Roy Edgar Hansen

EM-estimation and modeling of heavy-tailed processes with the multivariate normal inverse Gaussian distribution

The heavy-tailed multivariate normal inverse Gaussian (MNIG) distribution is a recent variance-mean mixture of a multivariate Gaussian with a univariate inverse Gaussian distribution. Due to the complexity of the likelihood function, parameter estimation by direct maximization is exceedingly difficult. To overcome this problem, we propose a fast and accurate multivariate expectation-maximization (EM) algorithm for maximum likelihood estimation of the scalar, vector, and matrix parameters of the MNIG distribution. Important fundamental and attractive properties of the MNIG as a modeling tool for multivariate heavy-tailed processes are discussed. The modeling strength of the MNIG, and the feasibility of the proposed EM parameter estimation algorithm, are demonstrated by fitting the MNIG to real world hydrophone data, to wideband synthetic aperture sonar data, and to multichannel radar sea clutter data.

Signal processing for AUV based interferometric synthetic aperture sonar

This paper presents signal processing techniques particularly suited for interferometric Synthetic Aperture Sonar (SAS) systems onboard Autonomous Underwater Vehicles (AUV) (or other platforms carrying high grade navigation systems). The signal processing is applied to data collected in a controlled rail experiment at Elba Island, Italy, using a wideband interferometric SAS and an Inertial Navigation System (INS). We evaluate different strategies in fusing sonar micronavigation by the Displaced Phase Center Antenna (DPCA) technique with Aided INS (AINS). We obtained highest navigation accuracy using DPCA as aiding sensor into the AINS, then using raw DPCA surge and sway in combination with the AINS attitude and position. Coarse cross correlation based bathymetry and full resolution interferometry (based on the interferogram) is tested on the full swath and objects. Coarse bathymetry is more reliable than the interferogram technique. Phase wraparounds are avoided by estimating the coarse bathymetry first, then using the full resolution phase estimates as correction. Although much work remains, this technique does show a clear potential in improving object classification ability.

Challenges in Seafloor Imaging and Mapping With Synthetic Aperture Sonar

Synthetic aperture sonar (SAS) is emerging as an imaging technology that can provide centimeter resolution over hundreds-of-meter range on the seafloor. Although the principle of SAS has been known for more than 30 years, SAS systems have only recently become commercially available. The success of SAS is critically dependent on overcoming several challenges related to the ocean environment. The sonar has to be positioned with accuracy better than a fraction of a wavelength along the synthetic aperture. We use the sensor itself for navigation, in combination with aided inertial navigation. The sound velocity has to be accurately estimated for successful focusing of SAS images. We calculate a simple rule of thumb for tolerance and show the effect of incorrect sound velocity. For nonstraight synthetic apertures, the bathymetry must be estimated. We use real aperture interferometry to map the scene before SAS processing. We calculate the required bathymetry accuracy and show the effects of insufficient mapping. Vehicle instability and nonstraight tracks, in combination with insufficient navigation accuracy, can cause grating lobes in the SAS images, which is not common in single-channel synthetic aperture radars. We show example imagery with severe grating lobes. In shallow waters, the acoustic signals will interact with the sea surface, possibly causing multipath. This will reduce the SAS quality. We use coherence to map the signal to multipath and, thereby, the valid sensor range. This paper illustrates the different challenges using examples from the HISAS 1030 interferometric SAS.

Introduction to Synthetic Aperture Sonar

SONAR is an acronym for SOund Navigation And Ranging. The basic principle of sonar is to use sound to detect or locate objects, typically in the ocean. Sonar technology is similar to other technologies such as: RADAR = RAdio Detection And Ranging; ultrasound, which typically is used with higher frequencies in medical applications; and seismic processing, which typically uses lower frequencies in the sediments. There are many good books that cover the topic of sonar (Burdic, 1984; Lurton, 2010; Urick, 1983). There are also a large number of books that cover the theory of underwater acoustics more thoroughly (Brekhovskikh & Lysanov, 1982; Medwin & Clay, 1998). The principle of Synthetic aperture sonar (SAS) is to combine successive pings coherently along a known track in order to increase the azimuth (along-track) resolution. A typical data collection geometry is illustrated in Fig. 1. SAS has the potential to produce high resolution images down to centimeter resolution up to hundreds of meters range. This makes SAS a suitable technique for imaging of the seafloor for applications such as search for small objects, imaging of wrecks, underwater archaeology and pipeline inspection. SAS has a very close resemblance with synthetic aperture radar (SAR). While SAS technology is maturing fast, it is still relatively new compared to SAR. There is a large amount of SAR literature (Carrara et al., 1995; Cumming & Wong, 2005; Curlander & McDonough, 1991; Franceschetti & Lanari, 1999; Jakowatz et al., 1996; Massonnet & Souyris, 2008). This chapter gives an updated introduction to SAS. The intended reader is familiar with sonar but not SAS. The only difference between traditional sonar and synthetic aperture is

Shadow Enhancement in Synthetic Aperture Sonar Using Fixed Focusing

A shadow cast by an object on the seafloor is important information for target recognition in synthetic aperture sonar (SAS) images. Synthetic aperture imaging causes a fundamental limitation to shadow clarity because the illuminator is moved during the data collection. This leads to a blend of echo and shadow, or geometrical fill-in in the shadow region. The fill-in is most dominant for widebeam synthetic aperture imaging systems. By treating the shadow as a moving target and compensating for the motion during the synthetic aperture imagery, we avoid the geometrical shadow fill-in. We show this to be equivalent to fixing the focus at the range of the shadow caster. This novel technique, referred to as fixed focus shadow enhancement (FFSE) can be used directly as an imaging method on hydrophone data or as a postprocessing technique on the complex SAS image. We demonstrate the FFSE technique on simulated data and on real data from a rail-based SAS, and on two different SAS systems operated on a HUGIN autonomous underwater vehicle.

Improving Sonar Performance in Shallow Water Using Adaptive Beamforming

Multipath propagation degrades the performance of active, bottom-imaging sonars in shallow-water environments. One way to avoid multipath interference is to use a vertical array with a narrow enough angular response to separate the direct bottom return from the multipath. However, this requires a large array and is often infeasible for practical reasons. In this study, we focus on the use of adaptive beamforming on the receiver side to reduce multipath interference and hence improve the signal-to-noise ratio (SNR). Using a small, dense receiver array, we apply classical and adaptive beamformers to real data collected by the NATO Undersea Research Centre in a shallow-water environment. Our results show that the adaptive minimum variance distortionless response (MVDR) beamformer offers an improvement in the estimated SNR compared to a conventional beamformer in most cases. However, the MVDR beamformer is suboptimal when the receiver consists of only a few elements. We propose using the low complexity adaptive (LCA) beamformer, which is based on the same optimization criteria as the MVDR beamformer, but is robust in a coherent environment without the need for spatial smoothing. For two to 4-element receivers, we observe an improvement of about 0.5-2.5 dB in the estimated SNR when using the LCA beamformer. In cases where the model indicates that the direct bottom return and the dominating multipath arrive from nearly the same angle, little or no improvement is observed. This is typically the case for first- or second-order multipaths reflected off the seafloor toward the receiver. The results from this study also show that with a small vertical array, a narrow mainlobe width is more important than low sidelobe levels, in terms of maximizing the SNR. Consequently, an unweighted conventional beamformer performs better than a conventional beamformer with a Hanning window applied for sidelobe suppression.

Change detection using Synthetic Aperture Sonar: Preliminary results from the Larvik trial

In April of 2011, FFI led a sea trial near Larvik, Norway on FFIs research vessel the H.U. Sverdrup II with participation by representatives from Canada, United States, and France. One objective of the sea trial was to acquire a data set suitable for examining incoherent and coherent change detection and automated target recognition (ATR) algorithms applied to Synthetic Aperture Sonar (SAS) imagery. The end goal is to produce an automated tool for detecting recently placed objects on the seafloor. To test these algorithms two areas were chosen, one with a comparatively benign seafloor and one with a boulder strewn complex seafloor. Each area was surveyed before and after deployment of objects. The survey time intervals varied from two days to eight days. In this paper we present the trial and show examples of SAS images and change detection of the images.

Bathymetric Capabilities of the HISAS Interferometric Synthetic Aperture Sonar

Multibeam echo-sounders have until now been the leading technology in seabed mapping, but typically have resolutions of around half a metre. Recently, synthetic aperture sonar (SAS) technology has matured to a commercial level, delivering sidelooking imagery with a resolution of a few centimetres to a range of several hundred metres. High resolution sidelooking imagery makes interferometry an extremely interesting technique for bathymetric processing. In this paper we discuss the theoretical accuracy in relative height mapping of the new HISAS interferometric SAS and compare the results with processing of simulated data. We also demonstrate SAS interferometry on real data collected with a prototype SAS mounted on a HUGIN AUV. Different filtering techniques are applied to the data, illustrating the trade-off between resolution, robustness and smoothness.

Relative Height Estimation by Cross-Correlating Ground-Range Synthetic Aperture Sonar Images

The relative height of the seafloor can be estimated by using two vertically displaced receivers. In this paper, we propose techniques to improve the accuracy of the estimated height. Our results are based on the use of synthetic aperture sonar (SAS) imaging, which implies coherent addition of complex images acquired from a moving platform. The SAS processing improves the along-track (or azimuth) resolution, as well as the signal-to-noise ratio (SNR), which in turn improves the estimated height accuracy. We show that the shift of the effective center frequency induced by coherent, frequency-dependent scattering affect the time-delay estimates from complex cross correlations, and we propose a correction technique for broadband signals with uneven magnitude spectra. To reduce the effect of geometrical decorrelation and increase the coherence between the images, we beamform the sonar images onto an a priori estimate of the seafloor height before correlating. We develop a mathematical model for the imaging geometry. Finally, we demonstrate our proposed estimators by providing relative seafloor height estimates from real aperture and SAS images, obtained during the InSAS-2000 experiment at Elba Island in Italy. In particular, we demonstrate that the SAS image quality is significantly improved by inclusion of the height estimates as a priori information.

Adaptive Beamforming Applied to a Cylindrical Sonar Array Using an Interpolated Array Transformation

In applications such as fishery sonar and navigation, cylindrical or spherical arrays are often used because of the need for a 360° field of view. However, adaptive beamforming methods, known for their high angular resolution and interference rejection capabilities, often rely on a Vandermonde structure of the steering vectors. This is generally not the case for nonlinear arrays. In this paper, we use an interpolated array transformation to map the data to a virtual linear array before adaptive beamforming. We evaluate the performance of two different adaptive beam- formers using simulations as well as experimental data from the SX90 fish finding sonar. We show that the adaptive minimum variance (MV) and amplitude and phase estimation of a sinusoid (APES) beamformers offer a significant improvement in azimuth resolution compared to the conventional delay-and-sum (DAS) beamformer. The APES beamformer offers slightly more reliable amplitude estimates in the direction of interest compared to the MV beamformer, at the cost of a somewhat lower azimuth resolution. When applied to data from the SX90 fish finding sonar, the MV beamformer offers a 40%-50% improvement in resolution, while the APES beamformer offers an improvement of 20%-30%.