valued rational approximation where the approximants are determined by the denominator polynomials whose coefficients are obtained by solving an inexpensive linear least-squares problem. No matrix multiplications or divisions but matrix-vector products are required in the whole process. A technique of scaling and recurrence enables our method to be more effective when the problem is for fixed A,b and many values of t. We also give a backward error analysis in exact arithmetic for the truncation errors to derive our new algorithm. Preliminary numerical results illustrate that the new algorithm performs well.