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.     

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.     

Ocean effects on time delay estimation requiring adaptation

In active sonar and in passive sonar localization, time delay is a fundamental parameter whose extraction is vital to the sonar function. The underlying time delay parameter (or parameter vector) contains information about the acoustic source (or reflector) as seen through the ocean at a receiver. The ocean effects require sonar adaptation. A tutorial review of ocean effects in time delay estimation is provided, with references to benchmark work. It covers coherence, time-delay estimation, localization, time-varying time delay estimation, the complexity of the ocean environment, and depth estimation using mode matching     

"Principal component inverse" algorithm for detection in thepresence of reverberation

Detection in the presence of reverberation is often difficult in active sonar, due to the reflection/diffusion/diffraction of the transmitted signal by the ocean surface, ground, and volume. A modelization of reverberation is often used to improve detection because classical algorithms are inefficient. A commonly used reverberation model is colored and nonstationary noise. This model leads to elaborate detection algorithms which normalize and whiten reverberation. In this paper, we focus on a more deterministic model which considers reverberation as a sum of echoes issued from the transmitted signal. The Principal Component Inverse (PCI) algorithm is used with this model to estimate and delete the reverberation echoes. A rank analysis of the observation matrix shows that PCI is efficient in this configuration under some conditions, such as when the transmitted signal is Frequency Modulated. Both methods are validated with real sonar surface reverberation noise. We show that whitening has poor performance when reverberation and target echo have the same properties, while PCI maintains the same performance whatever the reverberation characteristics. Further, we extend the algorithms to spatio-temporal data. We propose a new algorithm for PCI which allows better echo separation. This new method is shown to be more efficient on real spatio-temporal data     

Enhanced Kalman Filter Algorithm Using the Invariance Principle

Target tracking in multistatic active sonar systems is often limited in shallow-water environments due to the high level of bottom reverberation that produces false detections. Past research has shown that these false alarms may be mitigated when complete knowledge of the environment is available for discrimination, but these methods are not robust to environmental uncertainty. Recent work has demonstrated the existence of a waveguide invariant for active sonar geometries. Since this parameter is independent of specifics of the environment, it may be used when the environment is poorly known. In this paper, the invariance extended Kalman filter (IEKF) is proposed as a new tracking algorithm that incorporates dynamic frequency information in the state vector and uses the invariance relation to improve tracker discrimination. IEKF performance is quantified with both simulated and experimental sonar data and results show that the IEKF tracks the target better than the conventional extended Kalman filter (CEKF) in the presence of false detections.      

Using McDaniel's model to represent non-Rayleigh reverberation

Reverberation in low-frequency active sonar systems operating in shallow water has often been observed to follow non-Rayleigh statistical distributions. McDaniel's model, generalized to allow noninteger valued parameters, has shown promise as being capable of accurately representing real data with a minimal parameterization. This paper first derives an exact analytical expression for the cumulative distribution function (CDF) of the generalized McDaniel model and then compares it with numerical inversion of the characteristic function. Both methods are seen to provide adequate and equivalent precision; however the characteristic function inversion method is significantly faster. The latter CDF evaluation technique is then applied to the analysis of simulated and real data to show that, when minimal data are available, McDaniel's model can more accurately represent a wide variety of non-Rayleigh reverberation than the K or Rayleigh mixture models. This result arises from the generality of McDaniel's model with respect to the K-distribution (i.e., the K-distribution P_fa estimate can be dominated by model mismatch error) and to its compact parameterization with respect to the Rayleigh mixture (i.e., the Rayleigh mixture model P_fa estimate is usually dominated by parameter estimation error)     

Morphological and statistical approaches to improve detection in the presence of reverberation

The detection of a target echo in a sonar image is usually a difficult task since the reverberation, consisting of a large number of spurious echoes, generates a lot of false alarms. In this paper, we propose two new detectors derived from image processing algorithms. These detectors are respectively based on a morphological and a statistical contrast. Each detector only requires setting a few parameters. This setting is done using some prior knowledge about the data (shape of the emitted signal and the used antenna, characteristics of the reverberation). Nevertheless, an extensive statistical study of the detection performances proves that the proposed methods are robust and that even an imprecise setting of the parameters leads to satisfactory results. Applied to the real data, these detectors and their sequential combination lead to a significant improvement on the performances: The false alarm rate is drastically reduced while the detection probability is preserved. Based on different contrasts, these detectors have complementary behaviors. Therefore, a further improvement is achieved by a fusion of the different results to classify the remaining echoes as whether spurious or true detection.     

The Impact of Multipath on High-Resolution SAS Image Statistics

As with traditional sonar, synthetic aperture sonar (SAS) is susceptible to multipath contamination, reducing the quality and also modifying the statistics of the image. Such multipath contaminants may either be environmentally induced, as is often the case when attempting to image ranges greater than the water depth resulting in returns from the boundaries, or may be induced by the system's supporting structure itself. A clear understanding of such statistical impact is necessary to advance synthetic aperture formation algorithms and for predicting system performance. Broadband acoustic data suitable for SAS processing collected with a rail-mounted mobile-tower as part of the U.S. Office of Naval Research (ONR)-funded Sediment Acoustics eXperiment 2004 (SAX04) are analyzed in this paper. Analysis focused on both system structure and environmentally induced multipath using the $K$ -distribution shape parameter as a metric. High-resolution sonar imagery often exhibited significantly non-Rayleigh, heavy-tailed envelope statistics, characterized by a low equivalent $K$-distribution shape parameter. Analysis showed a clear and significant increase in the estimated shape parameter in the presence of multipath, representing a trend toward a Rayleigh-distributed envelope. A model for reverberation is presented to provide bounds of the statistical impact using observable image intensity level increases in synthetic-aperture-formed images caused by multipath contamination. This model further shows potential for statistical impact when multipath arrivals are of similar level as the direct path even when not observable in the image (e.g., within 10 dB).      

声相关海流剖面仪测速研究

声相关海流剖面仪(ACCP)适合深海测速,能够测得相对海底的绝对速度。文章在前人工作基础上,以声纳方程为基础,构造海底混响回波仿真模型,并对基于K irchhoff近似和利用微扰法的R ay le igh-R ice近似相结合的散射模型赋予新的物理意义,并将其应用到声相关测速仿真研究过程中,使仿真更加接近于海洋的实际环境。文章利用H ilbert变换进行包络检波来减小测速误差,并且根据接收信噪比得到了不同航速时能够达到最大底跟踪的距离,这与参考文献给出的结果是一致的。     

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     

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.     

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     

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     

High-frequency reverberation in shallow water

Monostatic reverberation measurements were collected in shallow water, over a coarse gravel and cobble bottom, 100 m deep, off the coast of Nova Scotia. Data were collected at frequencies of 21, 28, and 36 kHz using linear FM pulses of 2-kHz bandwidth and 0.160-s duration. An anchored, high-frequency active sonar array deployed at a depth of 42 m was used to collect the data. The reverberation measurements were compared with estimates computed with the NUWC generic sonar model (GSM). The data were reasonably well modeled for times greater than 0.2 s after pulse transmission by neglecting surface reverberation and using Lambert's rule for bottom backscattering with a scattering coefficient of -27 dB, independent of frequency. At all three frequencies, the data and model show a peak approximately 0.9 s after pulse transmission. This peak results from a focusing effect that the downward-refracting sound-speed profile has on the interaction of the rays with the bottom     

The Effect of Multipath on the Envelope Statistics of Bottom Clutter

Active sonar systems operating in shallow-water environments are often faced with high numbers of false alarms, generically referred to as clutter, arising from among other sources bottom scattering that results in heavy tails in the matched filter envelope probability density function compared with the Rayleigh distribution. In this paper, the effect of multipath propagation on the envelope statistics (i.e., the disparity from the Rayleigh distribution) is modeled through the use of the -distribution where the shape and scale parameters are formed from the autocorrelation function of the transmit waveform, the multipath structure, and the strength and spatial density of the bottom scatterers. Use of the -distribution is justified by showing that it is the limiting distribution of the sum of independent but not identically distributed -distributed random variables, which is representative of multipath when the bottom produces -distributed backscatter. The shape parameter, which drives the clutter statistics, is seen to be inversely proportional to bandwidth at bandwidths low enough that the multipath is not resolved and again at bandwidths high enough that all of the paths are resolved. As has been previously reported by LePage [IEEE J. Ocean. Eng., vol. 29, no. 2, pp. 330-346, 2004], multipath is shown to make clutter statistics more Rayleigh-like, which in this analysis equates to an increase in the -distribution shape parameter. The model is used to evaluate the effect on clutter statistics of varying environmental characterizations and system configurations where it is seen that, for a constant sound-speed profile, increasing the vertical aperture of the sonar, the center frequency, or surface roughness can lead to less multipath and, therefore, a reduction in the -distribution shape parameter and an increase in the probability of false alarm.     

Closed form bistatic reverberation and target echoes with variable bathymetry and sound speed

Some existing closed-form expressions for target echo and reverberation, assuming classical mode-stripping and Lambert's law in isovelocity water, are extended to the case of uniform slope bathymetry combined with range-independent linear sound speed and bistatic geometry. The analytical, or extremely fast numerical, calculation of signal-to-reverberation-ratio provides insight useful for sonar design, and operational research. There are three types of path, each of which may be important at some range: Those that only interact with one boundary, those that always interact with both boundaries and those that sometimes interact with both. Each provides a separate closed-form contribution. The earlier finding, that with Lambert's law the reverberation tends to follow the same range trend as the target echo, is slightly modified by the addition of refraction. The stronger reverberation from the low sound speed side of the duct tends to fall off slightly less slowly than the target echo according to the strength of the refraction. Some graphical examples show that the very large parameter space can be handled very easily.     

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.