Optimal and Near-Optimal Signal Detection in Snapping Shrimp Dominated Ambient Noise

The optimal detection of signals requires detailed knowledge of the noise statistics. In many applications, the assumption of Gaussian noise allows the use of the linear correlator (LC), which is known to be optimal in these circumstances. However, the performance of the LC is poor in warm shallow waters where snapping shrimp noise dominates in the range 2-300 kHz. Since snapping shrimp noise consists of a large number of individual transients, its statistics are highly non-Gaussian. We show that the noise statistics can be described accurately by the symmetric alpha-stable family of probability distributions. Maximum-likelihood (ML) and locally optimal detectors based on the detailed knowledge of the noise probability distribution are shown to demonstrate enhanced performance. We also establish that the sign correlator, which is a nonparametric detector, performs better than the LC in snapping shrimp noise. Although the performance of the sign correlator is slightly inferior to that of the ML detector, it is very simple to implement and does not require detailed knowledge of the noise statistics. This makes it an attractive compromise between the simple LC and the complex ML detector     

Signal detection for communications in the underwater acousticenvironment

Signal detection is a critical stage in the implementation of any effective communications system. The underwater acoustic environment, particularly in the presence of underwater vehicles, presents significant challenges to reliable detection without excessive false alarms. While there is often sufficient signal-to-noise ratio with respect to stationary broad-band background noise to permit reliable operation, the presence of strong event-like interference signals such as narrow-band signals and impulsive broad-band signals complicates the detection problem significantly. Frequency-hopped signals interleaved with quiescent bands are proposed as the basis of a robust detection system. These signals also make robust detection possible in a multi-access communications system. Two new detection algorithms that exploit the particular structure of these frequency-hopped signals are developed and their performance is analyzed. This analysis uses a modification of the doubly noncentral F-distribution that has not been used previously for such analysis. This distribution makes possible the direct calculation of probabilities of detection and false-alarm under interference and signal scenarios that cannot be analyzed using the better known noncentral F-distribution. With this analysis, the two developed detectors are shown to offer superior performance to that of either the CFAR detector or the binary data sequence detector. Experimental data confirms the theoretically derived results     

Functional inputs to passive correlation detectors for oscillatorytransient signals

This research investigates whether passive detection of transient signals can be improved by replacing received signals with functionals of the received signals in correlation detectors. Specifically, this paper assesses the impact of using energy spectrum and autocorrelation functional inputs to the cross-correlation (energy), bicorrelation, and tricorrelation detectors. Test signals with differing autocorrelation and energy spectrum properties are used in computer simulations with independent Gaussian noise to evaluate detector performance. Detection results are presented for the case when only two channels of input data are available to form the correlations, as well as the case when three and four channels of input data are available to form the higher order correlations. In the former case, it is shown that detection performance can be improved for the narrow-band signals by using the energy spectrum and autocorrelation functional inputs rather than the original received signal. In the latter case, it is shown that detection performance can be improved by using the autocorrelation input for the broadband signal and the energy spectrum input for the narrow-band signals, and that the tricorrelation detector performs best for the signals tested     

基于窄带混合高斯噪声的最佳检测

论文首先研究高斯柯西卷积噪声模型和窄带混合高斯噪声模型用来对混响建模,前者主要用于仿真分析,而后者因其参数有明确物理意义且可通过样本序列估计得到,因此被用于海洋的工程实现.文章重点研究混合高斯噪声背景下确知信号的非高斯最佳检测器的构造,并对检测器进行了仿真.验证结果表明混合高斯噪声背景下确知信号的非高斯最佳检测器检测性能优于常规的匹配滤波器3～4.5 dB.     

The use of spectral information in optimal detection of a source inthe presence of a directional interference

The detection of a passive sonar target in the presence of ambient noise and a plane wave interference is discussed. Intuitively, such a detector consists of a spatial filter which nulls the interference, followed by a temporal filter. In this paper we study the role of the a priori knowledge of the spectrum of the interference and/or signal in improving detector performance. We develop three different generalized likelihood ratio test (GLRT) detectors, resulting from different cases of prior spectral information. We show that, for all cases of known/unknown source and/or interference power spectrum, the GLRT detectors are, as expected, null steering systems. The depth and shape of the null, as well as the postbeamforming temporal filter, are different and are functions of the a priori known spectrum. Under the assumption that all signals and noise are zero-mean Gaussian processes, we analyze the performance of the different detectors and we exploit their dependency on the array beampattern, as well as on the source and interference signal-to-noise ratio. This analysis serves to identify scenarios where the use of prior spectral information leads to significant performance improvement     

A Statistical Analysis of the Detection Performance of a Broadband Splitbeam Passive Sonar

An operational passive sonar is required to detect signals from sources, which are subject to spatial and temporal coherence losses via modifications by the ocean environment. Furthermore, these signals are to be detected in the presence of frequency-dependent correlated noise fields. For a system which employs splitbeam cross-correlation processing, the spatial and spectral properties of the signal and noise are of significant import. Therefore, the exact probability density and cumulative distribution functions of the N-sampled correlator outputs of a splitbeam broadband passive sonar are derived for the case of Gaussian inputs which are described by arbitrary cross-spectral density matrices. The validity of approximating the exact probability density function (pdf) as a Gaussian distribution is investigated. The effect of signal coherence loss and noise correlation on the detection performance is considered and the associated processing loss is expressed as a degradation factor within the detection threshold equation     

Multichannel moment detectors for transients in shallow-water noise

This paper presents an evaluation of second, third, and fourth-order moments for the passive detection of transient signals in both simulated Gaussian noise and measured noise. The measured noise was recorded by a vertical array located near the San Diego, CA, harbor and is dominated at low frequencies by ship-generated noise. The detectors assume neither noise nor signal stationarity and can use single or multiple channels of data. Simulation results indicate that the fourth-order moment detector often performs better than the energy detector in the correlated measured noise, with increasing channel contributions to the moment function, resulting in increased gain. The results in simulated Gaussian noise likewise favor the fourth-order moment detector, at least for the signals with significant fourth-order moments, but the ability of the higher order detector to discriminate against correlated noise is evident. Analysis over a 30-min segment of the measured noise with selected signals demonstrates that fourth-order detection gains can be reliably expected as the noise statistics change.     

Statistics of biological noise and performance of generalizedenergy detectors for passive detection

Underwater noise due to snapping shrimp is highly impulsive, and often dominates the ambient noise environment of warm, shallow waters at frequencies above 1 kHz. We report here on the statistics of bandpass snapping shrimp noise data, and on the modeling of the joint distribution of the in-phase and quadrature components using bivariate versions of the generalized Gaussian (GG), generalized Cauchy, and Gaussian-Gaussian mixture models. We evaluate the performance of several generalized energy detectors for passive bandpass detection, by inserting stochastic signals into the noise data. Detection thresholds were measured for an integration time of 0.5 s and false alarm probabilities down to 1%. The locally optimum detector based on the mixture model gave the best weak signal detection performance, with an 8 dB reduction in detection threshold over conventional energy detection. A significance test detector based on the GG model performed 1-2 dB worse, but exhibited better strong signal performance     

A method minimizing the correlation properties of a noise field andimproving detection of signals embedded in anisotropic noise

This paper deals with the development of a processing technique that improves the signal-to-noise ratio (SNR) at the single sensor for a received signal that is embedded in a partially correlated noise field. The approach of this study is unique in that the noise is treated as being non-white and partially correlated. The concept of the proposed development is based on the time interval over which the temporal coherence or correlation properties of a noise field are defined. For narrowband signals, the associated temporal coherence period is much longer than the correlation time interval of the anisotropic noise field. Thus, a coherent integration of discontinuous segments of received signals will enhance the SNR at the single sensor by lowering the correlation properties of the associated non-white noise. Reconstruction of the narrow-band signal time series, with improved SNR at the sensor will allow the use of the existing high resolution techniques to be utilized more effectively by lowering their threshold values in order to detect very weak signals. The intention here is to integrate the characteristics of the real anisotropic noise field during the preliminary processing stages of the received signals by an array of sensors. Simulations show that the proposed method can be integrated in the signal processing functionality of sonar and radar systems     

Optimum and Suboptimum Detector Performance for Signals in Cyclostationary Noise

The detection of known and partially known signals in additive white Gaussian uonstationary noise is considered, with primary attention to the ease where the time-varying noise intensity parameter N_{o}(t) is a periodic function. Optimum receiver structures are derived for three detection cases, namely completely known signals, sinusoids with random phase, and sinusoids with both random amplitude and phase. It is demonstrated that optimum receiver performance can be achieved only if proper synchronization to the noise intensity N_{o}(t) is accomplished. Large performance penalties can be demonstrated when an improperly synchronized receiver is used. Consequently, suboptimum receivers that ignore the noise intensity time variations and therefore require no synchronization, have been considered, and their performance compared to their optimum counterparts. Depending on the type of time-varying noise intensity being considered, results show that performance differences between optimum and suboptimum receivers can be negligible in some cases, and yet can be substantial in other cases. Several examples have been worked out using two different forms for N_{o}(t) and corresponding performance evaluations have been carried out and presented graphically in terms of receiver error probability as a function of signal-to-noise ratio.     

基于分数阶傅里叶变换的水下目标速度估计

在高斯白噪声背景下,匹配滤波器作为线性调频信号的最优检测器,在水声信号处理中被广泛应用。 当发射信号为线性调频信号时,由水下目标径向速度引起的多普勒频移会造成回波和样本之间失配, 使匹配滤波器的检测性能下降,增加了目标速度估计的难度。 利用分数阶傅里叶变换对于线性调频信号的聚焦特性,提出了应用分数阶傅里叶变换的水下运动目标线性调频回波检测算法,完成对目标速度的估计, 推导目标运动速度与分数阶傅里叶变换阶数之间的关系,并对测量结果进行误差分析。 仿真测试表明,该算法可有效地估计混响背景下的目标径向速度,且具有良好的估计性能。     

On detecting linear frequency-modulated waveforms in frequency- andtime-dispersive channels: alternatives to segmented replica correlation

In modern active sonars, so-called “high-gain” waveforms are used to obtain processing gain for improved detection performance in reverberation. In time and frequency spread channels, the full processing gain of these waveforms is not achievable and robust detectors are needed. It is common practice to use a segmented replica correlator (SRC) detector for robust detection in such environments. In this paper, we show that an alternative processor formed by integrating the full replica correlator output magnitude squared, denoted RCI for replica correlator integrator, has advantages over the SRC when the waveform is linear frequency modulated (LFM). The RCI is better suited to the case of unknown time spreading through the use of a bank of integrators tuned for a wide range of spreading widths. The SRC, on the other hand, may be designed only for a fixed amount of distortion. Computer simulations are used to show how a multihypothesis RCI processor improves upon the fixed SRC by up to 4 dB over a realistic range of time spreading widths     

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.     

Particle-Velocity-Field Difference Smoothing for Coherent Source Localization in Spatially Nonuniform Noise

This communication considers the problem of estimating 2-D directions of arrival (DOAs) of multiple coherent signals under spatially nonuniform noise (spatially inhomogeneous temporary white noise) using an array of vector hydrophones. A novel preprocessing method called particle-velocity-field difference smoothing (PVFDS) is proposed. The key idea underlying the PVFDS is to remove the spatially nonuniform noise by using the matrix difference of pairs of particle-velocity data correlation matrices, and to decorrelate the coherent signals by summing these difference correlation matrices. Unlike most of other existing preprocessing techniques, such as spatial smoothing and forward–backward averaging, the PVFDS processing does not decrease the array aperture. For arbitrary array geometries, the PVFDS can resolve up to four coherent signals, and for centro–symmetric arrays, forward–backward averaging can double this number to eight. Monte Carlo simulations illustrate that the PVFDS-based eigenstructure algorithms can offer better performance than the particle-velocity-field smoothing (PVFS)-based counterparts.      

On Performance of Array Signal Processing

A unified treatment for performance evaluation of various array signal processors is presented. Detection performance is expressed in terms of the parameter of the power-type receiver operating characteristic (ROC) for optimum, beamformer, and null-steerer detectors. Estimation performance is analyzed in terms of the normalized mean-square error (MSE) for minimum mean-square error (MMSE) and maximum likelihood estimators (MLE's) under a varying noise environment. Sensitivity of the detection/estimation performance to the varying internal and directional noise sources is investigated. An interesting inverse relationship is presented between the normalized MSE of the MMSE estimator and the power-type ROC parameter for the optimum detector.     

Use of the kurtosis statistic in the frequency domain as an aid in detecting random signals

Power spectral density estimation is often employed as a method for signal detection. For signals which occur randomly, a frequency domain kurtosis estimate supplements the power spectral density estimate and, in some cases, can be employed to detect their presence. This has been verified from experiments with real data of randomly occurring signals. In order to better understand the detection of randomly occurring signals, sinusoidal and narrow-band Gaussian signals are considered, which when modeled to represent a fading or multipath environment, are received as non-Ganssian in terms of a frequency domain kurtosis estimate. Several fading and muitipath propagation probability density distributions of practical interest are considered, including Rayleigh and log-normal. The model is generalized to handle transient and frequency modulated signals by taking into account the probability of the signal being in a specific frequency range over the total data interval. It is shown that this model produces kurtosis values consistent with real data measurements. The ability of the power spectral density estimate and the frequency domain kurtosis estimate to detect randomly occurring signals, generated from the model, is compared using the deflection criterion. It is shown, for the cases considered, that over a large range of conditions, the power spectral density estimate is a better statistic based on the deflection criterion. However, there is a small range of conditions over which it appears that the frequency domain kurtosis estimate has an advantage. The real data that initiated this analytical investigation are also presented.     

Asymptotic detection performance of discrete power and higher-order spectra estimates

Several detection statistics are compared in the frequency domain based on the asymptotic probability of detection (APD) criterion. They include second-order, fourth-order, normalized fourth-order, and kurtosis estimates. The results show that for randomly occurring signals which can be characterized as non-Gaussian, the fourth-order, normalized fourth-order, and kurtosis estimates can have higher asymptotic probability of detection levels compared with second-order estimates. But only for the normalized fourth-order and kurtosis estimates do the results seem significant. Moreover, if a second-order estimate of the noise is available to normalize a fourth-order estimate of signal and noise, the resultant normalized fourth-order estimate has higher asymptotic probability of detection levels even for Gaussian signals. This result holds only when there is a significant positive covariance between the numerator and the normalizing noise sample in the denominator. On the other hand, if an independent noise sample is used to normalize a second-order or fourth-order estimate, the overall performance based on the asymptotic probability of detection will be degraded compared with the unnormalized second-order or fourth-order estimates, respectively.     

Passive sonar detection and localization by matched velocityfiltering

This paper presents a new bearings-only method of detecting and tracking low signal-to-noise ratio (SNR) wideband targets on a constant course and velocity trajectory. A track-before-detect strategy based on matched velocity filtering is adopted using spatial images constructed from a sequence of power bearing map (PBM) estimates accumulated during a track. To lower the threshold SNR for detection, a discrete bank of matched velocity filters integrates the PBM images over a range of hypothesized trajectories, such an approach eliminates the need to estimate the number of targets since signal detection is determined by comparing the output of each matched filter (MF) to a decision threshold. The distribution of the MF output is derived based on a single point target in diffuse noise assumption. Receiver operating characteristic curves show a definite detection gain under low SNR conditions for matched velocity filtering (track-before-detect) over detection from a single PBM     

Optimal tonal detectors based on the power spectrum

The detection of tonals embedded in noise is an important sonar function and the traditional power spectrum analysis method has been widely used for this purpose. Wagstaff et al. (1997) proposed the WISPR (Wagstaff's Integration Silencing PRocessor) family processors, which perform a nonlinear integration or combination of the power spectrum observations. In this paper, we analyze the statistical property of the power spectrum observations and develop novel tonal detectors by optimally integrating the spectrum observations. The optimal detectors are derived by using the method of maximum likelihood hypothesis test. The results from simulations and real sea trial data have shown that the proposed detectors are promising in detecting tonals     

Ocean bottom refraction seismograph (OBRS)

This paper describes a pop-up ocean bottom seismograph designed primarily for refraction surveys both on the continental shelf and in deep sea. Its development is the extension of our system based on seismic detectors located on the sea floor with radio transmission of seismic signals and used for seismic refraction studies on the continental shelf. The seismic detectors (vertical geophone or hydrophone and two orthogonally mounted horizontal geophones) are located outside of the pressure vessel on the main frame. Optionally, the seismic sensors may be decoupled from the main frame assembly. This decoupling is performed by a mobile arm positioning the separate three component sensor package on the sea floor.Contribution No. 455 of the Département Scientifique, Centre Océanologique de Bretagne.