Designing nonuniform linear arrays to maximize mutual information for bearing estimation

Estimating the bearing of a narrowband sound source using a towed horizontal array is a common array processing problem. This paper designs nonuniform linear symmetric arrays of fixed apertures for estimating the bearing of a sound source. Specifically, the hydrophone spacings for a symmetric linear array are chosen to maximize the upper bound on the mutual information between the true bearing and the estimated bearing in spatially white noise. The arrays maximizing the mutual information while nulling the forward endfire direction look significantly different from the uniform arrays commonly used in towed systems. Arrays maximizing mutual information are helpful when bearing estimation is considered as a quantization problem to assign the source to the correct partition. The optimal partitions for the array are designed using the Lloyd algorithm with an inner product distortion metric based on maximizing the likelihood function of the observations. In these approaches, increasing the mutual information and optimizing the partitions should reduce the probability of error (P(e)) in choosing the partition containing an unknown source. Simulation results with MAP and ML estimators demonstrate that the optimum arrays and partitions proposed here have a much lower P(e) than the uniform array and uniform partitions.     

The use of nonuniform element spacing in array processing algorithms

Most array signal processing algorithms use uniform element spacing to estimate source bearing. This paper demonstrates the benefit of using nonuniform element spacing in Bartlett, linear prediction (LP), and minimum variance (MV) array processing algorithms. By using optimum element spacing results obtained by previous investigators for sidelobe reduction of the Bartlett method, better MV and LP performances, in terms of array output power, are obtained.     

Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and Ornstein-Uhlenbeck noise types. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and the data sets suggest that 1/f^α noise spectra with increasing noise color (i.e. α) may lead to increasing asymmetry in the system, reducing the achievable amplification. Furthermore, we explore the effects of correlation time τ on stochastic resonance with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.     

Robust supergain beamforming for circular array via second-order cone programming

The phenomenon of supergain for a circular array and its robust beamforming are presented. The coplanar superdirective array gain of the circular array, although it is not so extreme as an endfire line array, outperforms a lot over that of a conventional delay-and-sum beamformer in isotropic noise fields when the inter-element spacings are much smaller than one-half wavelength. However, optimum beamforming algorithms can be extremely sensitive to slight errors in array characteristics. The performance are known to degrade significantly if some of underlying assumptions on the sensor array is violated. Therefore, white noise gain constraint is used to improve the robustness of the supergain beamformer against random errors. We show that the design of the weight vector of robust supergain beamformer can be reformulated as a form of second-order cone programming and resolved efficiently via the well-established interior point method. Results of computer simulation for a 24-element circular array confirm satisfactory performance of the approach proposed in this paper.     

Harmonic noise: Effect on bistable systems

The coordinate of a white noise driven harmonic oscillator is used as a stochastic source term in bistable dynamics. This new kind of Gaussian colored noise gives rise to resonance phenomena due to a peak in the spectrum. We investigate its effect on linear and bistable systems. We derive a Markovian approximation for driven bistable oscillators and overdamped systems. In the resonance region computer simulations were carried out using an extension of Fox' algorithm procedure for colored noise. We find an increase of the transition rates in bistable systems as compared with the case of bistable systems driven by white and exponentially correlated noise.     

空间关联白噪声影响下小世界神经元网络系统的同步动力学

以电耦合的Terman-Wang小世界神经元网络系统为研究对象, 研究了空间关联白噪声影响下神经元网络系统的同步动力学. 首先将动力学平均场近似理论扩展到受空间关联白噪声影响下的小世界网络系统中, 将描述网络系统动力学演化的2N维随机微分方程简化为11个确定性的矩微分方程. 其次, 基于动力学平均场近似理论所推导的矩方程, 讨论了空间关联噪声、网络结构参数对神经元网络系统同步动力学的关键影响, 发现较大的噪声空间关联系数、耦合强度及节点平均度均对神经元网络系统同步放电具有积极作用. 进一步地, 利用计算机仿真数值模拟原神经元网络系统的同步动力学, 并与基于动力学平均场近似理论所得到的结果进行比较, 发现二者具有较好的一致性.     

Estimation of coherent source bearings using variational techniques

We study the problem of bearing estimation in the case of coherent signal sources with the use of variational techniques for minimizing the target function defined on the basis of the ℓ_p norm. A regularization technique similar to projection onto a signal subspace of given dimension is proposed. The numerical calculation of the bearing estimate variance and its comparison with the maximum-likelihood estimate variance as well as with the Cramer-Rao bound (CRB) are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 265–273, March 2007.     

Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise

In this theoretical study, the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated. Both white and Ornstein-Uhlenbeck-type excitations are considered. In the white noise limit, the stationary Fokker-Plank-Kolmagorov equation is solved for the exact joint probability density function (PDF) of the response. The PDF is then used to obtain analytical expressions for the response statistics. It is shown that the expected value of the generator's output power is independent of the potential shape leading to the conclusion that under white noise excitations, bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single-well potential. In the case of Ornstein-Uhlenbeck (exponentially correlated) noise, an approximate expression for the mean power of the generator which depends on the potential shape, the generator's design parameters and the noise bandwidth and intensity is obtained. It is shown that there exists an optimal potential shape which maximizes the output power. This optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied.     

Near-field measurement of radiation levels of extended spatially uncorrelated sound sources

A method is considered for measuring the radiation levels of extended spatially uncorrelated sound sources in the near field in the case of their imprecise positioning with respect to the measurement system??a linear antenna array. An algorithm is proposed for synthesizing the vector of weight coefficients ensuring the given value of methodological measurement error under maximum suppression of external noise. Examples are given of numerical modeling and experimental testing of the method in natural conditions.     

Fast implementation of sparse iterative covariance-based estimation for source localization

Fast implementations of the sparse iterative covariance-based estimation (SPICE) algorithm are presented for source localization with a uniform linear array (ULA). SPICE is a robust, user parameter-free, high-resolution, iterative, and globally convergent estimation algorithm for array processing. SPICE offers superior resolution and lower sidelobe levels for source localization compared to the conventional delay-and-sum beamforming method; however, a traditional SPICE implementation has a higher computational complexity (which is exacerbated in higher dimensional data). It is shown that the computational complexity of the SPICE algorithm can be mitigated by exploiting the Toeplitz structure of the array output covariance matrix using Gohberg-Semencul factorization. The SPICE algorithm is also extended to the acoustic vector-sensor ULA scenario with a specific nonuniform white noise assumption, and the fast implementation is developed based on the block Toeplitz properties of the array output covariance matrix. Finally, numerical simulations illustrate the computational gains of the proposed methods.     

Lyapunov exponent of the random Schrödinger operator with short-range correlated noise potential

We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schrödinger equation with the white noise potential can be expressed through the Lyapunov exponent γ which we determine explicitly as a function of the noise intensity σ and the frequency ω. We find uniform two-parameter asymptotic expressions for γ which allow us to evaluate γ for different relations between σ and ω. The value of the Lyapunov exponent is also obtained in the case of a short-range correlated noise, which is shown to be less than its white noise counterpart.     

Irregular array motion and extended integration for the suppression of spatial aliasing in passive sonar

Conventional synthetic aperture processing uses motion of the sonar to increase aperture size and bearing resolution. Two recent papers discussed a different application in which synthetic elements are used to fill in an otherwise sparse passive array. This paper points out that ambiguities persist, even with synthetic elements, in the ideal case of a straight, uniform, sparse line array with constant velocity in the presence of plane wave signals. It is also shown that irregular motion such as acceleration introduces additional information which can be exploited to suppress the ambiguities. The degree of suppression in such an approach is independent of signal direction. If source stability supports extended coherent integration, then the acceleration and integration time required are both modest to achieve interesting levels of suppression. For a less stable source, a modified conventional beamformer is introduced which leverages acceleration over multiple snapshots to suppress the ambiguities. A post-beamformed processing stage involving a nonlinear deconvolution technique such as the CLEAN algorithm can further improve the result. A semi-coherent adaptation of CLEAN is shown to remove the residual ambiguities effectively in the presence of a moderate level of uncorrelated noise.     

Escape of Brownian Particles in the System Driven by Correlated White Noises:Comparison of Three Models

The relative escape rate (RER) in the bistable sawtooth system driven by correlated white noises was studied in the case of linear multiplicative noise coefficient.And we compare the RER of linear multiplicative noise coefficient with the RER of the piecewise constant multiplicative noise coefficient in the bistable sawtooth system,finally compare the RER of the bistable sawtooth potential with the RER of the quartic potential in the case of linear multiplicative noise coefficient.It can be seen that the form of the multiplicative noise coefficient and the nonlinearity of potential have an important influence on the resonant activation and the suppression of the RER.The resonant activation of the RER vanishes in the negative correlation when the multiplicative noise coefficient was shifted from piecewise constant to linear function in the bistable sawtooth potential.The suppression of the RER disappears in the negative correlation when thelinear potential is converted into nonlinear one.     

Escape of Brownian Particles in the System Driven by Correlated White Noises:Comparison of Three Models

The relative escape rate (RER) in the bistable sawtooth system driven by correlated white noises was studied in the case of linear multiplicative noise coefficient.And we compare the RER of linear multiplicative noise coefficient with the RER of the piecewise constant multiplicative noise coefficient in the bistable sawtooth system,finally compare the RER of the bistable sawtooth potential with the RER of the quartic potential in the case of linear multiplicative noise coefficient.It can be seen that the form of the multiplicative noise coefficient and the nonlinearity of potential have an important influence on the resonant activation and the suppression of the RER.The resonant activation of the RER vanishes in the negative correlation when the multiplicative noise coefficient was shifted from piecewise constant to linear function in the bistable sawtooth potential.The suppression of the RER disappears in the negative correlation when thelinear potential is converted into nonlinear one.``     

In situ calibration of atmospheric-infrasound sensors including the effects of wind-noise-reduction pipe systems

A worldwide network of more than 40 infrasound monitoring stations has been established as part of the effort to ensure compliance with the Comprehensive Nuclear Test Ban Treaty. Each station has four to eight individual infrasound elements in a kilometer-scale array for detection and bearing determination of acoustic events. The frequency range of interest covers a three-decade range-roughly from 0.01 to 10 Hz. A typical infrasound array element consists of a receiving transducer connected to a multiple-inlet pipe network to average spatially over the short-wavelength turbulence-associated "wind noise." Although the frequency response of the transducer itself may be known, the wind-noise reduction system modifies that response. In order to understand the system's impact on detection and identification of acoustical events, the overall frequency response must be determined. This paper describes a technique for measuring the absolute magnitude and phase of the frequency response of an infrasound element including the wind-noise-reduction piping by comparison calibration using ambient noise and a reference-microphone system. Measured coherence between the reference and the infrasound element and the consistency between the magnitude and the phase provide quality checks on the process.     

Optimal two-layer directive microphone array with application in near-field acoustical holography

Conventional near-field acoustical holography (NAH) is generally based on the free-field assumption, which can cause errors when interfering sources are present in practical environments. To cope with this problem, previous research suggested a combined pressure-velocity approach for NAH that provides certain advantages to rejection of interferences. This paper revisits this idea in a broader context of optimal array design and examines the feasibility of using unidirectional microphones in each channel of the array such that the robustness of inverse reconstruction is enhanced against interfering sources. As indicated in the simulation, the numerical noise in finite difference estimation of particle velocity can nullify the advantage of the well-conditioned velocity-based reconstruction. In the proposed approach, the characteristics of each array channel consisting of two microphones are tailored by taking into account not only the directivity, but also the robustness against self-noise. An objective function based on directivity index and white noise gain is exploited in a linear quadratic optimization of a two-element end-fire array. The proposed optimal array is validated in conjunction with the equivalent source model (ESM) -based NAH through numerical simulations, with an interfering source positioned behind the array. The results have shown the directive optimal array has yielded improved quality of images in comparison with conventional approaches in the presence of an interfering source and sensor noise.     

刚性圆柱体上圆阵波束形成性能分析

以环绕在刚性圆柱体上的均匀圆阵为阵列模型,分析了刚性圆柱体对圆阵响应的影响,在声场分解所得到的相位模式空间,推导了相位模式波束形成阵列和延迟求和波束形成阵列的白噪声增益和指向性指数的定量表达式,分析了它们在不同频率段的变化规律。在存在和不存在刚性圆柱体两种情况下,对两种阵列性能进行了对比分析。研究了圆阵与圆柱体之间存在间隙时对阵列接收信号及阵列性能的影响。仿真结果表明,在两种情况下相位模式波束形成处理都具有频率不变的指向性,但在低频段牺牲了阵列的鲁棒性;延迟求和波束形成处理在整个频率段具有较好的鲁棒性,但随频率的降低其波束指向性下降,直至变成各向同性阵列。存在刚性圆柱体时,两种阵列鲁棒性均有了一定的提高,前者的指向性不变,而后者的指向性得到了提高。圆阵与圆柱体之间的间隙会降低阵列在高频段的鲁棒性。      

Influence of low intensity noise on assemblies of diffusively coupled chaotic cells

The effect of time-correlated and white Gaussian noises of low intensity on one-dimensional arrays consisting of diffusively coupled chaotic cells is analyzed. An improvement or worsening of the synchronization between cells of the array driven by low-intensity colored noise is observed for a resonant interval of time correlation values. A comparison between colored and white noise and additive and multiplicative contribution has been carried out investigating the nonlinear cooperative effects of noise strength, correlation time, and coupling strength to control spatiotemporal chaos in coupled arrays of chaotic cells. The possibility to distinguish highly correlated areas of a diffusively coupled network of cells by using low-intensity time correlated noise is discussed. (c) 2001 American Institute of Physics.     

Acoustic multipath structure in direct zone of deep water and bearing estimation of tow ship noise of towed line array

In the towed line array sonar system, the tow ship noise is the main factor that affects the sonar performance. Conventional noise cancelling methods assume that the noise is towards the endfire direction of the array. An acoustic experiment employing a towed line array is conducted in the western Pacific Ocean, and a strange bearing-splitting phenomenon of the tow ship noise is observed in the array. The tow ship noise is split into multiple noise signals whose bearings are distributed between 10° and 90° deviating from the endfire direction. The multiple interferences increase the difficulty in recognizing the target for the sonar operator and noise cancellation. Therefore, making the mechanism clear and putting forward the tow ship noise splitting bearing estimation method are imperative. In this paper, the acoustic multi-path structure of the tow ship in deep water is analyzed. Then it is pointed out that the bearing-splitting phenomenon is caused by the main lobe of direct rays and bottom-reflected rays, as well as several side lobes of direct rays. Meanwhile, the indistinguishability between the elevation angle and the bearing angle due to the axial symmetry of a strict horizontal line array causes the bearing to deviate from the endfire direction. Based on the theory above, a method of estimating bearing of the tow ship noise in deep water is proposed. The theoretical analysis results accord with the experimental results, which helps to identify the target and provide correct initial bearing guidance for noise cancelation methods.     

Error bounds in diffusion tensor estimation using multiple-coil acquisition systems

We extend the diffusion tensor (DT) signal model for multiple-coil acquisition systems. Considering the sum-of-squares reconstruction method, we compute the Cramér–Rao bound (CRB) assuming the widely accepted noncentral chi distribution. Within this framework, we assess the effect of noise in DT estimation and other measures derived from it, as a function of the number of acquisition coils, as well as other system parameters. We show the applications of CRB in many actual problems related to DT estimation: we compare different gradient field setup schemes proposed in the literature and show how the CRB can be used to choose a convenient one; we show that for fiber-type anisotropy tensors the ellipsoidal area ratio (EAR) can be estimated with less error than other scalar factors such as the fractional anisotropy (FA) or the relative anisotropy (RA), and that for this type of anisotropy tensors, increasing the number of coils is equivalent to increasing the signal-to-noise ratio, i.e., the information of the different coils can be regarded as independent. Also, we present results showing the CRB of several parameters for actual DT-MRI data. We conclude that the CRB is a valuable tool to optimal experiment design in DT-related studies.