Array Shape Estimation Research Articles

Signals-of-Opportunity-Based Hydrophone Array Shape and Orientation Estimation

Signals-of-Opportunity-Based Hydrophone Array Shape and Orientation Estimation

Differentiable beamforming for adaptive ultrasound imaging

Differentiable beamforming (DB) is a powerful new approach to image reconstruction that optimizes the beamforming algorithm to the given imaging target via autodifferentiation. In DB, the beamformer is expressed as a function of some unknown parameters, e.g., the sound speed throughout the medium, the shape of a flexible transducer, or the position and orientation of a swept transducer. Gradient descent is then used to find the parameters that optimize the focusing quality of the beamformer. With the appropriate choice of focusing criterion, the optimal beamforming parameters coincide with the ground truth. We demonstrate DB in applications of ultrasound autofocusing and sound speed imaging, flexible array shape estimation for wearable applications, and sensorless freehand swept synthetic aperture imaging.

Ultrasound Imaging with Flexible Array Transducer for Pancreatic Cancer Radiation Therapy

Pancreatic cancer with less than 10% 3-year survival rate is one of deadliest cancer types and greatly benefits from enhanced radiotherapy. Organ motion monitoring helps spare the normal tissue from high radiation and, in turn, enables the dose escalation to the target that has been shown to improve the effectiveness of RT by doubling and tripling post-RT survival rate. The flexible array transducer is a novel and promising solution to address the limitation of conventional US probes. We proposed a novel shape estimation for flexible array transducer using two sequential algorithms: (i) an optical tracking-based system that uses the optical markers coordinates attached to the probe at specific positions to estimate the array shape in real-time and (ii) a fully automatic shape optimization algorithm that automatically searches for the optimal array shape that results in the highest quality reconstructed image. We conducted phantom and in vivo experiments to evaluate the estimated array shapes and the accuracy of reconstructed US images. The proposed method reconstructed US images with low full-width-at-half-maximum (FWHM) of the point scatters, correct aspect ratio of the cyst, and high-matching score with the ground truth. Our results demonstrated that the proposed methods reconstruct high-quality ultrasound images with significantly less defocusing and distortion compared with those without any correction. Specifically, the automatic optimization method reduced the array shape estimation error to less than half-wavelength of transmitted wave, resulting in a high-quality reconstructed image.

A Nonlinear Data-Driven Towed Array Shape Estimation Method Using Passive Underwater Acoustic Data

Large-aperture towed linear hydrophone array has been widely used for beamforming-based signal enhancement in passive sonar systems; however, its performance can drastically decrease due to the array distortion caused by rapid tactical maneuvers of the towed platform, oceanic currents, hydrodynamic effects, etc. In this paper, an enhanced data-driven shape array estimation scheme is provided in the passive underwater acoustic data, and a novel nonlinear outlier-robust particle filter (ORPF) method is proposed to acquire enhanced estimates of time delays in the presence of distorted hydrophone array. A conventional beamforming technique based on a hypothetical array is first used, and the detection of the narrow-band components is sequentially carried out so that the corresponding amplitudes and phases at these narrow-band components can be acquired. We convert the towed array estimation problem into a nonlinear discrete-time filtering problem with the joint estimates of amplitudes and time-delay differences, and then propose the ORPF method to acquire enhanced estimates of the time delays by exploiting the underlying properties of slowly changing time-delay differences across sensors. The proposed scheme fully exploits directional radiated noise targets as sources of opportunity for online array shape estimation, and thus it requires neither the number nor direction of sources to be known in advance. Both simulations and real experimental data show the effectiveness of the proposed method.

An Enhanced Data-Driven Array Shape Estimation Method Using Passive Underwater Acoustic Data

Beamforming-based signal enhancement technologies in passive sonar array processing often have poor performance due to array distortion caused by rapid tactical maneuvers of the towed platform, oceanic currents, hydrodynamic effects, etc. In this paper, an enhanced data-driven shape array estimation formulation is proposed using passive underwater acoustic data. Beamforming based on a hypothetically ideal array is firstly employed to perform the detection of narrow-band components from sources of opportunity, and the corresponding phases of these detected narrow-band components are subsequently extracted to acquire time-delay differences. Then, a weighted outlier-robust Kalman smoother is proposed to acquire enhanced estimates of the time-delay differences, since the underlying properties of slowly changing time-delay differences in the hydrophone array and diverse signal to interference and noise ratios in multiple narrow-band components are explored; and its Cramer–Rao Lower Bound is also provided. Finally, the hydrophone array shape is estimated based on the estimated time delay differences. The proposed formulation fully exploits directional radiated noise signals from distant underwater acoustic targets as sources of opportunity for real-time array shape estimation, and thus it requires neither the number nor direction of sources to be known in advance. The effectiveness of the proposed method is validated in simulations and real experimental data.

Array Shape Estimation of a Horizontal Suspension Hydrophone Line Array

A horizontal suspension hydrophone line array system for deep water target detection is demonstrated. Theoretical estimation of the array shapes at different array states is fulfilled through detailed kinetic analysis. When steady ocean forces solely exert on the array system from three orthogonal directions and the array is in the neutral-buoyancy state, the array shapes are parabola linetypes. When no ocean forces exert on the array system and the array is in the non-neutral buoyancy state, the static array shapes are catenary linetypes. The simulation results can guide the curve fitting process of the array shape estimation based on depth and attitude sensors.

Subarray Beam-space Adaptive Beamforming Combined with Array Shape Estimation based on Non-Acoustic Sensor

To address the issue of serious decline in performance of the array signal processing caused by the towed array shape distortion during maneuvering, this paper presents a new method of subarray beam-space adaptive beamforming combined with an array shape estimation method based on non-acoustic sensor. Firstly, the array shape through the approximate circular arc structure of the array segment between the adjacent sensor during maneuvering is preliminary calculated. Next, the final estimated array shape through a smooth processing method on the entire array shape by means of a calibration method using spline interpolation technique is achieved. This method is able to estimate the array shape in real time. The array steering vector based on the real-time estimation of the array shape is updated, using a subarray beam-space adaptive beamforming (SBABF) to reduce the demand of the number of the snapshots. And the beam-space covariance matrix converges fast within a few snapshots. The SBABF method combined with array shape estimation (AE-SBABF) was verified by simulation data and sea trial data processing results. During maneuvering, the AE-SBABF can not only improve the array processing gain of the target effectively, but also solve the left/right ambiguity problem well.

Approximately optimal distribution of depth sensors over towed array

Towed array shape estimation aided with non-acoustic sensors is widely used for its rather low computational complexity of solutions and rather explicit results. In addition, previous studies have emphasised that depth sensors' distribution has a dramatic influence on the accuracy of this kind of array shape estimation method. Established on the basic theory of towed array shape estimation using Kalman Filters, the approximately optimal distribution of a certain number of depth sensors over a certain number of discretised towed arrays yields the approximately best achievable performance in terms of minimum space average mean square error (AMSE), is addressed in this study. The effect of depth sensors' distribution has been discussed. Then an exact expression for the space AMSE is derived. The expression is simplified in a reasonable way considering the practical issues in order to calculate the minimum space AMSE rapidly and effectively. The performance assessments demonstrate the effectiveness of the newly proposed method.

Towed Array Shape Estimation Based on Single or Double Near-Field Calibrating Sources

Towed array shape estimation is a crucial step for most array processing algorithms, since the position uncertainty of hydrophone elements seriously degrades the algorithm performance. Different from conventional methods using far-field calibrating sources, this paper introduces two kinds of towed array shape estimation methods, the single near-field source-dependent method (S-NFSDM) and the double near-field source-dependent method (D-NFSDM), respectively. Under the assumption that the frequency and direction of calibrating sources are known, the proposed methods can obtain the position of every hydrophone element based on eigenvector technique and the geometric relationship between the calibrating sources and hydrophone elements. In S-NFSDM, the shape of each segment between adjacent array elements is assumed to be straight, which ensures a low computational load and high real-time capability. But in this way, S-NFSDM can only estimate the distortion of uniform linear arrays. To address this, the D-NFSDM is proposed to eliminate the linear constraint of adjacent elements in S-NFSDM. Not only can it ensure the estimation accuracy of element positions, but also estimate distorted non-uniform linear arrays. The Cramer–Rao lower bounds of the proposed S-NFSDM and D-NFSDM are derived in this paper. Numerical simulations demonstrate that the S-NFSDM and D-NFSDM have better estimation performance than the classical method and strong robustness for different array shapes. Moreover, the estimation accuracy of Multiple Signal Classification algorithm can be improved obviously through the proposed methods in the direction of arrival estimation.

Minimum length of damping section for towed array based on revised Paidoussis equation

Most of the non-acoustic methods for towed array shape estimation are based on the incorrect original Paidoussis equation. A comparison between solution to the original and revised Paidoussis equation is made to prove the significance of utilising the latter. In addition, considering relative characteristics of the revised Paidoussis equation and the critical point which exists on the cylinder, the minimum length of damping section added at the end of the cylinder is derived.

센서 바이어스를 보상하는 칼만필터 기반의 예인 선배열 센서 형상 추정 기법

TASS(Towed Array Sonar System) is a sonar system which tows the sensor array behind a platform. Array shape is generally assumed to be a straight line. But the array shape is often distorted by oceanic current or platform maneuvering which causes the performance loss of signal processing method like beamforming. So array shape estimation methods are needed. Typically the method based on Kalman filter using heading sensor is used. In practice, the measurement is corrupted by biases which are caused by rotation of the tow cable, varying magnetic fields and slowly varying stresses in the mechanical construction. Although they can't be calibrated but can be estimated. In this paper, we suggest the array shape estimation method based on Kalman filter compensating the sensor biases.

Passive Towed Array Shape Estimation Using Heading and Acoustic Data

This paper addresses the problem of array shape estimation for passive towed sonar systems during platform maneuvers. Directional noise fields due to distant shipping lanes can be exploited as sources of opportunity for online array shape calibration. In this paper, a nonparametric noise field model is used to form field directionality maps for time-varying array shapes to exploit point and spatially spread sources. This formulation requires neither the number nor location of sources in the field to be known or estimated. Using acoustic data, a maximum-likelihood array shape estimate is derived where the shape is modeled as a polynomial in heading. Additionally, a method for fusing the shape estimate with heading sensor data is introduced. Heading sensors may permanently fail or suffer from high levels of noise during turns; thus acoustic data can be used to compensate for malfunctioning heading sensors during turns. The combined estimate is filtered using a dynamical model that is valid for sharp turns and accounts for motion of the array perpendicular to tow heading. Multisource simulations are used to demonstrate the performance of the acoustic-based estimate and robustness of the combined estimate.

Heading and hydrophone data fusion for towed array shape estimation

This paper addresses the problem of towed array shape estimation for passive, horizontal sonar arrays. Beamforming and localization techniques significantly degrade when an assumed linear array bends due to tow platform maneuvers or ocean currents. In this paper, heading sensors along the array and acoustic hydrophone data are jointly used to estimate the shape of the array. Previously, heading data have been filtered using a dynamical motion model to reduce noise during turns. In recent work, a time-varying noise field directionality estimate that incorporates a dynamical model for the acoustic field provides a second, albeit biased, estimate of the array shape. In this paper, these two estimates are combined via adaptive weights to obtain improved shape estimates during maneuvers. A multi-source simulation is used to demonstrate the robustness of the combined array shape estimate when compared to the separate heading or acoustic sensor based techniques.

A Simplified Subspace Fitting Method for Estimating Shape of a Towed Array

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.

Generalization of the Subspace-Based Array Shape Estimations

This work describes a nonplane wave signal model for array shape estimation in ocean environments. Though existing array shape estimation methods, which utilize reference sources, show good performance in the environment where plane wave assumption is satisfied, their performances are degraded significantly in more realistic nonplane wave situation. The proposed subspace-based array shape estimation method, which generalizes the conventional subspace fitting method, works very well for both plane wave and nonplane wave environments. The Cramer-Rao lower bound is investigated to analyze the theoretical lower bound of the variance of the estimation. The simulation results indicate that the proposed method correctly estimates the shape of perturbed array regardless of reference source location.

Array shape estimation and tracking using active sonar reverberation

This paper concerns the problem of array shape estimation and tracking for towed active sonar arrays, using received reverberation returns from a single transmitted CW pulse. Uniform linear arrays (ULAs) deviate from their nominal geometry while being towed due to ship maneuvers as well as ocean currents. In such scenarios, conventional beamforming performed under the assumption of a ULA can sometimes lead to unacceptably high spatial sidelobes. The reverberation leaking through the sidelobes can potentially mask weak targets in Doppler, especially when the target Doppler is close to that of the mainlobe reverberation and the reverberation-to-target ratio (RTR) is very high. Although heading sensors located along the array can be used to provide shape estimates, they may not be sufficiently available or accurate to provide the required sidelobe levels. We propose an array shape calibration algorithm using multipath reverberation returns from each ping as a distributed source of opportunity. More specifically, a maximum likelihood (ML) array shape calibration algorithm is developed, which exploits a deterministic relationship between the reverberation spatial and Doppler frequencies causing it to be low rank in the space-time vector space formed across a single coherent processing interval (CPI). In this application, a sequence of overlapped CPI length snapshots of duration less than the CW pulse is used. The ML estimates obtained for each snapshot are tracked using a Kalman filter with a state equation corresponding to the water pulley model for array dynamics. Simulations performed using real heading sensor data in conjunction with simulated reverberation suggest that 8-10 dB improvement in sidelobe level may be possible using the proposed array shape tracking algorithm versus an algorithm that uses only the available heading information.

New towed-array shape-estimation scheme for real-time sonar systems

In real-time towed-array systems, performance degradation of array gain occurs when a line array that is not straight is assumed straight in the beamforming process. In this paper, a new method is proposed for array shape estimation. The novelty of this method is that it accounts for the variations in the tow ship's speed, which are typical during course alterations. The procedure consists of two steps. First, we solve for the tow-point induced motion in the time domain based on the constraints from the tow-point compass-sensor readings and from a discretized Paidoussis equation. At each time instance, the shape estimate is solved from a linear system of equations. We also show that this solution is equivalent to a previous frequency-domain solution while the new approach is much simpler. In the second step, we use the tail compass-sensor data to adjust the overall array shape. By noting that variations in the ship speed lead to a distortion in the normalized time axis, we first register the predicted tail displacement with the tail sensor readings along the time axis. Then, distortions in the estimated array shape over its length can be compensated accordingly. We also model a slow-changing bias between sensor zeros and remove systematic sensor errors. The effectiveness of the new algorithm is demonstrated with simulations and real sea-trial data.

Acoustic tracking of towed-array hydrophone positions during tow-vessel maneuvers

This paper describes an experiment in which a vessel towing an array of hydrophones executed a series of maneuvers designed to bring the array into orientations favorable for imaging noise sources on the tow-vessel. Signals from tracking beacons on the tow-vessel and transient signals from implosive sources deployed from a second vessel were received on the array hydrophones and were used to obtain independent estimates of hydrophone position. Array shape estimation and tracking algorithms are described and the results of applying these algorithms to the experimental data are presented.

Towed array shape estimation using multimodel partitioning filters

The problem of towed array shape estimation is reformulated and shown to be mathematically equivalent to the problem of state estimation with abruptly changing bias of the plant noise process. An algorithm belonging to the family of adaptive multimodel partitioning algorithms is subsequently applied to this problem, and its performance is comparatively evaluated with that of nonadaptive algorithms previously proposed through simulation experiments.

An adaptive tracking algorithm for direction finding and array shape estimation in a nonstationary environment

This paper presents an adaptive tracking algorithm for the subspace-based direction of arrival estimation of multiple sources in a nonstationary, environment. The nonstationarities are due to moving sources or to timevarying distortions of the sensor array shape. The proposed algorithm relies on the properties of a linear operator, referred to as the Propagator, which only exploits the linear independency of the source steering vectors. The Propagator allows not only the calibration of the array shape, but also the determination of the source and the noise subspaces without any eigendecomposition of the cross-spectral matrix of the received signals. A gradientbased adaptive algorithm is here proposed for the on-line estimation of the Propagator. A theoretical analysis of the behaviour of this algorithm in a nonstationary environment is given. Simulations are carried out in the case of moving sources and in the case of a time-varying array shape. They exhibit the good performances of the proposed algorithm.