Noise Vector Research Articles

Application of a recursive subspace identification algorithm to change detection

This paper presents a new change detection method with the aid of subspace identification. The proposed method is based on monitoring a change in variance of a statistic generated by a recursive subspace identification algorithm. An asymptotic property of the statistic is presented. Without changes during sampling, it is shown that, under relevant assumptions. the statistic converges in probability to a stack of noise vectors multiplied from the left side by a Toeplitz matrix. A numerical example illustrates that the proposed method can detect changes in the dynamics of a system, without being disturbed by changes in the dynamics of an input signal which are not our concern.

Parameter estimation: known vector signals in unknown Gaussian noise

This paper develops recursive, convergent estimators for the parameters of finite Gaussian mixtures with a common covariance matrix. The mean vectors (signals) of the component densities are assumed to be known. The motivation for the study stems from digital communication. The basic approach is first illustrated for the case of an independent identically distributed sequence of samples from a univariate mixture of M classes (symbols). This is accomplished through the development of a convergent stochastic approximation form of estimator for the common variance value. The asymptotic variance of the estimated variance is derived. A batch processing alternative that possesses a sufficient statistic is developed for the case of a fixed size sample set. Three generalizations are studied. The first extends from the case of the univariate data to multivariate data. The second generalization allows for the statistical dependence of successive vector signals. Finally, the case of dependent successive vector signals along with dependent successive additive noise vectors is treated. In each case, convergent estimators for all unknown parameters are developed. Many cases are illustrated with simulation experiments. Results presented are applicable to communication engineering, pattern recognition, and some special image processing problems.

Acoustical imaging of spheres above a reflecting surface

An analytical study using the MUSIC method of subspace imaging is presented for the case of spheres above a reflecting boundary. The field scattered from the spheres and the reflecting boundary is calculated analytically, neglecting interactions between spheres. The singular value decomposition of the response matrix is calculated and the singular vectors divided into signal and noise subspaces. Images showing the estimated sphere locations are obtained by backpropagating the noise vectors using either the free space Green’s function or the Green’s function that incorporates reflections from the boundary. We show that the latter Green’s function improves imaging performance after applying a normalization that compensates for the interference between direct and reflected fields. We also show that the best images are attained in some cases when the number of singular vectors in the signal subspace exceeds the number of spheres. This is consistent with previous analysis showing multiple eigenvalues of the time reversal operator for spherical scatterers [Chambers and Gautesen, J. Acoust. Soc. Am. 109 (2001)]. [Work performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.]

Alignment-based codeword-dependent cepstral normalization

This paper proposes the alignment-based codeword dependent cepstral normalization algorithm (ACDC/sub N/) which aims to alleviate the acoustical mismatch that occurs when the speech recognizer faces environmental conditions not observed in the training data. ACDC/sub N/ is based on the linear channel model of the environment originally proposed by Acero (1990) and on the CDCN solution to this model. ACDC/sub N/ substitutes the codebook (Gaussian mixture model) employed by CDCN for the state distributions employed by the recognizer's HMMs under the assumption that these HMM distributions will model the associated speech segments better than the general GMM distribution. The feature-frame to HMM-state association is obtained through an alignment of a first decoding-pass hypothesis. From this alignment, ACDC/sub N/ obtains an estimate of the environmental parameters (noise and channel vectors) which are then employed to obtain an MMSE estimate of the clean speech vectors, in a way similar to Aero's method. ACDC/sub N/ produces an overall reduction of the error rate of over 30 % in the noise range of 0 to 20 dB on experiments conducted on the Aurora-2 noisy digits database.

Approximate Bayesian Approach to Non-Gaussian Estimation in a Linear Model with Dependent State and Noise Vectors

This paper extends the results of Masreliez [8] on the design of non-Gaussian estimators for a more general class of the parameter estimation problem when the system state and the observation noise may be dependent and non-Gaussian simultaneously. It is shown that the proposed non-Gaussian algorithms can approximate with high precision the minimum mean square estimator. Application of the approach to the design of different optimal (and stable) estimation algorithms is illustrated. The efficiency of the proposed algorithms is tested in some simulation experiments.

Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance

We address the class of stochastic output-feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori. This problem is analogous to deterministic disturbance attenuation problems. We first design a controller which guarantees that the solutions converge (in probability) to a residual set proportional to the unknown bound on the covariance. Then, for the case of a vanishing noise vector field, we design an adaptive controller which, besides global stability in probability, guarantees regulation of the state of the plant to zero with probability one.

The Methodology of Stochastic Optimization of Parameters and Control Laws for the Aircraft Gas-Turbine Engines Flow Passage Components

This paper presents the main theses of stochastic approach to the multimeasure parameters and control laws optimization for the aircraft gas-turbine engines. The methodology allows us to optimize the engines taking into account the technological deflections which inevitably take place in the process of manufacturing of the engine's components as well as engine's control deflections. The stochastic optimization is able to find highly robust solutions, stable to inaccuracies in technological processes. The effectiveness of the methodology is shown by example of optimization problem solution to find the control laws for the flow passage controllable elements of the fourth generation aircraft mixed-flow turbofan engine. The use of information about the existing and advanced production technology levels during the optimization process, including some components manufacturing accuracy, allows us to considerably increase the probability of optimum solution implementation in practice. In real engine there are some components manufacturing deflections as well as control accuracy deflections. This results in a certain engine's performance deviation. An engine optimization classic deterministic approach cannot take into account this circumstance, so the probability of an optimum design implementation is too low.

Manufacturing Block Diagrams and Optimal Adjustment Procedures

This paper introduces a technique for modeling manufacturing systems using block diagrams. The blocks represent linear transformations of dimensionless noise vectors to normalized quality characteristic vectors. These block diagrams are used to model on-line adjustment procedures using generalized inverses. This adjustment strategy is shown to guarantee minimum quality loss as defined by Taguchi if the required adjustments have no active constraints, and is effective for coupled linear systems. The surface mount of large body packages serves as an example of the modeling techniques. Block diagrams of the surface mount process are developed for a production system incorporating on-line adjustments and for the same system without adjustments. Data from preproduction runs support the model’s predictions of bias, variance, and yield.

Output-feedback disturbance attenuation and adaptive control for stochastic nonlinear systems

We address the class of stochastic output-feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori. This problem is analogous to deterministic disturbance attenuation problems. We first design a controller which guarantees that the solutions converge (in probability) to a residual set proportional to the unknown bound on the covariance. Then, for the case of a vanishing noise vector field, we design an adaptive controller which, besides global stability in probability, guarantees regulation of the state of the plant to zero with probability one.

Sinusoidal interference rejection analysis of an LMS adaptive feedforward controller with a noisy periodic reference

This paper applies a new vector subspace model to determine the non-Wiener solutions of the LMS algorithm when the reference input is an arbitrary noisy periodic signal. The LMS weights are modeled as a deterministic time-varying mean plus a zero-mean fluctuating part. For the mean weight, each harmonic component of the periodic reference is shown to excite only a two-dimensional (2-D) subspace of the N-dimensional tap weight space. The fluctuating part of the weight is due to the reference noise that excites the full N-dimensional space. The power spectrum of the error is computed using the correlation function of the weight fluctuations. The error is shown to be primarily the sum of a white noise and the canceled periodic residual for an independent noise vector model. When the effects of the tapped delay line are incorporated in the model, the noise becomes colored with a spectrum centered about the canceled sinusoidal frequency. This weight model significantly simplifies the understanding of the non-Wiener behavior and can be applied to active noise cancellation problems when filters appear in the cancellation loop.

Padé-Z2estimator of determinants

We introduce the Pad\'e-${Z}_{2}$ (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determinants from the two ends of the hybrid Monte Carlo trajectories with pseudofermions. Our results on the ${8}^{3}\ifmmode\times\else\texttimes\fi{}12$ lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20% with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.

Existence and uniquenesstheorems for some stochastic parabolic partial differential equations

In this paper we will prove existence and uniqueness heorems for the stochastic differential equations with initial conditions is a white noise vector is positive white noise is a positive white noise matrix and f, g are real functions. We will show that these equations have solutions in the space (S)-1of generalized white noise distributions in a strong differentiation sense

Cancellation of polarized impulsive noise using an azimuth-dependent conditional mean estimator

The separation of signals from noisy vector measurements is obtained by taking advantage of the Middleton Class A model of noise amplitude and the correlation of the components of the noise process due to their polarization. The signal is assumed to be white Gaussian. Noise is a superposition of M non-Gaussian processes, each with a fixed azimuth of polarization. Neither the number of processes (M) nor their azimuths are known. The separation of signal from noise is based on the conditional mean estimators. In addition to the optimum estimator, which can be derived from a knowledge of the bivariate density functions, two suboptimum solutions for polarized noise are discussed: the circularly symmetric estimator and the azimuth-dependent one. Circular symmetry is suitable for the nonpolarized noise vector, whereas the azimuth-dependent estimator is tailored to polarized noise. The azimuth-dependent approach consists of two steps: first, the data vector process is discretized into azimuth sectors, and then, in those classified as noisy, the signal is separated from the noise. Statistical model parameters of random processes are estimated by using the optimum classification, based on the likelihood ratio test (decision-directed method). Iterative whitening methods are also discussed for correlated vector signals. Numerical examples show the effectiveness of the above technique in canceling polarized noise.

Estimation of Spatially Variable Aquifer Hydraulic Properties Using Kalman Filtering

Spatial variability of aquifer properties and hydraulic heads are modeled as random fields, and their estimates are achieved by Kalman filtering. The state-space equation is developed from a quasi-analytical solution of a first-order approximation of the governing stochastic flow equation. In the state-space system, the effects of aquifer heterogeneity and uncertainty in recharge are lumped linearly into a random noise vector that is correlated in time. To account for the correlated system noise, we reformulate the problem in terms of an augmented–state-space system and use the resulting Kalman filtering recursions to estimate transmissivities, storativities, and hydraulic heads, simultaneously. The filter is applied to a numerical experiment in which the statistical parameters of log aquifer properties are assumed to be known. The results indicate that under mild head gradients, head measurements alone are of limited value if the objective is to estimate the spatial distribution of aquifer transmissivity...

An efficient method in array processing for eliminating the signal cancellation phenomena of the differencing method

In this paper, it is found that the Differencing method will fail to resolve any signals in some cases for the reason that the signals are cancelled out completely. The condition in which the signal cancellation phenomenon will occur is derived. In order to overcome the drawback of the Differencing algorithm, an extension of the differencing method, named DCM by us, is proposed to resolve two highly correlated signals in unknown noise fields. By splitting a uniform linear array into two identical subarrays, the DCM algorithm makes use of the fact that the two subarrays possess identical covariance matrices of noise vectors, and that the covariance matrix R ̃ s of uncorrelated signals satisfies Φ R ̃ sΦ = R ̃ s , where Φ is a diagonal matrix which indicates the displacement invariance between the two subarrays, under the assumption that the signals and noise are stationary, zero-mean, random processes. Finally, the DOA estimation is performed by investigating the eigenstructure of the difference matrix of the covariance matrices (DCM) of the two subarrays.

Blind identification of multi-input multi-output system using minimum noise subspace

This article presents a new subspace based method for blind identification of a p-input/q-output system, where q>p. This method exploits a minimum noise subspace (MNS) to retrieve the system impulse responses. The MNS method requires only q-p noise vectors as opposed to all noise vectors needed by a standard subspace (SS) method. It is shown that the MNS can be obtained in a parallel structure from a set of tuples (combinations) of system outputs that form a properly connected sequence (PCS). The PCS exploits with minimum redundancy the diversity among system outputs. The MNS method is much more efficient in computation than the SS method, although the former is less robust to noise than the latter.

Maximum-likelihood bearing estimation with partly calibrated arrays in spatially correlated noise fields

The problem of using a partly calibrated array for maximum likelihood (ML) bearing estimation of possibly coherent signals buried in unknown correlated noise fields is shown to admit a neat solution under fairly general conditions. More exactly, this paper assumes that the array contains some calibrated sensors, whose number is only required to be larger than the number of signals impinging on the array, and also that the noise in the calibrated sensors is uncorrelated with the noise in the other sensors. These two noise vectors, however, may have arbitrary spatial autocovariance matrices. Under these assumptions the many nuisance parameters (viz., the elements of the signal and noise covariance matrices and the transfer and location characteristics of the uncalibrated sensors) can be eliminated from the likelihood function, leaving a significantly simplified concentrated likelihood whose maximum yields the ML bearing estimates. The ML estimator introduced in this paper, and referred to as MLE, is shown to be asymptotically equivalent to a recently proposed subspace-based bearing estimator called UNCLE and rederived herein by a much simpler approach than in the original work. A statistical analysis derives the asymptotic distribution of the MLE and UNCLE estimates, and proves that they are asymptotically equivalent and statistically efficient. In a simulation study, the MLE and UNCLE methods are found to possess very similar finite-sample properties as well. As UNCLE is computationally more efficient, it may be the preferred technique in a given application.

Random exploration of the three regular polytopes

There are just three regular polytopes (the hypercube, cross polytope and the simplex) in Euclidean (n>4) space. We calculate their dimensions, including the distance from the centroid to the periphery in a random direction-that of a white Gaussian-noise vector. As n/spl rarr//spl infin/, this distance becomes very predictable. It differs from the distance near which almost all of the volume and surface of the polytope lie.

Generating correlated gaussian random fields by orthogonal polynomial approximations to the square root of the covariance matrix

Monte Carlo simulations in geostatistics often require the generation of realizations of multi-dimensional Gaussian processes with prescribed mean and covariance over a specified grid Ω of sampling points in R:d In principle, given a factorization C = AAT of the process’ covariance matrix C, realizations can always be constructed from the product Aϵ where ϵ is a white noise vector with unit variance. However, this approach generally has a high computational cost when compared with techniques such as the spectral or turning bands methods. Nevertheless, matrix factorization has advantages in that it does not require any special structure, such as isotropy or stationarity of the covariance model, o r regularity of the sampling grid Ω. Therefore, in an effort to speed up the approach at the cost of some loss in accuracy, Davis (1987b) proposed approximating the square root A by a low order matrix polynomial in C. This paper explores the construction of such polynomial approximations in more detail The paper f...

Cyclic magnetization noise of nonlinear ferromagnetic cores

Cyclic magnetization noise of nonlinear amorphous core is investigated experimentally by both cross-correlation and frequency spectra techniques as a periodically nonstationary process. The noise properties of the material are presented in terms of temporal fluctuations of the hysteresis loop (HL) of the core, what is likely to be the most appropriate form for applied purposes. Two components of the HL fluctuations were distinguished by their location, correlation and frequency spectra parameters: (i) the ‘flicker’ component and (ii) the ‘Barkhausen’ component. The total frequency spectrum of such a periodically nonstationary process is found out to be of periodic structure and must be considered as a superposition of overlapping sideband spectra of the both noise components related to different harmonics, plus wide-frequency-range noise component. A general form of the modulation noise vector model is presented to determine a relationship between temporal fluctuation of the transfer characteristic of a general nonlinear circuit and complex noise modulation of the harmonics in the output signal.