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.     

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)     

Statistical normalization of spherically invariant non-Gaussian clutter

Conventional detection in active sonar involves comparing the normalized matched filter output power to a fixed preset threshold. Threshold crossings from contacts of interest are labeled as detections and those from undesired clutter echoes as false alarms. To maintain a constant false-alarm rate (CFAR) in the presence of strong transient clutter, the system can either increase the threshold or apply some function that suppresses this background down to an acceptable level. The latter approach leads to a more consistent background on the display, which enables operator-assisted detection. Background clutter suppression should not come at the expense of contact detection; to maximize the probability of detection (PD) for a given probability of false alarm (PFA), the likelihood ratio test (LRT) is used. However, the LRT does not address display issues, since the threshold that achieves a desired PFA varies with the input distribution. Ideally, the LRT output is monotonically transformed using a "statistical normalizer" (SN) that returns a consistent CFAR background without degrading the optimized PD. Within the radar community, clutter suppression is proposed using a LRT tuned to a K-distributed spherically invariant random vector (SIRV) model. However, this model does not lend itself to SN, as a closed-form expression for the LRT output density does not exist. In contrast, the proposed SIRV clutter model, with Pareto distributed power, leads to a closed-form density from which the SN function is readily derived. This combined Pareto-LRT/SN detector nearly matches the optimized PD performance of the K-distributed LRT and maintains a consistent CFAR background for display purposes.     

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.     

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).      

"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     

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.     

Mine avoidance techniques for underwater vehicles

It is shown that by implementing certain mine avoidance techniques, an underwater vehicle equipped with an obstacle avoidance sonar (OAS) and a navigation system can safely navigate an unknown minefield. The mine avoidance techniques take into account the physical limitations of the sonar and the navigation system, the maneuverability constraints on the underwater vehicle, and the required safe standoff distance from all mines. Extensive computer simulations have verified the mine avoidance capability in more than 50 different minefields. In all 50 simulations the vehicle reached a predetermined end point and maintained at least the specified, minimum safe standoff distance from each mine. The simulation accurately models the major difficulties associated with the sonar, the navigation system, and the vehicle dynamics. The sonar model includes surface, bottom, and volume reverberation; thermal, ambient, and flow noises; actual receiver and projector beam patterns; and false alarms and missed detections. The navigation system model contains the effects of biases, random noises, and scale factor errors. The vehicle dynamic model simulates angular velocities and accelerations associated with underwater vehicles     

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     

Measurements and modeling of low-frequency near-surface scattering statistics

High-resolution acoustic measurements of low-frequency near-surface backscattering at low grazing angles have been made in the open ocean using vertical arrays of coherent sources. Over the range of wind speeds (4-18 m/s) encountered, the normalized data amplitudes exhibited variable non-Rayleigh behavior, from near Rayleigh in the highest sea states to near lognormal in low-to-moderate sea states. Seven probability density function (pdf) models were fit to the data, with the three-component Rayleigh mixture providing the most consistent fits and the least errors. One pdf model, the Poisson-Rayleigh, provided not only good fits to many data sets, but also physical insights into the scattering process. This model's estimates of the expected number of discrete scatterers ranged from 200/km/sup 2/ at low wind speeds to 2000/km/sup 2/ at high wind speeds, consistent with the expected densities of fish and subsurface bubble clouds, respectively. These results are encouraging with regard to developing physical models capable of using local results (such as these) to accurately predict long-range reverberation and clutter statistics.     

主动声纳探测效能评估的HMG法

海洋水声环境时空变化显著,评估其对主动声纳探测效能的影响具有重要的理论意义和应用价值。提出HMG方法用以评估水声环境效应对主动声纳探测的影响。采用UMPE(The university of miami parabolic equation)、CANARY、JACKSON模型模拟特定海洋环境下的传播损失、环境噪声、混响分布,将模拟结果融入主动声纳检测概率模型,计算检测概率。评估结果发现近场检测概率较高,远场可检测的区域与声能汇聚区一致。     

Reverberation fluctuations from a smooth seafloor

High-frequency shallow-water reverberation statistics were measured from a smooth, sandy, featureless seafloor. The reverberation statistics are presented as a function of source frequency (20-180 kHz), grazing angle (30°, 20°, 9.5°), and source beamwidths (1.2°-2.75°). Generally, the reverberation statistics did not follow a Rayleigh fading model. The model dependence of the reverberation statistics exhibited a complex behavior that ranged from near Gaussian to beyond log-normal. The results show that small changes in the source frequency, grazing angles, and beamwidths caused large variations in the model dependence of the reverberation statistics     

Seafloor profiling by a wideband sonar: simulation,frequency-response optimization, and results of a brief sea test

An ahead-looking probe of some kind, optical or acoustic, is critical when one is attempting seafloor exploration from a mobile platform. A single-frequency, split aperture sonar system can be used for this purpose, but a wideband monopulse sonar offers many advantages. It computes a running estimate of the vertical directional cosine of the source of the echo, and can thus reveal the positions of multiple wave scatterers as long as their echoes can still be time resolved. Theoretical studies of its performance have been made previously, but were directly applicable only to extremely simple seafloor geometries. A new time-domain digital simulation that largely circumvents this limitation has been developed. The simulation also provides a means for testing the theory and optimizing system parameters. The reverberation model does not account for some features of acoustic backscattering such as diffraction, but it is believed to be adequate for the investigation of most signal processing aspects of the sonar system. The theory of the simulation is developed and several examples are presented and discussed. In addition, some preliminary results are presented from a sea test that used the air-sea interface as a surrogate seafloor     

多波束测深海底混响仿真研究

海底混响是海洋混响的重要组成部分,采用模拟仿真进行验证分析,是仿真技术的一项重要应用。采用单元散射模型,研究在单发射阵元下,分布在同一直线上多个接收阵元接收的海底回波,忽略声波传播的相位起伏,只考虑振幅起伏,将传播损失、声吸收系数、海底反射损失、海底沉积层密度等参数带入海底混响仿真数学模型,仿真海底混响,使其更加接近海底的实际情况。     

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。     

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     

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.