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1.
A submerged acoustic source radiates narrowband Gaussian noise. Its signal propagates to a remote, large aperture vertical array over a multipath channel whose characteristics may or may not be fully known. The primary concern of this study is the accuracy of source depth estimates obtainable from the array output. Cramer-Rao bounds for the depth estimate are calculated. When the velocity profile is known exactly, the value of the bound is quite insensitive to the precise form of the velocity profile. A bound calculated from a constant velocity profile yields an excellent approximation for many situations likely to be encountered in practice. Introduction of an unknown parameter into the velocity profile has little effect on the Cramer-Rao bound for depth. However, a maximum likelihood estimator of depth working with an inaccurate value of the unknown parameter performs poorly. To obtain satisfactory performance, one must estimate the unknown parameters along with the source depth. Simulations demonstrate the success of this approach  相似文献   

2.
Underwater acoustic transient signals are generated mechanically at known positions along a wharf. These signals are received by a wide aperture planar array of four underwater acoustic sensors, whose positions relative to the wharf are unknown. A method is described that enables the positions of the sensors to be estimated from accurate differential time-of-arrival measurements (with 0.1 /spl mu/s precision) as the signal wavefronts traverse the array. A comparison of the estimated positions with the nominal positions of the first three sensors, which form a 20-m-wide aperture horizontal line array, reveals a 2-cm displacement of the middle sensor from the line array axis. This slight bowing of the line array results in overranging (bias error of 3%) when the wavefront curvature method is used with the nominal collinear sensor positions to locate a static source of active sonar transmissions at a range of 59.2 m. The use of the spherical intersection method coupled with the estimated sensor positions of the line array provides an order of magnitude improvement in the range estimate (within 0.3% of the actual value). However, systematic ranging errors are observed when the sound propagation medium becomes nonstationary. Next, the differences in the arrival times of the direct path and boundary-reflected path signals at the middle sensor of the wide aperture line array are estimated using the differential phase residue of the analytic signal at the sensor output. These multipath delays are used to estimate the range and depth of the source. Although the average value of the multipath range estimates is within 0.5% of the actual value, the variance of the range estimates is 50 times larger when compared with the results of the spherical intersection and wavefront curvature methods. The multipath delay data are also processed to provide a reliable estimate of the temporal variation in the water depth enabling the tidal variation to be observed.  相似文献   

3.
We consider the role played by the sensor locations in the optimal performance of an array of acoustic vector sensors, First we derive an expression for the Cramer-Rao bound on the azimuth and elevation of a single far-field source for an arbitrary acoustic vector-sensor array in a homogeneous wholespace and show that it has a block diagonal structure, i.e., the source location parameters are uncoupled from the signal and noise strength parameters. We then derive a set of necessary and sufficient geometrical constraints for the two direction parameters, azimuth and elevation, to be uncoupled from each other. Ensuring that these parameters are uncoupled minimizes the bound and means they are the natural or “canonical” location parameters for the model. We argue that it provides a compelling array design criterion. We also consider a bound on the mean-square angular error and its asymptotic normalization, which are useful measures in three-dimensional bearing estimation problems. We derive an expression for this bound and discuss it in terms of the sensors' locations. We then show that our previously derived geometrical conditions are also sufficient to ensure that this bound is independent of azimuth. Finally, we extend those conditions to obtain a set of geometrical constraints that ensure the optimal performance is isotropic  相似文献   

4.
It is demonstrated that simple approximations are available for the Cramer-Rao lower bounds on estimates of range, bearing and frequency using a moving line array. The results are extended to include the effects of the partial coherence of the source  相似文献   

5.
6.
Various parameters associated with the track of a stable CW source moving with constant velocity are estimated using synthetic aperture and Doppler processing techniques. These include the source frequency before Doppler distortion by its motion, the relative speed between the source and a constant velocity receiver, the range at closest approach to the source track, and the relative bearing to the source. Different processing techniques are suggested for a range of signal stabilities and observation times. Frequency analysis, or Doppler processing, supplements conventional synthetic aperture processing, and for relatively unstable signals a synthetic Doppler method is recommended. This method makes use of a rapid scan of signals from a succession of sensors in a horizontal line array to stimulate a higher speed motion of the array  相似文献   

7.
This paper studies passive problems where the receiver extracts from the source radiated signature information concerning the parameters defining the relative source/receiver geometry. A model encompassing the fundamental global and local characteristics for passive positioning and navigation is presented. It considers narrow-band signals, imposes linear constraints on the geometry, and exhibits explicitly the symmetry between the space and time aspects. The analysis concentrates on questions of global geometry identifiability, emphasizing the passive global range acquisition. The maximum-likelihood processor is analyzed by studying the ambiguity structure associated with inhomogeneous passive narrowband tracking. Bounds on the global and local mean-square error performance are studied and tested via Monte Carlo simulations. By considering two limiting geometries, a distant and a close observer, simple approximate expressions for the mean-square errors are presented and compared to the exact bounds. Herein the study is restricted to stationary geometries where the source is located by an extended array (spatial diversity). Subsequent papers generalize the study to moving sources (temporal diversity) and to coupled geometries.  相似文献   

8.
The problem of source localization in shallow water in the presence of sensor location uncertainty is considered. The Cramer-Rao Bound is used to carry out a feasibility study for the joint source and sensor location problem when the multipath propagation channel is modeled as a known, deterministic waveguide. Unlike the free-space propagation channel, the boundedness of the shallow-water waveguide along its vertical axis provides the key to joint determination of the source and sensor location parameters. It is seen that, when a set of intuitive identifiability conditions are satisfied, numerical examples indicate that, for the scenarios considered, the resulting loss in accuracy with which the source location can be estimated due to sensor location uncertainty may be tolerable  相似文献   

9.
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  相似文献   

10.
The Cramer-Rao lower bounds on the cross-track translation and rotation of a displaced phase-center antenna (DPCA) in the slant range plane between two successive pings (known as DPCA sway and yaw in what follows) are computed, assuming statistically homogeneous backscatter. These bounds are validated using experimental data from a 118-182-kHz sonar, showing an accuracy of the order of 20 microns on the ping-to-ping cross-track displacements. Next, the accuracy required on the DPCA sway and yaw in order to achieve a given synthetic aperture sonar (SAS) beampattern specification, specified by the expected SAS array gain, is computed as a function of the number P of pings in the SAS. Higher accuracy is required when P increases to counter the accumulation of errors during the integration of the elementary ping-to-ping estimates: the standard deviation must decrease as P/sup -1/2/ for the DPCA sway and P/sup -3/2/ for the yaw. Finally, by combining the above results, the lower bounds on DPCA micronavigation accuracy are established. These bounds set an upper limit to the SAS length achievable in practice. The maximum gain Q in cross-range resolution achievable by a DPCA micronavigated SAS is computed as a function of the key SAS parameters. These theoretical predictions are compared with simulations and experimental results.  相似文献   

11.
This correspondence provides expressions for the Cramer-Rao lower bounds for the estimates of azimuth and elevation made with an arbitrary three-dimensional array of sensors. These results are formulated for a plane wave Gaussian signal in uncorrelated Gaussian noise. In addition, sufficient conditions on the array geometry are given which ensure that the azimuth and elevation angle estimates are uncoupled  相似文献   

12.
Although the existing array shape estimation methods using reference sources demonstrate good performance, most of the methods require at least two reference sources 2RS in known locations and the reference sources must be in far field. This communication proposes a simplified subspace fitting method that uses only a single reference source 1RS. In the proposed method, the horizontal and vertical positions of each sensor are modeled by applying fixed intersensor spacing and sensor angles, so that the unknown parameters of the cost function are reduced. Furthermore, the Cramer–Rao lower bound (CRLB) is investigated for the proposed method. The results of the numerical experiments indicate that the proposed method is practical for estimating the shape of a towed array.   相似文献   

13.
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).   相似文献   

14.
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.  相似文献   

15.
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  相似文献   

16.
From a designer viewpoint, a parametric array should not appear different from any other type of acoustic transducer and should be described by a limited set of design equations together with their range of validity. In this paper, these design equations are stated and discussed. They are used to optimize the acoustic parameters of an underwater communication system using parametric transduction and to evaluate its performance in terms of signal-to-noise ratio and data-rate limits as a function of transmission range. It turns out that, for a maximum data transmission rate at a given range, there is a set of optimum design parameters which is a function of the array size only. This means that, once given an operational range, the primary frequency, the electrical power, the maximum acoustic source level, and the directionality of the transducer can be deduced directly from the array diameter  相似文献   

17.
This paper is part of a series of three papers studying passive tracking problems arising in navigation and positioning applications. The basic question here lies with the determination of the position and dynamics of a point source being tracked by an omnidirectional observer, through demodulation of the Doppler effect induced on the radiated signals by the relative motions. A simple model, fitting a finite parameter nonlinear estimation context, is developed, the receiver designed, and its mean-square error performance studied. It is shown that, besides the speed and angle estimation, simultaneous global range passive tracking is possible. The signal model precludes range acquisition from synchronous measurement of the absolute phase reference: the global range estimation is attained by processing the higher order temporal modulations (varying Doppler). Quantifying the statistical and geometric performance tradeoffs, the work presents simple expressions and graphical displays that can be used as design tools in practical passive tracking problems. A subsequent paper considers the space/ time coupling issues, generalizing the study to the context where a moving source is tracked by a directional array.  相似文献   

18.
Spatial diversity equalization applied to underwater communications   总被引:1,自引:0,他引:1  
Underwater acoustic digital communication is difficult because of the nature of the fading multipath channels. Digital signal processing, such as adaptive equalization, is known to greatly improve the communication data rate by limiting intersymbol interference (ISI). However, existing underwater acoustic equalization studies are limited to single-channel techniques, and spatial diversity processing is limited to selection or combining. In this paper, we design minimum mean-square error (MMSE) equalizers jointly among all spatial diversity channels. We call this spatial diversity equalization (SDE). Results are based on a very sparse vertical array in a midrange underwater acoustic channel. We study the effect of element number and placement, the length of the equalization filters, and linear feedforward versus nonlinear decision feedback algorithms. A suboptimum equalizer combiner (EC) is studied to alleviate the computational intensity of JCE. We first design the system for a known acoustic channel; later, some results are verified using adaptive algorithms. Results are presented both in terms of the mean-square error (MSE) and the probability of a symbol error. The latter is important as it is the ultimate interest for a digital communication system. We found that system performance improves rapidly with an increase in the number of spatial channels  相似文献   

19.
Two adaptive algorithms for multipath time delay estimation   总被引:1,自引:0,他引:1  
The problem of time delay estimation (TDE) with multipath transmissions arises often in many sonar and radar systems. Two adaptive algorithms based on a parameter estimation approach are proposed to estimate the difference in arrival times of a signal at two separated sensors in the presence of multipath propagation. The first method uses an adaptive IIR filter to eliminate the multipath signal in each transmission channel prior to applying a constrained delay estimation algorithm to extract the time difference between the two received outputs. The second employs two constrained adaptive FIR filters to perform equalization of the multipath arrivals, and time delay is then derived using a constrained delay estimator similar to that in the first method. Computer simulations are presented to compare and contrast the tracing capability and convergence behavior of these multipath TDE methods  相似文献   

20.
A portable matched-field processing (MFP) system for tracking marine mammals is presented, constructed by attaching a set of autonomous flash-memory acoustic recorders to a rope to form a four-element vertical array, or "insta-array." The acoustic data are initially time-synchronized by performing a matched-field global inversion using acoustic data from an opportunistic source, and then by exploiting the spatial coherence of the ocean ambient noise background to measure and correct for the relative clock drift between the autonomous recorders. The technique is illustrated by using humpback whale song collected off the eastern Australian coast to synchronize the array, which is then used to track the dive profile of the whale using MFP methods. The ability to deploy autonomous instruments into arbitrary "insta-array" geometries with conventional fishing gear may permit nonintrusive array measurements in regions currently too isolated, expensive, or environmentally hostile for standard acoustic equipment  相似文献   

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