Towed array shape estimation using Kalman filters-theoreticalmodels

The dynamical behavior of a thin flexible array towed through the water is described by the Paidoussis equation. By discretizing this equation in space and time a finite-dimensional state-space representation is obtained where the states are the transverse displacements of the array from linearity in either the horizontal or vertical plane. The form of the transition matrix in the state-space representation describes the propagation of transverse displacements down the array. The outputs of depth sensors and compasses located along the array are shown to be related in a simple, linear manner to the states. From this state-space representation a Kalman filter which recursively estimates the transverse displacements and hence the array shape is derived. It is shown how the properties of the Kalman filter reflect the physics of the propagation of motion down the array. Solutions of the Riccati equation are used to predict the mean square error of the Kalman filter estimates of the transverse displacements     

Vibration induced in towed linear underwater array cables

Towed linear arrays of hydrophones are used in various applications, for example, seismic prospecting. Tow cable vibration is capable of causing output in the towed array system. Since one of the factors limiting acoustic sensitivity is self-noise, the general objective of this analysis is to investigate the nature of longitudinal and transverse cable vibrations, with the aim of minimizing vibration transmitted to the array. The equations of transverse cable motion are derived and solved for a single-póint excitation and for distributed-vortex excitation. The response to vortex-shedding excitation along the first 150 ft of array-end cable is quantitatively evaluated and compared with actual tow-trial measurements. Two types of longitudinal vibration are analyzed, one caused by direct excitation along the cable axis, and one caused indirectly by transverse cable vibration. Fluid drag and hysteretic damping are included in the analysis.     

波浪作用下缆船拖带系统非线性运动数值模拟

基于船舶操纵性运动方程和拖缆的三维动力学运动方程,提出了被拖点位置匹配的方法,建立了拖船—拖缆—被拖船系统整体非线性拖带动力学模型。为了考察被拖船航向稳定性与横向稳性的关系以及波浪载荷作用的影响,被拖船采用水平面四自由度运动方程,并引入了波浪的作用力和力矩。拖船采用PD控制方法较真实地模拟了拖船航向改变的运动过程。对一个拖船—拖缆—被拖船系统(5 000 t的拖船和3 000 t的被拖船)在时域内进行了规则波浪作用下拖带运动的模拟,计算结果表明被拖带船舶在波浪中运动呈现运动稳定、不稳定和临界状态3种可能的特性。根据模拟计算结果,认为波浪中拖带航向稳定是被拖带船舶保持稳性的必要条件。     

Performance comparison between vertical and horizontal arrays for geoacoustic inversion

Most of the research on model-based geoacoustic inversion techniques has concentrated on data collected using moored vertical receiver arrays. However, there are many advantages to considering geoacoustic inversion using a towed horizontal array. Towed arrays are easily deployed from a moving platform; this mobility makes them well suited for surveying large areas for sea-bed properties. Further, if a model-based geoacoustic inversion scheme uses both a towed source and array, the separation between the two can be kept short, which reduces the requirement for range-dependent modeling. Range-independent modeling is used for inverting all the horizontal array data considered in this paper. Using the Inversion Techniques Workshop Benchmark Test Cases, the performance of a horizontal (simulated towed) and vertical arrays are compared and found to be very similar. However, it will be shown that, for Benchmark Test Case 3, where the bathymetry is flat and a hidden bottom intrusion exists, a towed horizontal array is ideal for determining the range-dependent sea-bed properties. The practical advantages of using a towed array are clear and the purpose of this paper is to show that the performance is similar (and in some cases better) than using moored vertical arrays.     

Towed array shape estimation using Kalman filters-experimentalinvestigations

The problem of estimating the shape of a towed array instrumented with either depth sensors, compasses, or both in a discrete-time state-space formulation is treated in a companion paper by D. A. Gray et al. (to appear), in which the state-space representation is derived from a dynamical model of the propagation of tow-point-induced motion down the array. A Kalman filter is derived to recursively estimate the shape of this towed array, and solutions to the Riccati equation are used to predict the mean square error of the Kalman filter array shape estimates. The present study investigates the performance of this Kalman filter approach as an array shape estimator using both simulated examples and sea trial data. Fundamental to the Kalman filter approach is the model that describes the dynamical behavior of the towed array. The results of an experimental program that was undertaken to validate this model are also presented     

Combined Geoacoustic Inversion of Propagation and Reverberation Data

Sonar performance predictions in shallow water are strongly dependent on good knowledge of the geoacoustic and scattering properties of the seabed. One technique to extract information about the bottom is to use a towed source and a towed horizontal array. This towed system has been shown to be applicable for characterizing the bottom properties locally by inversion of the acoustic signals received directly on the towed array at short ranges. The same towed system has also been applied to extract bottom properties from long-range reverberation data providing effective bottom properties over a large area. However, independent geoacoustic inversion of the short-range propagation and long-range reverberation data can introduce low sensitivity and uncertainty in the extracted bottom properties. An attempt to resolve this low sensitivity and ambiguity is made by a simultaneous geoacoustic inversion of short-range propagation and long-range reverberation data with the intention of constraining the possible solutions of the bottom properties.      

主动式声纳列阵拖曳系统姿态数值计算

主动式声纳列阵拖曳系统是用于探测潜艇的新型声纳系统，为了准确探测潜艇的位置，必须首先预报声纳列阵的瓷态，本文通过对其三维力学模型的分析，得到该系统的运动微分方程，其中缆索的力学方程是基于Ablow和Milinazzo的模型，而对于拖体则运用六自由度空间运动方程模拟，结合边界条件，用有限差分法求解，通过对拖船的不同运动状态如匀速，变速和回转的计算，证明本文的方法对于预报声纳列阵的姿态是有效的。     

Temporal domain processing for a synthetic aperture array

A method for the synthesis of an aperture with improved bearing resolution and signal gain is described. The proposed method temporally synthesizes data from an overlap correlator, which is obtained by aperture domain averaging of phase differences. Previous studies, such as extended towed array measurements (ETAM), had a restriction in that the overlapped hydrophones between successive measurements of a towed array were required to have identical positions in space. In this paper, however, it is shown that the phase correction factors can be estimated without restriction on the positions of the overlapped hydrophones. This implies that the proposed method is able to utilize more snapshots to extend the towed array. Simulation results showed that the proposed method resulted in higher estimation accuracy than ETAM. In addition, the effects of coherency and other systematic errors on the proposed method were examined     

Time-domain geoacoustic inversion of high-frequency chirp signal from a simple towed system

An inversion method using a towed system consisting of a source and two receivers is presented. High-frequency chirp signals that have been emitted from the source are received after multiple penetrations and reflections from the shallow water sub-bottom structure and are processed for geoacoustical parameter estimation. The data are processed such that a good resolution and robustness is achieved via matched filtering, which requires information about the source signal. The inversion is formulated as an optimization problem, which maximizes the cost function defined as a normalized correlation between the measured and modeled signals directly in the time domain. The very fast simulated reannealing optimization method is applied to the global search problem. The modeled time signal is obtained using a ray approach. An experiment was carried out in the Mediterranean Sea using a towed source and receiver system. The inversion method is applied to the experimental data and results are found to be consistent with previous frequency-domain analyses using measurements from a towed horizontal array of receivers and measurements on a vertical array.     

拖曳线列阵声纳中隔振模块研究

介绍了作为隔振模块研究依据的拖缆抖动特性的试验研究结果及隔振模块理论分析方法 ,给出了隔振模块有关参数变化对隔振量影响的理论值 ,提供了隔振模块隔振量试验方法 ,某隔振模块隔振量的测量结果以及装与不装隔振模块情况下 ,声阵的拖曳噪声声压谱级的测量结果     

On the ability to estimate narrow-band signal parameters usingtowed arrays

Using the Cramer-Rao lower bound (CRLB) as an indicator of potential performance, the limits on the estimation and resolution capabilities of a towed line array of uniformly spaced hydrophones to provide frequency and bearing information about narrowband signals are examined. It is assumed that a monochromatic plane wave arrives at the array for each source. Several versions of the bounds are computed using different assumptions about which parameters have known values and about the way in which the samples are taken in space and in time. It is shown that the CRLB values for different situations can be compared to provide information about the effective use of a moving aperture for estimation of the parameters of narrowband signals arriving at the array. It is also shown that adding at least one hydrophone occupying a fixed position in space can improve the bearing estimates of a towed array by supplying additional frequency information if both the bearings and frequencies of the sources are unknown     

A computerized system for assessing towed array sonar functionalityand detecting faults

A computer-based system that processes hydrophone and beam noise data from a towed horizontal line array sonar has been developed. The system also produces various displays that can be used to help assess the functionality of the sonar and to identify faults that cause degraded performance. The system-and various statistics used for characterizing or quantifying a given aspect of the sonar's performance are discussed. The results are presented in visual formats to aid in rapid assessment and quantification of the sonar's performance. Examples obtained from the system during recent towed array ambient noise measurement exercises are given to illustrate its utility for real-time performance monitoring and its capability for providing clues to aid in fault localization     

A metamodel-based towed system simulation

The objective of this exercise was the development of a computer simulation of a US Navy towed system (towed body and line array) capable of near real-time predictive capabilities. The purpose of the computer simulation was to be able to determine the lateral motion of the towed body in response to ship maneuvers. The theoretical approach was to develop a spatial-domain computer simulation of each of the towed system components treated as a system, and then develop a “metamodel” of the response by using simple algebraic expressions. At-sea trials were conducted aboard US Navy vessels to verify the simulation and fine-tune its performance.     

规则波作用下水下拖缆数值分析研究

研究了水面波浪对水下拖缆的干扰。首先基于集中质量法给出了三维非均匀拖缆在规则波作用下的数学模型,然后通过四阶龙格库塔方法进行数值求解,并根据仿真计算讨论了拖缆在不同波浪作用下的稳态响应特性。仿真结果表明,水下拖缆在规则波的作用下,不仅作近似的简谐振动,还会在横向、垂向产生一个偏移量,且随浪向角的变化呈现不同的响应特征。     

Measurement of towed array position, shape, and attitude

A practical method is described for the three-dimensional determination of the position, shape, and attitude of a hydrophone array towed from a surface vessel. It provides successive snapshots of the array configuration with a maximum rate of about three per minute. The method is intended as an alternative to the use of fixed test ranges and provides results suitable for validating computer models of array motion. It uses the travel-time differences of impulsive waves measured across the array. The waves are generated by two explosive charges dropped from consorts. Results of a typical experiment are presented as an illustrative example. The array position relative to the tow ship is obtained to within an accuracy of a few metres     

Methods of array element localization for a towed underwateracoustic array

The location of the hydrophones on a towed underwater acoustic array as a function of time (array element localization) is needed for signal processing. Methods to perform this localization using least squares polynomial fitting to data from depth sensors, heading sensors, and sensors detecting a ping from a single source are discussed. Arc distance along the array is used as the independent parameter so that all solutions are constrained to be space curves. Examples of application to real data are presented, and techniques to discriminate against bad sensor data are discussed     

Measurements of the wall pressure spectra on a full-scale experimental towed array

Turbulent wall pressure data acquired during tests of a full-scale experimental towed array over a range of tow speeds in straight tows and turns is presented. The experimental towed array contained a linear array of sensors mounted at the fluid–solid interface to measure the spectra of the wall pressure fluctuations due to the cylindrical turbulent boundary layer. The physics are dominated by the growth of a thick, high Reynolds number turbulent boundary layer at arc length Reynolds numbers as high as 9×10⁸. The measured wavenumber-frequency spectra, autospectra, cross-spectral decay and convection velocities are presented. A well-defined convective ridge exists in the wavenumber-frequency spectra obtained during straight tows and turns. Turns give rise to a complicated fluid–structure interaction problem, but do not lead to the separation of the turbulent boundary layer. As the array moves through a turn, flow-induced vibrations of the array are shown to dominate the spectra at low frequencies, with more rapid decay in the measured coherence occurring at higher frequencies. The use of tow speed as a velocity scale is shown to collapse autospectra and convection velocities.     

Towed-array history, 1917-2003

Towed-array research and development over 86 years is examined from the inventions of Dr. H. C. Hayes during World War I to multiple arrays towed by oil exploration ships in 2003. Time lines of the effort over the years are presented for array applications to military surface ships, submarines, and for oil exploration efforts. Military surface ship towed-array systems from the Hayes electric eel effort to the SQR-14, SURTASS, ETASS, and APL/Johns Hopkins dual towed arrays are reviewed. Submarine towed-array programs from the early 1960s to today are described and a prediction of future towed-array development is presented.     

The maximum likelihood estimator for acoustic synthetic apertureprocessing

The maximum likelihood estimator of source amplitude, bearing, and frequency for a moving towed line array of equispaced elements is discussed. A two-dimensional search in equivalent phase and frequency variables is found to yield the best estimates of the unknown parameters. Application to a physical experiment and comparison with the Cramer-Rao bound verify the unity of the approach     

Geoacoustic Information Content of Horizontal Line Array Data

This paper examines the effectiveness of horizontal line arrays (HLAs) for matched-field inversion (MFI) by quantifying geoacoustic information content for a variety of experiment and array factors, including array length and number of sensors, source range and bearing, source-frequency content, and signal-to-noise ratio (SNR). Emphasis is on bottom-moored arrays, while towed arrays are also considered, and a comparison with vertical line array (VLA) performance is made. The geoacoustic information content is quantified in terms of marginal posterior probability distributions (PPDs) for model parameters estimated using a fast Gibbs sampler approach to Bayesian inversion. This produces an absolute, quantitative estimate of the geoacoustic parameter uncertainties which can be directly compared for various experiment and array factors.