Source Localization Performance Research Articles

Source localization at very long ranges in the presence of large-scale spatial variability

Large-scale spatial variability in the ocean environment results in uncertain sound-speed variations on the order of 10–15 m/s, a potentially significant factor in many ocean acoustic applications. The effect of this variability on source localization performance at a range of one megameter is investigated. The optimum uncertain field processor (OUFP) [A. M. Richardson and L. W. Nolte, J. Acoust. Soc. Am. 89, 2280–2284 (1991)], in its narrow-band and wideband forms, is introduced as an alternate and superior processor to the traditional Bartlett processor for this application. The Bartlett processor, which assumes the environmental parameters to be the average values, essentially ignores the large-scale spatial fluctuations. Optimally incorporating a priori information about the environmental and source parameters, as does the OUFP, makes this processor robust to uncertainty in these parameters and provides an upper bound on localization performance. Measures such as a posteriori distributions of source location, the probability of correct localization, and the standard deviation of range estimation error reveal that the spatial variability has a significant degrading effect on localization performance, the magnitude of which is dependent on the source frequency. Results are discussed for 25- and 75-Hz sources as well as their coherent and random combinations. [Research supported by ONR (Ocean Acoustics).]

Narrow-band source localization in the presence of internal waves for 1000-km range and 25-Hz acoustic frequency

The effects of internal waves on low-frequency (25 Hz) narrow-band source localization performance are investigated at a very long range (1000 km). Sound-speed perturbations induced by internal waves obeying the Garrett–Munk spectral model are incorporated into the normal mode solution to the wave equation using the adiabatic approximation. Sensitivity of source localization on the internal wave modal content is examined. For the entire range of signal-to-noise ratios (SNR) and degrees of internal-wave field structure, the optimal uncertain field processor (OUFP) provides both the signal processing algorithm as well as the limitations on source localization performance. For high SNR, the localization errors are local and the performance level of the OUFP is predicted by the hybrid Cramer–Rao lower bound (CRLB). In fairly structured internal-wave environments, significant performance gains are made optimally localizing the source. Under very random internal-wave environments, the environmental variability limits the performance of all signal processing algorithms.

Robust wideband matched-field processing with a short vertical array

This paper addresses the problem of matched-field passive localization of broadband underwater acoustic sources with a short vertical array. In previous work, incoherent averaging of narrow-band Bartlett ambiguity surfaces has been proposed to improve the robustness of matched-field processing (MFP) to environmental uncertainties. While computationally efficient, the effectiveness of this approach is dependent on the type of environmental mismatch present. In this paper, to provide robust source localization performance for short arrays, an alternative wideband MFP method is proposed which utilizes the fourth-order statistics of the data. The method is “coherent” in that it exploits cross-frequency dependencies in the random acoustic channel response. The proposed coherent wideband minimum variance method with environmental perturbation constraints (MV-EPC) consists of minimizing the squared output power of a beamformer subject to constraints defined across the signal band. The constraints are designed to provide robustness over an ensemble of random environmental realizations. Monte Carlo simulation results using a canonical shallow-water scenario indicate that the coherent wideband MV-EPC method yields improved probability of correct localization performance versus incoherent averaging of narrow-band Bartlett ambiguity functions with a short array above a threshold signal-to-noise ratio.

Narrow-band source localization in the presence of internal waves

The effects of internal waves on low-frequency (25-Hz) narrow-band source localization performance are investigated at very long ranges (1000 km). Sound-speed perturbations induced by an internal-wave obeying the Garrett–Munk spectrum are incorporated into the normal mode solution to the wave equation using the adiabatic approximation. Sensitivity of source localization on the internal wave modal content is examined. For the entire range of signal-to-noise ratios (SNR) and degrees of randomness in the internal wave field, the optimal uncertain field processor (OUFP) provides both the signal processing algorithm as well as the limitations on source localization performance. For high SNR, the localization errors are local and the performance level of the OUFP is predicted by the hybrid Cramer–Rao lower bound (CRLB). In fairly structured internal-wave environments, significant performance gains are made optimally localizing the source. Under very random internal-wave environments, the environmental variability limits the performance of all signal processing algorithms. [Research supported by ONR (Ocean Acoustics).]

Inversion for geometric and geoacoustic parameters in shallow water: Experimental results

Experimental results on the estimation of both geometric and geoacoustic parameters in shallow water are presented. Genetic algorithms are used for estimation of the forward model parameters; the estimated parameters are then used by a standard Bartlett processor for source localization. A stationary source at a range of 5.6 km and a moving source at ranges from 5.8–7.7 km were successfully localized in range and depth using a single frequency Bartlett processor. The results indicate that global estimation of the forward model parameters significantly improves source localization performance.

COMPUTATIONALLY EFFICIENT MONTE CARLO ESTIMATION ALGORITHMS FOR MATCHED FIELD PROCESSING IN UNCERTAIN OCEAN ENVIRONMENTS

In this paper, Monte Carlo estimation techniques are presented for computationally efficient implementation of two methods for matched field source localization in uncertain ocean channels. In the Optimal Uncertain Field Processor (OUFP), Monte Carlo integration is used to integrate out the environmental parameters and thus estimate the a posteriori distribution of the source location parameters. In the Minimum Variance Beamformer with Environmental Perturbation Constraints (MV-EPC), Monte Carlo estimation of the signal correlation matrix averaged over the ensemble of environmental realizations is used to estimate the beamformer constraints. Using the OUFP, detection performance bounds are evaluated which indicate that source position uncertainty affects performance much more than environmental uncertainty. An upper bound on source localization performance is also obtained indicating that for short observation times a threshold signal-to-noise ratio (SNR) exists, dependent upon environmental uncertainty, below which source localization performance rapidly degrades. Among robust minimum variance beamforming methods, the MV-EPC method demonstrated superior probability of correct localization (PCL), both in single source scenarios and in the presence of interference. The OUFP at high SNR and the MV-EPC at large observation times both achieved near perfect source localization performance, although for large environmental uncertainty the OUFP provides an upper bound on P CL .

MATCHED FIELD SOURCE LOCALIZATION WITH A HORIZONTAL LINE ARRAY

Matched field source localization performance is investigated for a source in aft endfire of a horizontal line array operating in a deep water environment. Simulations are used to investigate the performance for ideal conditions and in the presence of noise. In particular, the effects of uncertainty in experimental geometry and mismatch in sound speed profile are considered. It is shown that the performance is sensitive to the vertical tilt of the array for relatively small tilt angles of less than 5º. However, the horizontal array is robust to mismatch in the gradient of the sound speed profile at the bottom of the water column. The results of the simulations are interpreted in terms of the characteristics of acoustic propagation in the environment.

Environmental data assimilation in matched-field processing with a random normal mode model

Numerical acoustic propagation models used in matched-field processing typically assume that ocean environmental parameters, such as the range-dependent sound-speed profile, are either known exactly or are characterized by stationary prior statistics. However, neither of these modeling approaches is well suited for accurately assimilating measurements of the correct ocean realization into the calculation of point-source acoustic wave front statistics. In this paper, environmental data is assimilated into a random adiabatic normal mode propagation model by calculating the conditional correlation matrix of an acoustic wave front given a set of contemporaneous sound-speed profile measurements made at different points in space. First-order perturbation theory is used to map the conditional statistics of Gaussian-distributed excess sound-speed variations into an estimate of the conditional point-source wave front correlation matrix. Minimum variance beamforming with environmental perturbation constraints [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1419 (1992)] conditioned on current environmental measurements is demonstrated as a means of exploiting this random wave front model to achieve improved matched-field source localization performance. [Work supported by ONR.]

Matched-field processing in a shallow-water channel with a random bottom

An important source of uncertainty in shallow-water propagation models used for minimum variance (MV) matched-field processing is bottom roughness or irregular bathymetry. A perturbative solution to the Helmholtz equation which gives the point source field in a shallow-water waveguide with rough boundaries has been derived in [W. Kuperman and H. Schmidt, J. Acoust. Soc. Am. 86, 1511–1522 (1989)]. This formulation yields an expression for the point-source wave front correlation matrix which is determined by the coherent field and a scattered field generated by random secondary sources at the bottom interface. Alternatively, adiabatic normal modes and first-order perturbation of the horizontal modal wave numbers also provides a solution for the wave front correlation matrix in terms of the second-order statistics of the random bottom depth. In this paper, matched-field source localization performance under both these models is evaluated for several MV beamforming approaches. Minimum variance beamforming with environmental perturbation constraints [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1418 (1992)] is demonstrated to be an approach which can exploit these random propagation models to achieve robust matched-field source localization. [Work supported by ONR.]

Source imaging and sidelobe suppression using time-domain techniques in a shallow-water waveguide

Source localization in a shallow-water waveguide, using harmonic (cw) techniques, is typically complicated by the repetitive sidelobe structure of the acoustic field. For this reason, much interest has been shown recently in the development and implementation of time-domain methods, which should achieve better performance because of their additional frequency-averaging capability. In a previous publication [C. S. Clay, J. Acoust. Soc. Am. 81, 660–664 (1987)], the basis for optimum signal transmission and source localization in a waveguide using time-domain techniques was described. In this present work a simple two-layer Pekeris model with shallow water depth (20 m) and short range (1500 m) has been used to compute image resolution and sidelobe suppression as a function of frequency bandwidth, number of modes, and the number of receivers in an array. The results indicate that source localization performance is most strongly dependent upon the bandwidth and number of modes available to carry the signal transmission. The physical mechanism for narrowing the source image and suppressing sidelobes is spatial averaging of the acoustic field due to variation of the horizontal wave numbers for the modes as a function of frequency. Improvements in mode sampling, by increasing the number of receivers, also reduced the level of sidelobes, but did not improve the resolution of the image.

Source localization performance and the array beampattern

Passive localization of sources in space is done using data collected by an array of sensors. The performance of all source location estimation (SLE) algorithms depends on the source-array geometry. In this paper we study this dependence and we show that array localization ability is uniquely determined by a single scalar function — the array beampattern. By analyzing absolute lower bounds on the mean-square-error (mse) of the source location estimates in different scenarios we exploit the relation between features of the array beampattern and the best achievable array localization performance. The beampattern is characterized by its sidelobes level and smoothness, its beamwidth and its mainlobe curvature. We study the effect of these features on source localization properties such as sensitivity to the presence of other sources, resolution ability, sensitivity to ambiguous estimates, etc. Passive Ortung von Quellen im Raum wird mit von Sensorfeldern aufgenommenen Daten durchgeführt. Die Leistungsfähigkeit aller Algorithmen zur Ortung von Quellen hängt von der Quellen-Antennen Geometrie ab. In diesem Aufsatz wird letztere Abhängigkeit untersucht, und es wird gezeigt, daß das Lokalisierungsvermögen einer Antenne eindeutig von einer einzelnen skalaren Funktion, der Richtcharateristik, bestimmt ist. Es wird bei der Untersuchung der absoluten unteren Grenze des erwarteten quadratischen Fehlers der Ortsschätzung der Quellen bei verschiedenen Szenarien die Beziehung zwischen Merkmalen der Richtcharakteristik und dem besten erreichbaren Ortungsvermögen der Antenne ausgenutzt. Die Richtcharakteristik wir beschrieben durch die Höhe und Glattheit der Nebenkeulen, die Keulenhalbwertsbreite und die Krümmung der Hauptkeule. Wir untersuchen die Auswirkungen dieser Merkmale auf die Lokalisierungseigenschaften, wie z.B. Empfindlichkeit bezüglich der Anwesenheit anderer Quellen, Auflösungsvermögen, Empfindlichkeit bezüglich mehrdeutiger Schätzungen, etc. La localisation passive de sources dans l'espace est réalisée à l'aide de données collectées par un réseau de capteurs. Les performances de touts les algorithmes d'estimation de position de source (SLE) dépendent de la géométrie source-réseau. Nous étudions dans cet article cette dépendance et nous montrons que la capacité de localisation du réseau est déterminée uniquement par une fonction scalaire simple — le modèle de voie du réseau. Par une analyse des bornes inférieures absolues des estimées au sens de l'erreur aux moindres carrés (mse) de la position de la source pour différents scénarios nous exploitons la relation existant entre les caractéristiques du modèle de voie du réseau et la meilleure performance de localisation possible du réseau. Le modèle de voie est caractérisé par le niveau de ses lobes secondaires et leur lissage, sa largeur de voie et la courbure du lobe principal. Nous étudions l'effet de ces caractéristiques sur les propriétés de localisation de source telles que sensibilité à la présence d'autres sources, capacité de résolution, sensibilité aux estimées ambigues, etc.

Environmental mismatching effects on source localization processing in mode space

In this paper the source localization performance degradation of the matched field processing (MFP) caused by environmental mismatch has been discussed for HRMM processor [E. C. Shang, J. Acoust. Soc. Am. 86, 1960–1964 (1989)] in mode space analytically. By using the approximate modal eigenvalue solution, the analytic expressions for describing the impacts of water-depth mismatch in a Pekeris waveguide and sediment-type mismatch have been derived. By using the modal perturbation theory an indicator for assessing the range performance degradation caused by sound-speed profile (SSP) mismatch has been proposed. Analytic results have been verified by numerical simulations.

Source imaging and sidelobe suppression using time‐domain techniques in a shallow‐water waveguide

Source localization in a shallow‐water waveguide, using harmonic (cw) techniques, is typically complicated by the repetitive sidelobe structure of the acoustic field. For this reason, much interest has been shown recently in the development and implementation of time‐domain methods, which should achieve better performance because of their additional frequency‐averaging capability. In a previous publication [C. S. Clay, J. Acoust. Soc. Am. 81, 660–664 (1987)], the basis for optimum signal transmission and source localization in a waveguide using time‐domain techniques was described. In the work reported here, using a simple two‐layer model with shallow water depth (20 m) and short range (1500 m), the variation in time‐domain source image resolution and sidelobe suppression as a function of frequency bandwidth, mode selection, and hydrophone receiver emplacement has been investigated. The results indicate that source localization performance is most strongly dependent upon the bandwidth and number of modes available to carry the signal transmission. The physical mechanism for narrowing the source image and suppressing sidelobes is spatial averaging of the acoustic field due to variation of the horizontal wave numbers for the modes as a function of frequency. Improvements in mode sampling, by increasing the number of receivers, also served to reduce the level of sidelobes, but did not improve the resolution of the image. [This work was sponsored by the Naval Oceanographic and Atmospheric Research Laboratory.]

SQUID arrays for simultaneous magnetic measurements: calibration and source localization performance

Recently developed small arrays of SQUID- (superconducting quantum interference device) based magnetic sensors can, if appropriately placed, locate the position of a confined biomagnetic source without moving the array. A technique is presented having a relative accuracy of about 2% for calibrating such sensors having detection coils with the geometry of a second-order gradiometer. The effects of calibration error and magnetic noise on the accuracy of locating an equivalent current dipole source in the human brain are investigated for five- and seven-sensor probes and for a pair of seven-sensor probes. With a noise level of 5% of peak signal, uncertainties of about 20% in source strength and depth for a five-sensor probe are reduced to 8% for a pair of seven-sensor probes, and uncertainties of about 15 mm in lateral position are reduced to 1 mm for the configuration considered. >