Azimuth Estimation Research Articles

Experimental study on identifying anomaly azimuth based on acoustic vector array of borehole acoustic reflection imaging

Accurate anomaly azimuth identification is a major challenge in borehole acoustic reflection imaging. We develop an azimuth estimation method using an acoustic vector array to address this issue. This method is rigorously tested through a physical simulation experiment in a water-filled tank using a monopole acoustic source and an acoustic receiver station composed of eight azimuthal elements. Our method involves the synthesis of multiazimuth acoustic pressure waveforms recorded by the receiver into multicomponent particle velocity waveforms. These waveforms are paired and subjected to coordinate conversion, yielding multiple groups of orthogonal component particle velocity waveforms. Each group undergoes polarization analysis to obtain the direction of particle polarization on the horizontal plane and isolate the principal component particle velocity waveform. Using the particle polarization direction, the amplitude of the multiazimuth acoustic pressure waveform, and the type of echo mode, we accurately determine the azimuth of the anomaly, facilitating the creation of a spatial distribution image of the anomaly. Further validation of this method is conducted through a large-scale physical simulation experiment in a deepwater lake using a borehole acoustic reflection imaging instrument. The obtained experimental data are used to validate the effectiveness of this method. Finally, considering an actual logging environment, the feasibility of this method in a borehole environment is verified using numerical simulations and field data of acoustic detection of nearby wells. The present findings demonstrate that this novel method considerably enhances the accuracy and stability of the measurement of anomaly azimuth based on the particle polarization direction. In addition, this method effectively harnesses acoustic pressure and particle velocity in borehole acoustic reflection imaging, exhibiting superior noise robustness, mitigating noise, and improving the signal-to-noise ratio of the echoes.

Self correction technique for amplitude and phase errors of underwater acoustic arrays based on variable decibel Bayesian inference

Abstract Direction of arrival (DOA) estimation of underwater targets is an important research direction in the field of underwater acoustic array signal processing. Due to factors such as assembly errors and component aging, amplitude and phase errors between each channel of the array are common, resulting in distortion of the array flow pattern matrix. At the same time, the non-uniform distribution of noise intensity at the positions of each array element further increases the difficulty of DOA for underwater targets. Based on the characteristics of sparse spatial distribution of underwater targets, this paper uses the flexibility of hyperparametric modeling to construct an array observation signal graph model. On this basis, the effects of amplitude and phase errors and non-uniform noise on the array model are added, and a comprehensive observation model with clear distribution types of amplitude and phase errors, signals, and noise is established. The variational Bayesian inference theory is used to obtain closed solutions of various variables and parameters, so as to achieve joint estimation of target azimuth and error parameters. Simulation results and sea trial data processing results show that the algorithm can achieve amplitude and phase error self correction while completing DOA estimation in the absence of prior information on the number of sources.

An improved histogram algorithm for DOA estimation based on single vector acoustic system

The integration of a singular vector acoustic system onto an unmanned underwater platform can lead to achieving unambiguous direction finding across the entire space. To enhance the direction-finding capabilities of the single vector acoustic system for low noise target, a refined histogram algorithm utilizing coherent spectrum weighting is suggested. A comparative evaluation and analysis of the target azimuth estimation performance of the enhanced histogram algorithm, traditional frequency-weighted histogram algorithm, and energy-weighted histogram algorithm are carried out. Through computer simulations, it is observed that the three Direction of Arrival (DOA) algorithms exhibit comparable direction-finding capabilities for wideband signals, whereas for single-frequency signals, the improved histogram algorithm surpasses the two conventional algorithms in direction-finding accuracy. Specifically, at a signal-to-noise ratio (SNR) of −40 dB, the azimuth estimation root mean square error (RMSE) is approximately 2°. Findings from sea trials indicate that the improved histogram algorithm displays a narrower spectral peak width and robust resistance to noise interference, thereby substantiating the effectiveness of the enhanced histogram algorithm.

Spatial Spectrum Estimation of Weak Scattering Wave Signal in Range-Doppler Domain

How to enhance the desired signal with low signal-to-noise ratio (SNR) is a difficult problem in the estimation process of the direction-of-arrival (DOA) of the target scattering wave signal. In this paper, the feasibility of spatial spectrum estimation in the Range-Doppler (RD) domain is analyzed in principle, and the SNR gain expression of weak scattering wave signal is derived when constructing multi-snapshots virtual array data. On this basis, the mutual eigenvector singular value decomposition (MESVD) method based on RD domain mode excitation is proposed, which can robustly and effectively estimate the direction of the coherent weak signals. Simulation experiments verify that the RD domain spectral estimation method has the ability to simultaneously obtain the direction of multiple weak target scattering waves, and the direction-finding accuracy can reach the Cramer–Rao bound (CRB) of conventional spectral estimation method. The results of Monte Carlo experiments show that the root-mean-square-error (RMSE) of azimuth estimation of RD domain spatial spectrum estimation method is 5.76° lower than that of a conventional multiple signal classification (MUSIC) method. In addition, the practicability of the proposed method is demonstrated by comparing the DOA estimation results of a set of real data with Automatic Dependent Surveillance-Broadcast (ADS-B) data.

Underwater Coherent Source Direction-of-Arrival Estimation Method Based on PGR-SubspaceNet

In the field of underwater acoustics, the signal-to-noise ratio (SNR) is generally low, and the underwater environment is complex and variable, making target azimuth estimation highly challenging. Traditional model-based subspace methods exhibit significant performance degradation when dealing with coherent sources, low SNR, and small snapshot data. To overcome these limitations, an improved model based on SubspaceNet, called PConv-GAM Residual SubspaceNet (PGR-SubspaceNet), is proposed. This model embeds the global attention mechanism (GAM) into residual blocks that fuse PConv convolution, making it possible to capture richer cross-channel and positional information. This enhancement helps the model learn signal features in complex underwater conditions. Simulation results demonstrate that the underwater target azimuth estimation method based on PGR-SubspaceNet exhibits lower root mean square periodic error (RMSPE) values when handling different numbers of narrowband coherent sources. Under low SNR and limited snapshot conditions, its RMSPE values are significantly better than those of traditional methods and SubspaceNet-based enhanced subspace methods. PGR-SubspaceNet extracts more features, further improving the accuracy of direction-of-arrival estimation. Preliminary experiments in a pool validate the effectiveness and feasibility of the underwater target azimuth estimation method based on PGR-SubspaceNet.

Refined Aircraft Positioning Based on Stochastic Hybrid Estimation with Adaptive Square-Root Unscented Particle Filtering

The positioning of civil aviation aircraft relative to a geographic reference point on Earth in a Cartesian frame is significant to detect the deviations from the desired path, especially for high-altitude airports or special airports based on performance-based navigation (PBN). To obtain these critical deviations during aircraft approach and landing, it is fundamental to estimate the continuous flight variables and discrete flight modes simultaneously with enough accuracy. With the coordinate conversion between the North, East, and Down (NED) frame and the geographic coordinate system based on World Geodetic System 1984 (WGS-84) considered, this study proposed a non-linear stochastic hybrid estimation algorithm with adaptive square-root unscented particle filtering (ASR-UPF) to estimate the true path. The probabilities of mode transition, represented by the normal cumulative density function of continuous states, determine whether to proceed with mode transitions. In addition, the adaptive update characterized by tracking variable noise and the importance sampling distributions based on the results of square-root unscented Kalman filtering (SR-UKF), as a comparative study of continuous system filtering, were used. The experiments illustrated the ASR-UPF is able to reduce the state estimation error more effectively, and more promptly track the error caused by incorrect mode estimation with adaptability compared to the SR-UKF. A further test with real flight data indicates that the proposed method gives the refined estimation of position and azimuth in NED frame.

Assessment of hydraulic fracture height and distribution using timelapse crosswell shear-wave data

An in-depth study of the impact of hydraulic fracturing operations on the Marcellus shale formation and overburden is presented by analyzing a unique timelapse crosswell seismic survey suitable for four-component shear wave vector rotations in order to study fracture azimuth and intensity. The borehole source used for the survey generated both oriented compressional and shear wave energy, and the seismic acquisition included perpendicular source orientations at each shot level to allow isolation of fast and slow shear modes using the Alford rotation and linear transform technique. Estimates of fast shear azimuth and slow shear time delay before and after hydraulic fracturing indicate fracture creation throughout the overburden above the Marcellus shale and a possible vertical breach of the bounding Tully limestone formation. The magnitude of the timelapse change is consistent between travel-time and slow shear lag inversion, but the absolute change is small, suggesting that the increase in fracture intensity may not be significant. These results point to operational inefficiencies during hydraulic fracturing operations that could negatively impact production and pose risks to future development. The study demonstrates the value of crosswell seismic surveys for reservoir monitoring and highlights observations that might be missed by a monitoring program that does not include timelapse seismic data and analysis of shear wave changes due to hydraulic fracturing.

IMU/Magnetometer-Based Azimuth Estimation with Norm Constraint Filtering.

A typical magnetometer-based measurement-while-drilling (MWD) system determines the azimuth of the bottom hole assembly during the drilling process by employing triaxial accelerometers and magnetometers. The geomagnetic azimuth solution is susceptible to magnetic interference, especially strong magnetic interference and so a rotary norm constraint filtering (RNCF) method for azimuth estimation, designed to support a gyroscope-aided magnetometer-based MWD system, is proposed. First, a new magnetic dynamical system, one whose output is observed by the magnetometers triad, is designed based on the Coriolis equation of the desired geomagnetic vector. Second, given that the norm of the non-interfered geomagnetic vector can be approximated as a constant during a short-term drilling process, a norm constraint procedure is introduced to the Kalman filter. This is achieved by the normalization of the geomagnetic part of the state vector of the dynamical system and is undertaken in order to obtain a precise geomagnetic component. Simulation and actual drilling experiments show that the proposed RNCF method can effectively improve the azimuth measurement precision with 98.5% over the typical geomagnetic solution and 37.1% over the KF in a RMSE sense when being strong magnetic interference environment.

Enhancing azimuth estimation in low-resolution underwater acoustic lens systems for advanced communication and positioning

Here we aimed to enhance azimuth estimation to accurately locate a communication partner’s position by utilizing a low-resolution underwater acoustic lens system for communication. We proposed a method to accurately estimate the direction-of-arrival (DoA) by finding the center of gravity of the focal distribution using two adjacent elements of the transducer array. Ranging was to be based on time-of-flight (ToF). The method’s effectiveness was evaluated by two-dimensional finite difference time domain simulation. The lens’s focused sound field was calculated and the array was designed based on the result. DoA and ToF were estimated from the received signals and evaluated by comparing them with the true values under conditions involving 1-, 2-, and 3- users. The results confirmed DoA estimation with an error of almost 4°, even when using a lens system with an azimuth resolution of 10°. As the number of users increased, the maximum error value increased, though slightly.

Обобщённое неравенство Крамера – Рао в случае совместного пеленгования по азимуту и углу места в условиях сложной электромагнитной обстановки

In this work, a generalized expression is obtained for the Cramer–Rao lower bound in the case of a joint estimation of azimuth and elevation angle in an arbitrary coordinate system in which the vector complex radiation pattern is determined, under conditions of a complex electromagnetic environment, including the presence of noise correlation in spatial channels and differences in its intensity. A theorem is formulated for the Fisher information of joint estimates of azimuth and elevation angle in the case of a multi-channel detector-direction finder with an antenna system described in the selected coordinate system by a vector complex radiation pattern. Dependences of the root-mean-square error of direction finding in azimuth and elevation on the signal-to-noise ratio and true directions to the radio source are obtained, calculated using known and generalized expressions for the Cramer–Rao lower bound. The condition for the applicability of the existing and proposed in the article expression for the Fisher information matrix is obtained. The concept of the “energy” center of the antenna system is given. To confirm the reliability of the obtained generalized expressions for the lower bound of the dispersion of the Cramer–Rao inequality, statistical modeling is carried out. The use of the obtained expressions in practice will allow the most optimal synthesis of antenna devices depending on the structure and characteristics of the direction finder antenna system, the number of antennas and the characteristics of the radio receiving path. Generalized expressions for the lower Cramer–Rao bound are the foundation for organizing the operation of intelligent radio monitoring systems, allowing for a well-founded choice of the optimal antenna array structure that provides the required direction-finding efficiency.

Ocean Bottom Distributed Acoustic Sensing for Oceanic Seismicity Detection and Seismic Ocean Thermometry

AbstractA T‐wave is a seismo‐acoustic wave that can travel a long distance in the ocean with little attenuation, making it valuable for monitoring remote tectonic activity and changes in ocean temperature using seismic ocean thermometry (SOT). However, current high‐quality T‐wave stations are sparsely distributed, limiting the detectability of oceanic seismicity and the spatial resolution of global SOT. The use of ocean bottom distributed acoustic sensing (OBDAS), through the conversion of telecommunication cables into dense seismic arrays, is a cost‐effective and scalable means to complement existing seismic stations. Here, we systematically investigate the performance of OBDAS for oceanic seismicity detection and SOT using a 4‐day Ocean Observatories Initiative community experiment offshore Oregon. We first present T‐wave observations from distant and regional earthquakes and develop a curvelet denoising scheme to enhance T‐wave signals on OBDAS. After denoising, we show that OBDAS can detect and locate more and smaller T‐wave events than regional OBS network. During the 4‐day experiment, we detect 92 oceanic earthquakes, most of which are missing from existing catalogs. Leveraging the sensor density and cable directionality, we demonstrate the feasibility of source azimuth estimation for regional Blanco earthquakes. We also evaluate the SOT performance of OBDAS using pseudo‐repeating earthquake T‐waves. Our results show that OBDAS can utilize repeating earthquakes as small as M3.5 for SOT, outperforming ocean bottom seismometers. However, ocean ambient natural and instrumental noise strongly affects the performance of OBDAS for oceanic seismicity detection and SOT, requiring further investigation.

Azimuth estimation based on CNN and LSTM for geomagnetic and inertial sensors data

Although estimating the azimuth using a geomagnetic sensor is very useful, the estimation error may be very large due to the surrounding geomagnetic disturbance. We proposed a novel method for preprocessing appropriately for geomagnetic and inertial sensor data to be suitable for the proposed Artificial Neural Network model and training method for the model. As a result, the probability of azimuth estimation error within 1 degree is 96.4% with regression estimation. For classification estimation, when the azimuth estimation probability is 90% or more, the probability that the azimuth estimation error is within 1 degree is 100%.

Natural Seismic Event Analysis Based on Signal and Source Characteristics from two Experiments in Antarctica.

This study presents geophysical data from two passive seismic measurements conducted at two different sites in Antarctica. We analyzed the signals mainly in the frequency domain through the multitaper method to extract some spectral characteristics of the signals that would have been out of reach through the usual FFT approach. The power spectral density of the signals carries information about the processes that generated them, allowing its correlation with their source origin and type, either natural or anthropogenic. We deal with three different source types: calving, wind, and anthropogenic origins. The former is closely related to glacier dynamics, being modulated by the prevailing atmospheric processes. At both locations the wind noise is prevalent, complicating the analysis of other events like calving. We have used data classification, estimation of the source azimuth, and seismic apparent velocity to demonstrate the viability of using geophysical methods to study glacier elastic parameters and dynamics. Moreover, the calving rate can yield a wider and more independent understanding of glacier hydrodynamics and may help to estimate the future response of the polar areas to a changing environment.

COUPLED C-ESPRIT-BASED AZIMUTH AND ELEVATION ANGLE ESTIMATION WITH MINIMUM VARIANCE

This paper presents a method for conjugate estimation of azimuth and elevation angles based on the minimum variance C-ESPRIT method. The conjugate estimation method with minimum variance is a modification of the robust method based on the ESPRIT method with minimum variance and differs from it in that it does not require prior matching of signal duplicates. When modeling the signal acquisition from a unmanned aerial vehicle and processing it with the ESPRIT method, the data were distorted. Several signals were not displayed and noise appeared, which prevented the estimation of the signal arrival direction. The paper presents an efficient algorithm that can estimate the direction of arrival based on uncorrelated and one-dimensional signals. The method of conjugate estimation with minimum variance, when compared to the method of conjugate estimation without minimum variance, has been shown to improve the signal by a factor of 10. This improvement in signal quality allows one to conclude that the method is highly efficient. The C-ESPRIT-based minimum variance conjugate azimuth and location angle estimation method uses a robust minimum variance method with a conjugate rotation matrix to process a second subarray of data. An important aspect of the method is that it uses information from all array elements without grouping them and without computing the mean of the covariance matrices.

DeepEar: Sound Localization With Binaural Microphones

The binaural microphone, which refers to a pair of microphones with artificial human-shaped ears, is widely used in hearing aids and spatial audio recording to improve sound quality. It is crucial for such devices to find the voice direction in many applications such as binaural sound enhancement. However, sound localization with two microphones remains challenging, especially in multi-source scenarios. Most previous work utilized microphone arrays to deal with the multi-source localization problem. Extra microphones yet have space constraints for deployment in many scenarios ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> . <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> ., hearing aids). Inspired by the fact that humans have evolved to locate multiple sound sources with only two ears, we propose DeepEar, a binaural microphone-based sound localization system. To this end, we design a multisector-based neural network to locate multiple sound sources simultaneously, where each sector is a discretized region of the space for different angle of arrivals. DeepEar fuses explicit hand-crafted features and implicit latent sound representatives to facilitate sound localization. More importantly, the trained DeepEar model can adapt to new environments with a minimum amount of extra training data. The experiment results show that DeepEar substantially outperforms the state-of-the-art binaural deep learning approach by a large margin in terms of sound detection accuracy and azimuth estimation error.

Estimating seismometer component orientation of the Brazilian seismographic network using teleseismic P-wave particle motion analysis and directional statistics

Seismometer component orientation is one of the most critical parameters for seismology, especially for methods that take wave field polarization effects into account, such as receiver functions, seismic anisotropy, surface wave dispersion and seismic tomography. Using P-wave particle motion combined with directional statistics, we estimated the orientation for 90 stations of the Brazilian Seismographic Network (RSBR), corresponding to 105 seismometers. The difference between the number of stations (90) and seismometers (105) is due to instrument replacement during station operation. We observed that 81 seismometers have an orientation of ±5° and 19 seismometers greater than ±5°. Only one seismometer has an orientation greater than 90° (BOAV station). ON and BR are the subnetworks of RSBR with the largest number of seismometers with orientation errors bigger than ±10° (6 for each one) and NB is the only subnetwork with no misoriented station. All the estimated orientations were close to the measured in the field, which is evidence that our approach is more accurate to detect misoriented stations than previous studies that analyzed the orientation of RSBR stations. The Watson's U2 statistical test indicated that the back azimuth deviations for Precambrian Basement and Phanerozoic Cover were significantly different, suggesting that the regional geology could affect back azimuth estimates.

A Customized Extended Kalman Filter for Removing the Impact of the Magnetometer's Measurements on Inclination Determination.

Normally, a three-dimensional orientation determination algorithm that is used in a magnetic and inertial measurement unit calculates the inclination (including both the pitch and roll) of rigid bodies by fusing the measurements of the gyroscope, as well as the measurements of both the accelerometer and the magnetometer. The measurements of the magnetometer can be helpful in improving the inclination estimation accuracy; however, once the measurements of the magnetometer are disturbed by ferromagnetic materials, the inclination estimation accuracy could be significantly decreased. Hence, a better approach should be followed in terms of not employing the measurements of the magnetometer for inclination determination. In order to achieve this goal, the component of the measurement of the magnetometer that is used for the improvement of the inclination estimation accuracy, along with the measurement of the accelerometer at each sampling time instant, is abandoned. Consequently, the remaining component of the measurement of the magnetometer, which is perpendicular to the measurement of the accelerometer, is used for the azimuth determination. After applying this process, the extended Kalman filter (EKF) is proposed for the inclination and azimuth estimations. Through experiments, the EKF is compared with three algorithms that were recently proposed with the same objective as this work, and the extracted outcomes show that the EKF approach clearly outperforms these three algorithms.

Six‐Component Earthquake Synchronous Observations Across Taiwan Strait: Phase Velocity and Source Location

AbstractWith the development of rotational seismometers, especially the high‐sensitivity optical seismometers, rotational motions have shown increasing benefits for calculation of dispersion curves, estimation of back azimuth and many other applications. Here we present the six‐component observations of 2019 Hualien mww6.1 earthquake simultaneously on both sides of Taiwan Strait. Seismograms and time‐frequency spectrums show that the attenuations for rotations are more significant than translations. Calculations of the surface wave phase velocity are performed for both stations through single‐station records, indicating a distinct difference owning to the instrument installation conditions and site effect. Comparison of theoretical dispersion curves is consistently in trends with estimations, and reveals the influence of higher‐mode surface waves. For the first time, we locate the source of a earthquake through intersection of two stations' back azimuths estimated through rotational methods. Results of comparing to translational polarization verify that rotational observation can distinctly reduce the deviation of source location.

Performance comparison of conventional and striation-based beamformers for underwater bearing detection of pulse sources.

The multi-path and dispersion properties of shallow water waveguides make conventional beamforming (CBF) face issues such as beam shift, broadening, splitting, output distortion, and array gain reduction. In this paper, the striation-based beamforming (SBF) is investigated to address these issues. SBF differs from CBF by utilizing frequency-shift processing along interference striations. The performance difference between CBF and SBF is compared. It demonstrates that under ideal waveguide modeling with pulse sources, SBF can achieve a beam output response that is close to the plane wave condition. The speed term of SBF's response is approximately independent of modal indexes, which equips SBF to form a unique beam output and guarantee the beam resolution. The processing of consistent signals along the striation maintains the optimal signal correlation, which makes SBF ensure the output fidelity and array gain. To shift the mainlobe of SBF to the source azimuth, the time delay related to the waveform truncation point can be introduced to pre-compensate the array signals. There exist two theoretical accuracy limits to using the truncation. First, truncation time corresponds to the waveform point at r0/c (r0 is the source range), and the mainlobe of SBF is directed to the source azimuth. Second, truncation corresponds to the pulse peak point, and the azimuth estimation accuracy of SBF gets close to CBF. Simulations and experimental results are given as illustrations.

Azimuthal, range, and depth tracking of marine mammal sounds using a drifting acoustic vector sensor and hydrophone array platform

Deep-water acoustic tracking of marine mammals typically requires correlating hydrophone signals across both short and large-aperture hydrophone arrays. Here, we demonstrate how a single drifting, depth-controlled platform can obtain two and three-dimensional positional fixes of marine mammal sounds using an acoustic vector sensor and short-aperture arrays, both mounted on an autonomous drifting platform. In February and June 2023 two autonomous opto-acoustic drifters were deployed 50km off San Diego, CA at 250 m depth in 1030 m deep water. Both drifters were equipped with a CTD and acoustic recording system comprised of a 1.75 m aperture vertical hydrophone array, a tetrahedral hydrophone array, and either a 2-D Geospectrum M-35 or 3-D Wilcoxon VS-209 acoustic vector sensor. Throughout the two to three-day deployments, all acoustic sensors detected numerous marine mammal calls, including humpback whales and a pod of common dolphins. Estimates of azimuth and elevation were obtained from the simultaneously sampled acoustic vector sensor and hydrophone arrays, while multi-path and cross-platform processing were employed to extract range information. The results suggest that sparse deployments of drifting vector sensor platforms may be able to map biological distributions over spatial scales that would otherwise require larger numbers of hydrophone-only platforms. [Work supported by ONR TFO.]