Statistical modeling of interferometric signals in underwater applications

International audienceCurrent sonar and radar applications use interferometry to estimate the arrival angles of backscattered signals at time-sampling rate. This direction-finding method is based on a phase-difference measurement between two close receivers. To quantify the associated bathymetric measurement quality, it is necessary to model thestatistical properties of the interferometric-phase estimator. Thus, this paper investigates the received signal structure, decomposing it into three different terms: a part correlated on the two receivers, an uncorrelated part and an ambient noise term. This paper shows that the uncorrelated part and the noise term can be merged into a unique, random term damaging the measurement performance. Concerning the correlated part, its modulus can be modeled either as a random or a constant variable according to the type of underwater acoustic application. The existence of these two statistical behaviors is verified on real data collected from different underwater scenarios such as a horizontal emitter-receiver communication and a bathymetric seafloor survey. The physical understood of the resulting phase distributions makes it possible to model and simulate the interferometric-signal variance (associated with the measurement accuracy) according to the underwater applications through simple hypotheses

Simulation on large scale of acoustic signals for array processing

International audienceDue to operational constraints for underwater data acquisition, simulating realistic sonar data, like images, swath bathymetry profiles or interferometric signals, is crucial for tuning detection and classification algorithms according to sensors settings, sea-bottom nature and topography. Moreover, the robustness of any performance estimation or prediction can be greatly enhanced, as soon as such a simulation tool provides a modular and flexible underwater world representation (multiple sensors, environments and acquisition conditions). For signal and array processing, it is essential not only to generate the signal energy backscattered by a resolution cell, but also to produce a phase information that conveys its theoretical statistical properties. To this end, this paper proposes a Brownian motion-based approach to generate complex Gaussian signals from the contribution of a set of extended single scatterers inside a resolution cell. The resulting process preserves the conservation of energy when integrating on surfaces, as well as the decorrelation between different areas of the sea bottom, and the right interference between two sensors for interferometric applications

Advanced interferometric techniques for high resolution bathymetry

International audienceCurrent high-resolution side scan and multibeam sonars produce very large data sets. However, conventional interferometry-based bathymetry algorithms underestimate the potential information of such soundings, generally because they use small baselines to avoid phase ambiguity. Moreover, these algorithms limit the triangulation capabilities of multibeam echosounders to the detection of one sample per beam, i.e., the zero-phase instant. In this paper we argue that the correlation between signals plays a very important role in the exploration of a remotely observed scene. In the case of multibeam sonars, capabilities can be improved by using the interferometric signal as a continuous quantity. This allows consideration of many more useful soundings per beam and enriches understanding of the environment. To this end, continuous interferometry detection is compared here, from a statistical perspective, first with conventional interferometry-based algorithms and then with high-resolution methods, such as the Multiple Signal Classification (MUSIC) algorithm. We demonstrate that a well-designed interferometry algorithm based on a coherence error model and an optimal array configuration permits a reduction in the number of beam formings (and therefore the computational cost) and an improvement in target detection (such as ship mooring cables or masts). A possible interferometry processing algorithm based on the complex correlation between received signals is tested on both sidescan sonars and multibeam echosounders and shows promising results for detection of small in-water targets

Empirical Interferometric Phase Variance Formulas for Bathymetric Applications

National audienceCurrent sonar and radar applications use interferometry to estimate the arrival angles of backscattered signals. This direction-finding method is based on a phase-difference measurement between two close receiving arrays. To model the associated bathymetric error, it is necessary to know the second-order moment of the interferometric phase estimator. This paper explains the connection between bathymetric variance and interferometric phase variance and the difficulty in the evaluation of the phase second-order estimation. Thus, a brief statistical overview of the interferometric phase estimator for fully developed speckle signals (called here RMPC for random modulus partially correlated signals) is introduced in this paper. The focus of this paper is the derivation of simple empirical variance that matches the exact values in both single-look and multilook cases. For the sake of constituency, the construction of these empirical approximations is based on a modified asymptotic expression of the second order for the phase estimator assuming high signal-to-noise ratio. In order to perform these derivations, it appears necessary to introduce a new kind of signal (namely, CMPC for constant modulus partially correlated signal) whose modulus is assumed constant. This family of signals, whose physical existence is also investigated, appears as an alternative way to derive RMPC empirical formulas. The link between RMPC and CMPC signals is established through the conditional expectation of the signal modulus. Finally, the existence of these two statistical behaviors is tested over real underwater data

Interferometric angle estimation for bathymetry performance analysis

International audienceThe quality of depth measurements used in either sonar or radar applications determines the confidence on the mapping accuracy. Several methods can be considered to determine this depth measurement, ranging from amplitude-based detection, interferometry, to complex signal-based detection, such as so-called high-resolution methods. This paper is devoted to the analysis of interferometry accuracy according to the nature of the recorded signal. Indeed, the level of fluctuation of the received signal depends on the remote-sensing application under consideration. In applications where both transmitter and receiver are linked with a direct path, e.g. underwater positioning applications or some underwater acoustic communication systems, neither a backscattering nor multipath effects increases the intrinsic fluctuating nature of signal. Conversely, in sonar bathymetry or radar earth-surface relief applications, the received signal suffers from reflection or backscattering effects, resulting in a more probable random behavior. Hence, the goal of this paper is first to investigate the behavior of two different signal models (stable and fluctuating targets), second to determine the associated signal fluctuation level, and finally, to intend to relate their interferometry accuracies. The different expressions of the interferometry accuracy will make it possible to adapt the accuracy computation of interferometry measurements to the application under consideration. Furthermore, a set of easy-to-use interferometry-accuracy expression will result from the statistical analysis, enabling simple topographic performance prediction

Sonars cartographiques et interférométrie associée

National audienceL'interférométrie est une technique qui prend une place de plus en plus importante dans les applications sonars et en particulier pour les sonars cartographiques. Ceci s'explique par la simplicité de mise en ?uvre de cette technique et le gain de précision qu'elle apporte. Cet article propose d'analyser les fonctionnements de différents types de sonars cartographiques, en particulier les sonars latéraux et multifaisceaux. Dans un premier temps sont analysés les fonctionnements spécifiques de ceux-ci, en mode classique puis en mode interférométrique. Si cette technique s'adapte très bien à ces appareils de télédétection, le traitement des données nécessite quelques précautions avant de pouvoir reconstruire de manière tridimensionnelle, l'environnement du fond sous marin. Ces précautions concernent les hypothèses de base à respecter ainsi que la prise en considération de l'impact du bruit sur la qualité de la phase interférométrique. En définitive, l'interférométrie reste une technique simple qui permet d'accroître les performances des outils de télédétection sous marine

Analysis of Vernier interferometers for sonar bathymetry

International audienceUnderwater bathymetry applications are based on the estimation of the echoed target spatial oordinates in order to map the sea bottom. A quick and reliable approach consists in carrying out the interferometry method. This direction-finding technique estimates the arrival angle of backscattered signals through the propagation time delay between two close sensors. This time delay can be determined from the phase difference between signals received by each sensor, but its value is limited to a 2π-length interval due to the computation of the complex argument operator. As the effective phase difference may exceed this range, according to spacing between sensors, a 2π rotation counter may be introduced within the direction-finding signal processing in order to remove the phase ambiguity. This paper introduces the Vernier principle in order to remove the 2π-phase ambiguity, enhancing the main assets and analyzing the best interferometer configuration to minimize the drawbacks. Mastering this technique allows the use of individual phase-angle samples for both sidescan sonars and multibeam echosounders, thus increasing the target detection capabilities by bringing out an image-like bathymetric resolution

Improving spatial resolution of interferometric bathymetry in multibeam echosounders

International audienceMost multibeam echosounders used in seafloor mapping perform the interferometry method for bathymetry measurement, based on the zero-crossing of the phase difference between two sub-arrays. In this approach, only one sounding is computed per formed beam, and the spatial resolution is linked to the beam footprint extent. Using the whole content of the phase-difference signal vs. time makes it possible to ideally get a bathymetry data sampled at the very resolution of the digitized signal. However, this approach compels the phase difference to be unambiguous. Indeed, when the phase difference is determined through the argument operator, the resulting value is truncated within a 2pi-length interval. To tackle this hitch, this paper presents and compares techniques to remove the phase ambiguity based upon interferometry, cross correlation and high-resolution methods. Figures are illustrated by results obtained on a shipwreck, enhancing the difficulties of each removal technique

Sonars cartographiques et interférométrie associée

National audienceL'interférométrie est une technique qui prend une place de plus en plus importante dans les applications sonars et en particulier pour les sonars cartographiques. Ceci s'explique par la simplicité de mise en ?uvre de cette technique et le gain de précision qu'elle apporte. Cet article propose d'analyser les fonctionnements de différents types de sonars cartographiques, en particulier les sonars latéraux et multifaisceaux. Dans un premier temps sont analysés les fonctionnements spécifiques de ceux-ci, en mode classique puis en mode interférométrique. Si cette technique s'adapte très bien à ces appareils de télédétection, le traitement des données nécessite quelques précautions avant de pouvoir reconstruire de manière tridimensionnelle, l'environnement du fond sous marin. Ces précautions concernent les hypothèses de base à respecter ainsi que la prise en considération de l'impact du bruit sur la qualité de la phase interférométrique. En définitive, l'interférométrie reste une technique simple qui permet d'accroître les performances des outils de télédétection sous marine

Coherent probabilistic error model for interferometric sidescan sonars

International audienceInterferometry is widely used in bathymetric applications to relate short time delays between two separate sensors to wavefront arrival angles. The main difficulty of this method concerns its sensitivity with regard to the distance between the two sensor receivers, commonly called baseline. Indeed, the baseline, which is only a few wavelengths long, is sufficient to triangulate the direction of an echo, which can be several hundred meters away. Due to the usual short baseline size, the direction of arrival (DOA) resulting from an interferometric measurement is very sensitive to noise, which can reduce accuracy and handicap the data for immediate use. Interferometric measurements are confined to a $2pi$-length interval, and yet, the time-delay dynamic range can go beyond this length. As a result, the phase delay is estimated with a $2pi$-modulo ambiguity. This study focuses on the accuracy problem and tries to make a bathymetric performance estimation. The statistical behavior of the interferometric signal is the keystone of the problem as it allows the bathymetric measurement error to be derived. Because of the very singular nature of the interferometric signal, the noise aspect is not analyzed as a classical additive perturbation, but as a decorrelation between receivers. Thus, a coherent error fusion (CEF) makes it possible to directly integrate the impact of several degrading phenomena into the interferometric-phase probability density function (pdf) and thus, to improve the bathymetric performance prediction compared with a classical root mean squared error (RMSE) integration. Finally, the CEF prediction model is tested on real data collected with a 455-kHz sidescan sonar, and compared with the RMSE-based prediction approach