Statistical characterization of active sonar reverberation using extreme value theory

The statistics of reverberation in active sonar are characterized by non-Rayleigh distributed amplitudes in the normalized matched filter output. Unaccounted for, this property can lead to high false-alarm rates in fixed-threshold detectors. A new approach to modeling threshold-crossing statistics based on extreme value theory is proposed, which uses the generalized Pareto distribution as the unique asymptotic model of the tail distribution, valid at large thresholds. Methods of parameter estimation are discussed and applied to active sonar reverberation collected on a hull-mounted sonar system. The statistics of reverberation in active sonar are found to generally have a power-law behavior in the tails with a shape parameter that is persistent in time and bandwidth dependent. The threshold needed for accurate parameter estimation is generally found to be well below that of typical fixed-threshold detectors.     

Signal excess in K-distributed reverberation

Active sonar systems have recently been developed using larger arrays and broad-band sources to counter the detrimental effects of reverberation in shallow-water operational areas. Increasing array size and transmit waveform bandwidth improve the signal-to-noise ratio-and-reverberation power ratio (SNR) after matched filtering and beamforming by reducing the size of the range-bearing resolution cell and, thus, decreasing reverberation power levels. This can also have the adverse effect of increasing the tails of the probability density function (pdf) of the reverberation envelope, resulting in an increase in the probability of a false alarm. Using a recently developed model relating the number of scatterers in a resolution cell to a K-distributed reverberation envelope, the effect of increasing bandwidth (i.e., reducing the resolution cell size) on detection performance is examined for additive nonfluctuating and fluctuating target models. The probability of detection for the two target models is seen to be well approximated by that for a shifted gamma variate with matching moments. The approximations are then used to obtain the SNR required to meet a probability of detection and false-alarm performance specification (i.e., the detection threshold). The required SNR is then used to determine that, as long as the target and scatterers are not over-resolved, decreasing the size of the resolution cell always results in an improvement in performance. Thus, the increase in SNR obtained by increasing bandwidth outweighs the accompanying increase in false alarms resulting from heavier reverberation distribution tails for K-distributed reverberation. The amount of improvement is then quantified by the signal excess, which is seen to be as low as one decibel per doubling of bandwidth when the reverberation is severely non-Rayleigh, as opposed to the expected 3-dB gain when the reverberation is Rayleigh distributed.     

Adaptive pulselength correction (APLECORR): a strategy for waveformoptimization in ultrawideband active sonar

This paper describes adaptive pulselength correction (APLECORR), an environmentally adaptive technique for optimizing the detection performance in wide-band active sonars in so-called doubly spread channels. It works by allocating available transmit energy to frequency bands according to the in situ measured reverberation and ambient noise spectra. It optimizes the waveform and the detection processor at the same time. It is appealing in its simplicity and achieves significant gains whenever the reverberation-to-noise ratio is not constant across frequency, thus its applicability to wide-band systems. The method extends easily to PRN and other non-FM waveforms. The paper includes a proof that time spreading and frequency-spreading distortion have an approximately equivalent effect if the waveform is linear or hyperbolic frequency modulation     

Simulation of non-Rayleigh reverberation and clutter

The simulation of active sonar reverberation time series has traditionally been done using either a computationally intensive point-scatterer model or a Rayleigh-distributed reverberation-envelope model with a time-varying power level. Although adequate in scenarios where reverberation arises from a multitude of scatterers, the Rayleigh model is not representative of the target-like non-Rayleigh reverberation or clutter commonly observed with modern high-resolution sonar systems operating in shallow-water environments. In this paper, techniques for simulating non-Rayleigh reverberation are developed within the context of the finite-number-of-scatterers representation of K-distributed reverberation, which allows control of the reverberation-envelope statistics as a function of system (beamwidth and bandwidth) and environmental (scatterer density and size) parameters. To avoid the high computational effort of the point-scatterer model, reverberation is simulated at the output of the matched filter and is generated using efficient approximate methods for forming K-distributed random variables. Finite impulse response filters are used to introduce the effects of multipath propagation and the shape of the reverberation power spectrum, the latter of which requires the development of a prewarping of the K distribution parameters to control the reverberation-envelope statistics. The simulation methods presented in this paper will be useful in the testing and evaluation of active sonar signal processing algorithms, as well as for simulation-based research on the effects of the sonar system and environment on the reverberation-envelope probability density function.     

Active sonar detection in shallow water using the Page test

The use of active sonar in shallow water results in received echoes that may be considerably spread in time compared to the resolution of the transmitted waveform. The duration and structure of the spreading and the time of occurrence of the received echo are unknown without accurate knowledge of the environment and a priori information on the location and reflection properties of the target. A sequential detector based on the Page test is proposed for the detection of time-spread active sonar echoes. The detector also provides estimates of the starting and stopping times of the received echo. This signal segmentation is crucial to allow further processing such as more accurate range and bearing localization, depth localization, or classification. The detector is designed to exploit the time spreading of the received echo and is tuned as a function of range to the expected signal-to-noise ratio (SNR) as determined by the transmitted signal power, transmission loss, approximate target strength, and the estimated noise background level. The theoretical false alarm and detection performance of the proposed detector, the standard Page test, and the conventional thresholded matched filter detector are compared as a function of range, echo duration, SNR, and the mismatch between the actual and assumed SNR. The proposed detector and the standard Page test are seen to perform better than the conventional thresholded matched filter detector as soon as the received echo is minimally spread in time. The use of the proposed detector and the standard Page test in active sonar is illustrated with reverberation data containing target-like echoes from geological features, where it was seen that the proposed detector was able to suppress reverberation generated false alarms that were detected by the standard Page test     

Fast maximum likelihood estimation of signal parameters using theshape of the compressed likelihood function

A computationally efficient fast maximum-likelihood (FML) estimation scheme, which makes use of the shape of the surface of the compressed likelihood function (CLF), is proposed. The scheme uses only multiple one-dimensional searches oriented along appropriate ridges on the surface of the CLF. Simulations indicate that the performances of the proposed estimators match those of the corresponding maximum-likelihood estimators with very high probability. The approach is demonstrated by applying it to two different problems. The first problem involves the estimation of time of arrival and Doppler compression of a wideband hyperbolic frequency modulated (HFM) active sonar signal buried in reverberation. The second problem deals with estimating the frequencies of sinusoids. A threshold analysis of the proposed scheme is carried out to predict the signal-to-noise ratio (SNR) at which large estimation errors begin to occur, i.e., the threshold SNR, and its computational complexity is discussed     

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。     

Pseudorandom realization of transient acoustic waves scattered fromrandomly rough patches

A simple numerical technique is developed for generating pseudorandom realizations of three-dimensional (3-D) transient acoustic waves that are scattered from two-dimensional (2-D) patches of randomly rough surfaces. The rough surface height of a patch is represented numerically in the 2-D horizontal wavenumber plane by choosing a scheme for interpolation between pseudorandom complex coefficients. Using this approach, the realizations of the patches can be generated from experimentally measured roughness power spectra, and phase information is generated in the frequency domain that leads to time spreads in the time domain. The acoustic scattering is modeled here with first-order perturbation theory. The boundary conditions considered here are pressure-release, rigid, and fluid-fluid. Three different spatial windows are considered for defining the patches. In the time domain, the time spreads of the scattered waveforms agree with predictions. In the frequency domain, the phase is seen as a random walk. The solutions developed here can be used with normal mode propagation models or ray propagation models     

Theoretical accuracy of Doppler navigation sonars and acoustic Doppler current profilers

This paper addresses the problem of Doppler shift estimation in Doppler sonar systems. The analysis focuses on the single-beam geometry formed by a circular planar array and considers both narrow-band (or so-called incoherent) and wide-band (or coherent) Doppler sonars, transmitting, respectively, one long continuous-wave pulse and a train of short continuous-wave pulses. The correlation function of the reverberation signal at the beam output is derived for volume reverberation. Directive transmission or reception and a combination of both is considered. Estimation theory is applied to derive the Cramer-Rao bound of the Doppler parameter estimate. The effect of pulse duration, sonar geometry, beamwidth, and signal-to-noise ratio are discussed. The accuracy of coherent and incoherent systems is compared for a specific case.     

Signal recovery in a reverberation-limited environment

The problem of recovering signals masked by reverberation is considered. Reverberation data from a shallow-water active sonar experiment in conjunction with simulated echoes are used to examine the potential for signal recovery offered by adaptive filtering and prediction. The deterministic least squares lattice filter is the central adaptive estimator of choice. The prediction error lattice is used to selectively "whiten" the composite process by controlling the algorithm adaptation speed. This is shown to result in significant signal enhancement for low-Doppler echoes masked by reverberation. Adaptive noise canceling with multiple reference beams is shown to be successful in extracting even zero-Doppler echoes from the reverberation background.     

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     

An oceanic reverberation model

A simple model of the surface, volume, and bottom reverberation received by a moving platform as a function of time following the tranmission of a narrow-band pulsed signal is described. Both the time-varying power level and the underlying power spectrum are predicted. The model includes the effects of platform motion, transmit signal windowing, transmit and receive beam patterns, and the environment (surface, volume, and bottom backscattering strengths, the scatterer velocity distributions for surface waves and current layers, and sound absorption). An isospeed sound speed profile is assumed and reflections at the surface and bottom boundaries are not permitted. Also described is a matched filter-envelope detector receiver model for post processing of the reverberation spectra.     

A model/data comparison for shallow-water reverberation

A bottom-scattering model based on sediment small scatterers, single scattering approximation is presented, which is combined with a normal-mode-based reverberation model. The combined model (for total reverberation) is compared with measurements of shallow-water reverberation from the 2001 Asian Sea International Acoustic Experiment (ASIAEX) in the East China Sea. Reverberation intensities as a function of time and frequency are compared with theoretical predictions with reasonable agreement. The effects of the rough sea surface on the reverberation are also discussed.     

神舟四号高度计波形数据预处理和信息提取

神舟四号(SZ-4)高度计在国内首次提供了星载雷达高度计回波波形数据.本文中作者分析了SZ-4高度计回波波形的特点,完成波形数据的预处理,并在此基础上完成初步的信息提取.在数据预处理方面,通过SZ-4高度计水陆边界处波形的特点,提出了波形最大幅度控制的方法,筛选回波波形.在波形归一化处理过程中,发现SZ-4高度计波形中存在双峰现象,并指出第二个峰为异常波形区.在波形信息提取方面,利用波形重新跟踪得到的半功率点计算出SZ-4高度计高度跟踪补偿误差,并根据高度计天线指向角和回波波形下降沿斜率之间的关系,从波形后沿提取天线指向角信息.分析结果表明,SZ-4高度计天线指向比较平稳,而跟踪补偿由于变化较大,在计算海面高度时,应作为一项误差源被考虑到.     

A low sidelobe technique for the direct measurement of scatteringfunctions

Effective communication and echolocation depends strongly upon the coherence of the channel through which the signal is propagated. Under certain conditions, the average coherence or equivalently, the spreading of a random channel may be described by a scattering function (SF). This represents a second order (energy) measure of the average delay, Doppler, and more generally, the spatial (azimuthal) spread that the signal experiences. The SF is analogous to the point spread function (PSF) discussed in the image processing literature and likewise describes the amount of “blurring” imposed upon the signal or scene transmitted. The SF will be briefly reviewed and its measurement by both direct (high resolution channel probing) and indirect (deconvolution) methods will be discussed. A new direct method using specially designed waveform pairs and a twin or uncertainty product (UP) receiver structure is introduced. Unlike high resolution matched filter implementations for direct probing that are limited by the fixed volume constraint of ambiguity functions, the UP receiver produces vanishing sidelobes and hence more nearly approximates a desirable two-dimensional delta characteristic. The improvement gained in SF measurement is illustrated by the results of an experiment in which the UP receiver and traditional matched filter implementations were used to directly probe an ocean multipath channel     

A model for numerical simulation of nonstationary sonar reverberation using linear spectral prediction

An innovative approach to the numerical generation of nonstationery reverberation time series is presented and demonstrated. The computer simulated reverberation time series are of high quality, in that they are accurate representations of those which would result from an actual sonar system (transmit/receive and horizontal/ vertical beampatterns; pulse type, shape, length, and power; frequency and sampling rate), platform (speed and depth), and environment (wind speed and direction, backscattering strengths, and propagation loss). Volume, surface, and/or bottom reverberation as seen by a multiple beam sonar on a moving platform is generated. The approach utilizes recent developments in linear spectral prediction research in which the spectra of stochastic processes are modeled as rational functions and algorithms are used to efficiently compute optimal estimates of coefficients which specify the spectra. A two-fold sequence is formulated; first, the expected reverberation spectra for all beams are predicted and, second, the stochastic time series are generated from the expected spectra. The expected spectra are predicted using a numerical implementation, referred to as the REVSPEC (reverberation spectrum) model, of a general formulation of Faure, Ol'shevskii, and Middleton. Given the spectra, the Levinson-Durbin method is used to solve the Yule-Walker equations of the autoregressive formulation of linear spectral prediction. The numerical implementation of the approach, referred to as the REVSIM (reverberation simulation) model, produces nonstationary coherent multiple-beam reverberation time series. The formulation of the REVSIM model is presented and typical results given. A comparison is made between the simulation outputs of the REVSIM model and those of the REVGEN (reverberation generator) model, a standard well-accepted time series simulation model, to demonstrate the validity of the new approach.     

General motion estimation from correlation sonar

The displacement of a sonar array can be estimated accurately using the correlation of bottom reverberation signals, at successive sweeps. This is the principle of the pulsed correlation log. In this paper, the conditions and accuracy of array horizontal translation estimation are analyzed. The case of a three-dimensional array is considered first, to show that in this case arbitrary translation and rotation can be estimated. The case of a plane array is then analyzed and it is shown that such an array allows estimation of horizontal translation. The derivation relies on modeling the space-time correlation function of bottom reverberation, which is assumed isotropic. Both directive and omnidirectional transmissions are considered. Accuracy of displacement estimates are derived, showing the influence of wavelength, grazing angle, bandwidth, number of overlapping hydrophones, and reverberation-to-noise ratio     

A Subwaveform-Based Retracker for Multipeak Waveforms: A Case Study over Ukai Dam/Reservoir

Retracking altimeter waveforms over inland water bodies is a challenging task as a wide range of waveform is encountered while the retracking algorithms are available only for a handful of echo shapes. One such waveform shape widely encountered in lakes and reservoirs is the multipeak echo. These echoes are produced when the interacting surface in the altimeter footprint is not homogeneous and a number of different types of surfaces contribute to the resulting waveform. The widely used conventional retrackers, namely the Brown, Beta-5, Ice-2, OCOG, and threshold, can retrack a number of different waveform shapes such as the Brown like waveforms, specular waveforms, and rectangular waveforms but may not perform well for multipeak waveforms. In this article, a technique has been demonstrated to identify the different subwaveforms within a multipeak waveform and identify the subwaveform corresponding to the target at nadir. The subwaveform that is reflected from the nadir surface is identified from apriory information about the surface topography of the area. The subwaveform is then retracked using the 50% threshold to find the correct retracked range and water height. This technique has been tested for nine cycles of SARAL SIGDR data on Ukai reservoir, Gujarat, India, and found to perform much better than the other retrackers, particularly for multipeak waveforms.     

Statistics of broad-band bottom reverberation predictions in shallow-water waveguides

A new coherent reverberation model developed at the Naval Research Laboratory, Washington, DC, and the Supreme Allied Commander Atlantic Undersea Research Centre, La Spezia, Italy, is exercised in the 17-750-Hz band to estimate the degree of non-Rayleighness of shallow-water reverberation envelopes as a function of waveguide multipath, system bandwidth, directivity, and frequency. Findings suggest that reverberation from diffuse, but non-Gaussian, scatterer distributions is significantly more Rayleigh for multipath environments than for equivalent environments excited by a single or small number of modes or for broadside receiver array processing that extracts narrow angles of reception. These findings suggest that the problem of non-Rayleigh reverberation in shallow-water waveguides can be ameliorated through the use of tuned ensonification and reception schemes, which retain high probabilities of detection while reducing the associated probability of false alarm.