Azimuth Estimation Research Articles

UCA Root-MUSIC With Sparse Uniform Circular Arrays

Several algorithms for direction-of-arrival (DOA) estimation with uniform circular arrays rely on the beamspace transform as it allows computationally efficient estimation of the angles-of-arrival. The performance of such estimators is degraded if the array has a small number of elements. We introduce adaptations to UCA Root-MUSIC resulting in an algorithm that delivers accurate azimuth estimates in a search-free way even when the number of antenna elements is insufficient to apply traditional beamspace-based algorithms. We validate our algorithm by means of several examples based on synthetic and experimental data.

Misperception of exocentric directions in auditory space

Previous studies have demonstrated large errors (over 30°) in visually perceived exocentric directions (the direction between two objects that are both displaced from the observer’s location; e.g., Philbeck et al. [Philbeck, J. W., Sargent, J., Arthur, J. C., & Dopkins, S. (2008). Large manual pointing errors, but accurate verbal reports, for indications of target azimuth. Perception, 37, 511–534]). Here, we investigated whether a similar pattern occurs in auditory space. Blindfolded participants either attempted to aim a pointer at auditory targets (an exocentric task) or gave a verbal estimate of the egocentric target azimuth. Targets were located at 20–160° azimuth in the right hemispace. For comparison, we also collected pointing and verbal judgments for visual targets. We found that exocentric pointing responses exhibited sizeable undershooting errors, for both auditory and visual targets, that tended to become more strongly negative as azimuth increased (up to −19° for visual targets at 160°). Verbal estimates of the auditory and visual target azimuths, however, showed a dramatically different pattern, with relatively small overestimations of azimuths in the rear hemispace. At least some of the differences between verbal and pointing responses appear to be due to the frames of reference underlying the responses; when participants used the pointer to reproduce the egocentric target azimuth rather than the exocentric target direction relative to the pointer, the pattern of pointing errors more closely resembled that seen in verbal reports. These results show that there are similar distortions in perceiving exocentric directions in visual and auditory space.

Joint azimuth, elevation, and time of arrival estimation of diffuse sources

In this paper, we estimate the azimuth, the elevation, and the time of arrival of diffuse sources using the covariance matching estimator (COMET) algorithm. Previous works dealt with azimuth estimation of diffuse sources or azimuth and time of arrival estimation of point sources. However, in realistic situations, a tridimensional diffuse source localization is needed, which is the main objective of this paper. We show that the dimensionality of the COMET algorithm can be reduced by separating the estimation of the different source powers and the noise variance from that of the remaining parameters, namely the azimuth, the elevation, the time of arrival, and the corresponding angular and temporal spreads. As COMET still involves a multidimensional nonlinear optimization, we choose, in this purpose, the alternating projection algorithm to alleviate the corresponding complexity. The multiple signal classification (MUSIC) algorithm is processed to initialize the so-resulted algorithm. Simulations of the proposed algorithm are carried in different contexts and compared to the Cramer-Rao Bound, MUSIC algorithm, and dispersed signal parametric estimation simulation results.

Strategic listener movement in a model of auditory distance perception

A mobile listener has the potential to exploit dynamic auditory cues to judge sound source distance. One such cue is motion parallax, which employs a sequence of azimuth estimates from interaural time differences to triangulate sound source location. However, distortions due to reverberation and competing sources complicate matters, so it is of interest to know what active strategies listeners might adopt to arrive at robust location estimates. One hypothesis is that not all listener motion trajectories are equally‐beneficial for distance estimation. Trajectories designed via certain optimisation criteria might lead to faster and more robust estimates in a wider range of environments. Eight listener motion strategies were tested, from naive approaches such as random walks and head‐rotation only to more sophisticated techniques based on sequential Monte Carlo methods. In the latter case, strategies included movement towards the expected source location, or in the most informative direction, or movement reducing overall uncertainty. Evaluation in a simulated acoustic environment with single sources under both anechoic and reverberant conditions demonstrated that moving towards the most likely source location led to the most accurate estimation of distance and subsequent tracking of a moving source. Significant problems remain in estimating distance in multi‐source conditions.

원형 배열 안테나의 DoA 추정 알고리즘 성능 분석

본 논문은 GPS 신호를 수신할 때 재머신호의 제거를 위한 성능 개선을 목적으로 2차원 원형 배열 안테나를 이용한 도래각(DoA : Direction of Arrival) 추정 알고리즘의 성능 분석에 관한 것이다. 배열 안테나를 사용하여 DoA를 추정한 후 공간 필터링을 수행함으로서 원하지 않는 방향으로부터의 재머신호를 널링(nulling)시키고, 원하는 방향으로의 빔을 형성하므로서 수신 신호의 품질을 개선할 수 있다. 논문에서는 4 소자와 7 소자 원형 배열 안테나에서 재머신호의 각도와 전력을 고정시킨 후 DoA 추정을 위하여 MUSIC, MinNorm 알고리즘을 적용한다. 이들 알고리즘의 성능 분석을 위하여 추정 결과와 추정 오차를 컴퓨터 시뮬레이션을 통하여 계산한다. 추정 결과 신호대 잡음비가 양호한 경우 Azimuth각과 Elevation각 추정에서는 MUSIC과 MinNorm이 우월하며, 신호대 잡음비가 낮은 경우 MUSIC이 MinNorm보다 우월한 성능을 보인다. 【This paper relates to the performance analysis of DoA estimation algorithm in 2-dimensional circular array antenna for the receiving of GPS signal which is used for the performance improvement by elimination of jammer signal. By performing the spatial filtering after the DoA estimation in array antenna, the quality of receiving signal can improve by the nulling of jammer signal from the undesired direction and the forming of beam from the desired direction. In this paper, the MUSIC and MinNorm algorithm used for DoA estimation were applied after fixing the angle and power of jammer signal in 4 element and 7 element circular array antenna. In order to performance analysis, the estimation result and estimation error were computed by computer simulation. As a result, the MUSIC and MinNorm were fairly good in azimuth and elevation angle estimation of DoA in case of good signal to noise ratio and the MUSIC has better performance compared to MinNorm in case of poor signal to noise ratio.】

Effect of coherent noise on single-station direction of arrival estimation

Polarization analysis of multi-component seismic data is used in both exploration seismology and earthquake seismology. In single-station polarization processing, it is generally assumed that any noise present in the window of analysis is incoherent, i.e., does not correlate between components. This assumption is often violated in practice because several overlapping seismic events may be present in the data. The additional arrival(s) to that of interest can be viewed as coherent noise. This paper quantifies the error because of coherent noise interference. We first give a general theoretical analysis of the problem. A simple mathematical wavelet is then used to obtain a closed-form solution to the principal direction estimated for a transient incident signal superposed with a time-shifted, unequal amplitude version of itself, arriving at an arbitrary angle to the first wavelet. The effects of relative amplitude, arrival angle, and the time delay of the two wavelets on directional estimates are investigated. Even for small differences in angle of arrival, there may be significant error (>10°) in the azimuth estimate.

Detection and characterization of seismic phases using continuous spectral estimation on incoherent and partially coherent arrays

Seismic arrays are employed in the global monitoring of earthquakes and explosions because of their superior ability to detect and estimate the direction of incident seismic arrivals. Traditional beamforming and f–k analysis require waveform semblance over the full array aperture and cannot be applied in many situations where signals are incoherent between sensors. The NORSAR and MJAR arrays are two primary IMS stations where this is the case for high-frequency regional phases. Large intersite distances and significant geological heterogeneity at these arrays result in waveform dissimilarity which precludes coherent array processing in the frequency bands with optimal SNR. Multitaper methods provide low variance spectral estimates over short time-windows and seismic arrivals can be detected on single channels using a non-linear spectrogram transformation which attains local maxima at times and frequencies characterized by an energy increase. This detection procedure requires very little a priori knowledge of the spectral content of the signal. The transformed spectrograms can be beamformed over large-aperture arrays or networks according to theoretical time-delays resulting in an incoherent detection system which does not require waveform semblance at any frequencies. We outline a real-time automatic detection system for regional phase arrivals on the NORSAR array and demonstrate how stable and accurate slowness and azimuth estimates can be obtained for quite marginal signals. In the case of partially coherent arrays, the procedure described may provide stable, if low resolution, estimates which can subsequently be refined using coherent processing over subsets of sensors. In particular, we illustrate how the spectrogram beamforming method facilitates a stable and accurate slowness estimate for the incoherent high-frequency Pn arrival at the MJAR array in Japan from the 2006 October 9 underground nuclear test in North Korea.

Large Manual Pointing Errors, but Accurate Verbal Reports, for Indications of Target Azimuth

Many tasks have been used to probe human directional knowledge, but relatively little is known about the comparative merits of different means of indicating target azimuth. Few studies have compared action-based versus non-action-based judgments for targets encircling the observer. This comparison promises to illuminate not only the perception of azimuths in the front and rear hemispaces, but also the frames of reference underlying various azimuth judgments, and ultimately their neural underpinnings. We compared a response in which participants aimed a pointer at a nearby target, with verbal azimuth estimates. Target locations were distributed between 20 degrees and 340 degrees. Non-visual pointing responses exhibited large constant errors (up to -32 degrees) that tended to increase with target eccentricity. Pointing with eyes open also showed large errors (up to -21 degrees). In striking contrast, verbal reports were highly accurate, with constant errors rarely exceeding +/-5 degrees. Under our testing conditions, these results are not likely to stem from differences in perception-based versus action-based responses, but instead reflect the frames of reference underlying the pointing and verbal responses. When participants used the pointer to match the egocentric target azimuth rather than the exocentric target azimuth relative to the pointer, errors were reduced.

Matlab software for the analysis of seismic waves recorded by three-element arrays

We develop and implement an algorithm for inverting three-element array data on a Matlab platform. The algorithm allows reliable estimation of back azimuth and apparent velocity from seismic records under low signal-to-noise conditions. We start with a cubic spline interpolation of the waveforms and determine the differences between arrival times at pairs of array elements. The time differences are directly computed from cross-correlation functions. The advantages of this technique are (a) manual picking of the onset of each arrival is not necessary at each array element; (b) interpolation makes it possible to estimate time differences at a higher resolution than the sampling rate of the digital waveforms; (c) consistency among three independent determinations provides a reliability check; and (d) the value of apparent velocity indicates the nature of the recorded wavelet and physically checks the results. The algorithm was tested on data collected by a tri-partite array (with an aperture of ∼250 m) deployed in 1998 by the National Data Center of Israel, during a field experiment in southern Israel, 20 km southwest of the Dead Sea. The data include shallow explosions and natural earthquakes under both high and low signal-to-noise conditions. The procedure developed in this study is considered suitable for searching of small aftershocks subsequent to an underground explosion, in the context of on-site inspections according to the Comprehensive Nuclear-Test-Ban Treaty (CTBT).

Erratum for ‘Azimuth and elevation estimation for noncircular signals’

Erratum for ‘Azimuth and elevation estimation for noncircular signals’

Azimuth and elevation estimation for noncircular signals

A novel 2D direction-finding algorithm for noncircular signals using two parallel linear arrays, called the extended rank reduction (ERARE) algorithm, is presented. The method needs only 1D search for joint azimuth and elevation estimation. The azimuth and elevation angles estimated by ERARE are paired automatically.

A Novel Direction-Finding Algorithm for Directional Borehole Radar

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A directional borehole radar system has been developed for the purpose of 3-D imaging of subsurface targets in a single-hole measurement. The radar system is equipped with a uniform circular array consisting of four dipole antennas as a receiver in order to realize azimuth bearing sensitivity. We propose a new direction-finding (DF) algorithm that is suitable for directional borehole radar measurement, and we apply this algorithm to actual field measurement data. This algorithm is based on the Adcock DF antenna principle where the complex time series (analytic signal) expression, the optimization, and the filtering procedure are incorporated to provide more accurate estimation. The algorithm was first verified in a transmission measurement in boreholes with a cross-hole configuration (15 m apart from each other) by estimating a direction of the incident wave from a transmitter to the receiver. Finally, the algorithm was applied to single-hole measurement data to demonstrate the ability to detect the 3-D location of a subsurface tunnel which was located 5.5 m from the borehole. The result showed fairly good agreement with the actual location of the tunnel, i.e., to an azimuth estimation error of within 10 <formula formulatype="inline"><tex>$^{\circ}$</tex></formula>. </para>

A Hybrid UCA-RARE/Root-MUSIC Approach for 2-D Direction of Arrival Estimation in Uniform Circular Arrays in the Presence of Mutual Coupling

A new hybrid algorithm that combines the uniform circular array-RAnk REduction (UCA-RARE) and Root-MUSIC algorithm for 2-D direction-of-arrival (DOA) estimation of azimuth and elevation angle is presented for uniform circular arrays in the presence of mutual coupling. To describe mutual coupling and platform effects we rely on the circular symmetry and expand the open-circuit voltages into a limited number of phase modes. This number of phase modes only depends on the electromagnetic dimensions of the UCA and is independent of the severity of mutual coupling in the UCA. The UCA-RARE algorithm is then applied to estimate the azimuth angle independent from the elevation angle. Next, for each azimuth angle we perform a new search-free rooting algorithm based on the expansion of the array manifold into a double Fourier series. By considering several examples, it is shown that even in the presence of severe mutual coupling the proposed combined technique yields very robust DOA estimations for azimuth angle as well as for elevation angle

High-Frequency Tsunami Signals of the Great Indonesian Earthquakes of 26 December 2004 and 28 March 2005

Abstract Tsunamis generated by the great Indonesian earthquakes of 26 December 2004 (Mw 9.3) and 28 March 2005 (Mw 8.6) produced high-frequency (&amp;gt;5 mHz) dispersed signals recorded by hydrophone stations offshore from Diego Garcia and Cape Leeuwin, Australia, and by many seismic stations in the Indian Ocean and on the coast of Antarctica. For the first and greater earthquake, the dispersed energy is commonly observed to 30 mHz and, in one case, to 60 mHz. The high-frequency signals are consistent with being generated at pointlike sources. The earliest arriving tsunami signals originate from a point near 4.3° N, 93.8° E, determined using event- to-station distances estimated by matching predicted dispersion to observations. The location is further constrained with azimuth estimates from an array of hydrophones. Fine structure in the tsunami signal indicates a second high-frequency source just south of Great Nicobar Island near 6.5° N, 93.6° E. The point sources are located close to the maximum slip area determined in several other seismic and tsunami studies. The dispersion of much later-arriving energy is consistent with travel over longer paths, and matches predictions for reflections of the tsunami from bathymetric features in the Indian Ocean basin. For the 28 March 2005 tsunami, the high- frequency dispersion is observed at the Diego Garcia hydrophone station and the AIS seismic station, and tsunami signals without apparent dispersion are seen at four other seismic stations. Phase velocities estimated at hydroacoustic stations agree with linear dispersion theory at frequencies above 12 mHz.

Acoustic positioning using a tetrahedral ultrashort baseline array of an acoustic modem source transmitting frequency-hopped sequences

Acoustic communications and positioning are vital aspects of unmanned underwater vehicle operations. The usage of separate units on each vehicle has become an issue in terms of frequency bandwidth, space, power, and cost. Most vehicles rely on acoustic modems transmitting frequency-hopped multiple frequency-shift keyed sequences for command-and-control operations, which can be used to locate the vehicle with a good level of accuracy without requiring extra signal transmission. In this paper, an ultrashort baseline acoustic positioning technique has been designed, simulated, and tested to locate an acoustic modem source in three dimensions using a tetrahedral, half-wavelength acoustic antenna. The position estimation is performed using the detection sequence contained in each message, which is a series of frequency-hopped pulses. Maximum likelihood estimation of azimuth and elevation estimation is performed using a varying number of pulse and various signal-to-noise ratios. Simulated and measured position estimation error match closely, and indicate that the accuracy of this system improves dramatically as the number of pulses processed increases, given a fixed signal-to-noise ratio.

Azimuth and elevation estimation for multiple sound sources using two‐dimensional frequency domain binaural model

Direction of arrival (DOA) estimation for multiple sound sources with only two sensors as the human being does is proposed. The frequency domain binaural model (FDBM) [Nakashima et al., Acoust. Sci. Technol. 24, 172–178 (2003)] was proposed as one binaural model. The method uses sound diffraction to estimate DOAs and segregate sound sources. The binaural model can estimate one‐dimensional DOA, namely, azimuth. However, human beings can estimate not only azimuth of DOA but also elevation of that. In order to achieve an estimate of both azimuth and elevation simultaneously, a new DOA estimation algorithm based on interaural phase and level differences is proposed as a part of frequency domain binaural model. Results of DOA characteristics of the proposed binaural model estimation on multiple sound sources’ condition is compared with that of human auditory characteristics. As a result, it was confirmed that performance on accuracy of DOA estimation depends on power level ratio among sound sources. [Research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant‐in‐Aid for Scientific Research (C), 2006, 18500135 and carried out by the Cooperative Research Project Program of the RIEC, Tohoku University (Grant No. H16.A02).]

Robust estimates of 3D reflector dip and azimuth

Much of seismic stratigraphy is based on the morphology of seismic textures. The identification of reflector terminations and subtle changes in dip and azimuth allows us to infer coherent progradational and transgressive packages as well as more chaotic slumps, fans, and braided-stream complexes; infill of karsted terrains; gas seeps; and, of course, faults and angular unconformities. A major difficulty in estimating reflector dip and azimuth arises at discrete lateral and vertical discontinuities across which reflector dip and azimuth change. The smearing across these boundaries produced by traditional dip and azimuth estimations is avoided by using temporally and spatially shifted multiple windows that contain each analysis point. This more robust estimation of dip and azimuth leads to increased resolution of well-established algorithms such as coherence, coherent amplitude gradients, and structurally oriented filtering. More promising still is the analysis of high-resolution dip and azimuth through volumetric estimates of reflector curvature and angular unconformities. This new technique is demonstrated using two land data volumes, one from the Louisiana salt province and the other from the fractured Fort Worth basin.

Sumatra tsunamis recorded on hydophones and seismic stations in the Indian Ocean

Tsunamis generated by the great Indonesian earthquakes of 26 December 2004 (Mw 9.3) and 28 March 2005 (Mw 8.6) produced high‐frequency dispersed signals (5 to 60 MHz) recorded by hydrophone and seismic stations in and around the Indian Ocean. For the first and greater earthquake, the dispersed energy is frequently observed to 30 MHz and in one case to 60 MHz. The high‐frequency signals are consistent with pointlike sources. The earliest‐arriving tsunami signal is located to a source at 4.3N, 93.8E using event‐to‐station distances estimated by measuring dispersion and azimuth estimates using an array of hydrophones. Fine structure in the tsunami signal indicates a second high‐frequency source just south of Great Nicobar Island. The dispersion of later‐arriving energy matches predictions for reflections of the tsunami from bathymetric features in the Indian Ocean basin. For the 28 March 2005 tsunami, the high‐frequency dispersion is observed at the Diego Garcia hydrophone station and the AIS seismic station, and tsunami signals without apparent dispersion are seen at four other seismic stations. Phase velocities are estimated at hydroacoustic arrays and agree with linear dispersion theory at frequencies above 12 MHz.

P-Wave Traveltime Analysis and Thomsen Parameters Inversion in Orthorhombic Media

An orthorhombic (ORT) model is the simplest azimuthally anisotropic model used to describe realistic fractured reservoirs (e.g., vertical cracks embedded in an anisotropic background media or orthogonal fracture systems in purely isotropic matrix). In this paper, we calculate the omnidirectional reflection traveltime of P-wave in single orthorhombic media with horizontal interface by using the ray trace method. The reflection Pwave traveltime-distance curves show strong azimuthal anisotropy. Using the Niche Genetic Algorithms (NGA), inversion of reflection traveltime of three common-midpoint (CMP) lines provides us with a good estimation of azimuth, P- wave vertical velocity and Thomsen anisotropic parameters.

Direction of arrival estimation of coherent sources based on arbitrary plane arrays

A method of direction of arrival (DOA) estimation of coherent sources is proposed, which is based on arbitrary plane arrays. After constructing the mathematical model of coherent sources, virtual array transformations and MUSIC algorithm are used to realize the azimuth estimation of coherent sources, which improved the DOA estimation performance greatly. According to the computer simulation, its validity is confirmed.