Colored Noise Fields Research Articles

A High-Precision Algorithm for DOA Estimation Using a Long-Baseline Array Based on the Hearing Mechanism of the Ormia Ochracea.

Inspired by the Ormia Ochracea hearing mechanism, a new direction of arrival estimation using multiple antenna arrays has been considered in spatially colored noise fields. This parasitoid insect can locate s cricket’s position accurately using the small distance between its ears, far beyond the standard array with the same aperture. This phenomenon can be understood as a mechanical coupled structure existing between the Ormia ears. The amplitude and phase differences between the received signals are amplified by the mechanical coupling, which is functionally equivalent to a longer baseline. In this paper, we regard this coupled structure as a multi-input multi-output filter, where coupling exists between each pair of array elements. Then, an iterative direction-finding algorithm based on fourth-order cumulants with fully coupled array is presented. In this manner, the orientation of the mainlobe can direct at the incident angle. Hence, the direction-finding accuracy can be improved in all possible incident angles. We derive the Cramér-Rao lower bound for our proposed algorithm and validate its performance based on simulations. Our proposed DOA estimation algorithm is superior to the existing biologically inspired direction-finding and fourth-order cumulants-based estimation algorithms.

Iterative methods for DOA estimation of correlated sources in spatially colored noise fields

Direction of arrival (DOA) estimation in the presence of correlated sources and unknown spatially colored noise field is concerned in this paper. We develop two iterative approaches to jointly estimate the angle parameters and unknown nonuniform noise covariance matrix from multi-snapshot sensor array data. Specifically, we show that both methods allow to obtain the estimates by explicit formulas: i) By concentrating the ML estimation problem with regard to all nuisance parameters, the proposed method provides a concise derivation of the concentrated likelihood function; ii) compact expressions of the estimates of the parameters of interest from sparse Bayesian learning (SBL) principle are also presented. This technique can be deemed as an alternative to ML estimation, and it provides better accuracy often at a lower computational cost. In spatially colored noise fields, the proposals are free of any further structural constraints that are usually imposed on the received signals in most existing direction finding approaches. Extensive simulations and experimental results are presented to demonstrate the satisfying performance of the proposed methods.

Open Ising model perturbed by classical colored noise

We investigate the non-Markovian dynamics of an open Ising model simulated by a superconducting circuit. The quantum many-body system is weakly coupled to a white, pink- or blue-colored environment. The relaxation of the system in the strong inter-qubit interaction regime shows a metastable behaviour. In comparison with the dissipative system in the Markovian limit, the negative memory of the blue-colored noise weakens the system's relaxation. However, for the pink-colored noise the relaxation rate of the system is enhanced due to the positive memory effect. The understanding of quantum many-body systems responding to different colored noise fields is necessary for designing the environment of superconducting qubits in a large scale quantum processor.

Rotation operator approach for the dynamics of non-dissipative multi-state Landau–Zener problems: Exact solutions

The paper investigates exact time-dependent analytical solutions of the Landau–Zener (LZ) transitions for spin one-half subjected to classical noise field using rotation operator approach introduced by Zhou and co-authors. The particular case of the LZ model subjected to colored noise field is studied and extended to arbitrary spin magnitude. Transition probabilities are derived regardless of the initial configuration of the system and are found to be functions of the sort for Stokes constant. It is observed that the latter may be completely evaluated provided we have knowledge of the phase difference between noise in x− and y−directions. Transition probabilities are found to depend not only on the LZ parameter and noise frequency, but also on the states involved in the study. In particular, the coherence of the system is sustained for an exceedingly long time when many levels are considered in an atom and if in addition, the LZ parameter tends to unity and the noise' frequency is low.

Strongly Consistent Model Order Selection for Estimating 2-D Sinusoids in Colored Noise

The problem of jointly estimating the number as well as the parameters of 2-D sinusoidal signals, observed in the presence of an additive colored noise field, is considered. We begin by establishing the strong consistency of the nonlinear least squares estimator of the parameters of 2-D sinusoids, when the number of sinusoidal signals assumed in the field is incorrect. Based on these results, we prove the strong consistency of a new family of model order selection rules.

Utilization of Noise-Only Samples in Array Processing With Prior Knowledge

For array processing, we consider the problem of estimating signals of interest, and their directions of arrival (DOA), in unknown colored noise fields. We develop an estimator that efficiently utilizes a set of noise-only samples and, further, can incorporate prior knowledge of the DOAs with varying degrees of certainty. The estimator is compared with state of the art estimators that utilize noise-only samples, and the Cram\'{e}r-Rao bound, exhibiting improved performance for smaller sample sets and in poor signal conditions.

Maximum Likelihood Direction Finding in Spatially Colored Noise Fields Using Sparse Sensor Arrays

We consider the problem of maximum likelihood (ML) direction-of-arrival (DOA) estimation of narrowband signals using sparse sensor arrays, which consist of widely separated subarrays such that the unknown spatially colored noise field is uncorrelated between different subarrays. We develop ML DOA estimators under the assumptions of zero-mean and non-zero-mean Gaussian signals based on an Expectation-Maximization (EM) framework. For DOA estimation of non-zero-mean Gaussian signals, we derive the Cramér-Rao bound (CRB) as well as the asymptotic error covariance matrix of the ML estimator that improperly assumes zero-mean Gaussian signals. We provide analytical and numerical performance comparisons for the existing deterministic and the proposed stochastic ML estimators. The results show that the proposed estimators normally provide better accuracy than the existing deterministic estimator, and that the nonzero means in the signals improve the accuracy of DOA estimation.

Accurate Angle-of-Arrival Measurement Using Particle Swarm Optimization

As one of the major methods for location positioning, angle-of-arrival (AOA) estimation is a significant technology in radar, sonar, radio astronomy, and mobile communications. AOA measurements can be exploited to locate mobile units, enhance communication efficiency and network capacity, and support location-aided routing, dynamic network management, and many location-based services. In this paper, we propose an algorithm for AOA estimation in colored noise fields and harsh application scenarios. By modeling the unknown noise covariance as a linear combination of known weighting matrices, a maximum likelihood (ML) criterion is established, and a particle swarm optimization (PSO) paradigm is designed to optimize the cost function. Simulation results demonstrate that the paired estimator PSO-ML significantly outperforms other popular techniques and produces superior AOA estimates.

Influence of velocity spatiotemporal correlations on the anomalous scaling exponents of passive scalars

In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer–Ohkitani–Yamada (GOY) shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She–Leveque velocity field, introduced by She, et al. We observe that extended self-similarity scaling exponents H(p)/H(2) of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.

Novel algorithm on DOA estimation for correlated sources under complex symmetric Toeplitz noise *

To cope with the scenario where both uncorrelated sources and coherent sources coexist, a novel algorithm to direction of arrival (DOA) estimation for symmetric uniform linear array is presented. Under the condition of stationary colored noise field, the algorithm employs a spatial differencing method to eliminate the noise covariance matrix and uncorrelated sources, then a Toeplitz matrix is constructed for the remained coherent sources. After preprocessing, a propagator method (PM) is employed to find the DOAs without any eigendecomposition. The number of sources resolved by this approach can exceed the number of array elements at a lower computational complexity. Simulation results demonstrate the effectiveness and efficiency of the proposed method.

Maximum likelihood DOA estimation in unknown colored noise fields

Direction-of-arrival (DOA) estimation in unknown noise environments is an important but challenging problem. Several methods based on maximum likelihood (ML) criteria and parameterization of signals or noise covariances have been established. Generally, to obtain the exact ML (EML) solutions, the DOAs must be jointly estimated along with other noise or signal parameters by optimizing a complicated nonlinear function over a high-dimensional problem space. Although the computation complexity can be reduced via derivation of suboptimal approximate ML (AML) functions using large sample assumption or least square criteria, nevertheless the AML estimators still require multi-dimensional search and the accuracy is lost to some extent. A particle swarm optimization (PSO) based solution is proposed here to compute the EML functions and explore the potential superior performances. A key characteristic of PSO is that the algorithm itself is highly robust yet remarkably simple to implement, while processing similar capabilities as other evolutionary algorithms such as the genetic algorithm (GA). Simulation results confirm the advantage of paring PSO with EML, and the PSO-EML estimator is shown to significantly outperform AML-based techniques in various scenarios at less computational costs.

Optimal Utilization of Signal-Free Samples for Array Processing in Unknown Colored Noise Fields

Many algorithms for direction-of-arrival (DOA) estimation require the noise covariance matrix to be known or to possess a known structure. In many cases, the noise covariance is, in fact, estimated from separate measurements. This paper addresses the combined effects of finite sample sizes, both in the estimated noise covariance matrix and in the data with signals present. It is assumed that a batch of signal-free samples is available in addition to the signal-containing samples. No assumption is made on the structure of the noise covariance. In this paper, the asymptotic covariance of the weighted subspace fitting (WSF) algorithm is derived for the case in which the data are whitened using an estimated noise covariance. The expression obtained suggests an optimal weighting that improves performance compared to the standard choice. In addition, a new method based on covariance matching is proposed. Both methods are asymptotically statistically efficient. The Cramer-Rao lower bound (CRB) on the covariance of the estimate for the data model is also derived. Monte Carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results

Array processing for signals with non-zero means in colored noise fields

Array processing in spatially correlated noise fields is a difficult problem which cannot be solved without constraining either the noise or the signals in various ways. In this paper we assume that the signals impinging on the array have non-zero means. We show that the problem of array processing in completely general spatially colored noise fields is solvable under the previous assumption. In fact we argue that the non-zero mean signal assumption probably is one of the simplest conditions which makes array processing in colored noise possible. We also present a maximum-likelihood (ML) methodology for signal detection and parameter estimation. The derivation of the ML processor under the aforementioned assumption is conceptually straightforward and its implementation is standard. We provide a statistical analysis of the ML signal parameter estimator along with an expression for the associated Cramer–Rao bound (CRB) matrix. Finally, we include some numerical examples to show the type of performance that can be achieved by the estimation and detection approach proposed in this paper.

Least squares estimation of 2-D sinusoids in colored noise: asymptotic analysis

This paper considers the problem of estimating the parameters of real-valued two-dimensional (2-D) sinusoidal signals observed in colored noise. This problem is a special case of the general problem of estimating the parameters of a real-valued homogeneous random field with mixed spectral distribution from a single observed realization of it. The large sample properties of the least squares (LS) estimator of the parameters of the sinusoidal components are derived, making no assumptions on the type of the probability distribution of the observed field. It is shown that if the disturbance field satisfies a combination of conditions comprised of a strong mixing condition and a condition on the order of its uniformly bounded moments, the normalized estimation error of the LS estimator is consistent asymptotically normal with zero mean and a normalized asymptotic covariance matrix for which a simple expression is derived. It is further shown that the LS estimator is asymptotically unbiased. The normalized asymptotic covariance matrix is block diagonal where each block corresponds to the parameters of a different sinusoidal component. Assuming further that the colored noise field is Gaussian, the LS estimator of the sinusoidal components is shown to be asymptotically efficient.

Sensitivity of parametric direction finding to colored noise fields and undermodeling

A fundamental assumption for most direction finding algorithms is that the spatial correlation structure of the background noise (i.e., the correlation from sensor to sensor) is known to within a multiplicative scalar. In practive, this is often achieved by measuring the array covariance when no signals are present, a procedure which is unavoidably subjected to errors. The presence of undetected weak signals gives rise to similar perturbations. In this paper, the effect of such modeling errors on parametric estimation techniques is examined. First-order expressions for the mean square error (MSE) of the parameter estimates are derived for the deterministic and stochastic maximum likelihood methods and the weighted subspace fitting technique. The spatial noise correlation structures that lead to maximum performance loss are identified under different assumptions. In case of high signal-to-noise ratio, it is found that the MSE can be increased by a factor equal to the number of sensors in the array, as compared to spatially white noise. Furthermore, it is demonstrated that the presence of a relatively weak (− 15 dB) undetected signal can result in a large bias (≈1°) on the estimates of the other signal directions.

Broad-band detection based on two-dimensional mixed autoregressive models

Two detectors for broadband plane waves in colored noise fields that use a linear array are described. The signal spectrum, arrival angle, and noise field coloration are not known a priori. Using a two-dimensional mixed autoregressive model, a generalized-likelihood-ratio test and its weak-signal equivalent, the Rao test, are derived. The performances of the proposed detectors are shown by computer simulations to be superior to those of conventional Fourier-based methods. Detection results for real data are presented. >

Parametric methods for spatial signal processing in the presence of unknown colored noise fields

Two methods for estimation of noise correlations along an array of sensors are presented. Both rely on a parametric (autoregressive moving average) noise model. The model has the advantage of describing the noise correlations by a small number of parameters and can be applied to a great variety of physical noises. The first method is related to the calculation of the likelihood of whitened observations, and the second is related to Pisarenko's method (1973) applied to whitened observations. Both methods are obtained by optimization of a criterion and are iterative. The noise estimates can be used for sensor-output whitening and it then provides a means to improve array processing performance. The two methods perform well, both on simulated and real data. However, the first method seems simpler and more robust than the second. >