IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007 971 Relative Height Estimation by Cross-Correlating Ground-Range Synthetic Aperture Sonar Images Torstein Olsmo Sæbø, Member, IEEE, Roy Edgar Hansen, Member, IEEE, and Alfred Hanssen, Senior Member, IEEE Abstract—The relative height of the seafloor can be estimated by using two vertically displaced receivers. In this paper, we pro- pose 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 ac- quired 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 cor- rection technique for broadband signals with uneven magnitude spectra. To reduce the effect of geometrical decorrelation and in- crease the coherence between the images, we beamform the sonar images onto an a priori estimate of the seafloor height before cor- relating. We develop a mathematical model for the imaging ge- ometry. Finally, we demonstrate our proposed estimators by pro- viding 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 esti- mates as a priori information. Index Terms—Bathymetry, coherence, cross correlation, height estimation, interferometry, synthetic aperture sonar (SAS), time- delay estimation. I. INTRODUCTION D ETAILED seabed mapping plays an important role in a number of different areas such as offshore exploration, marine research, environmental surveillance, and military applications. Typically, multibeam echo sounders (MBE), or alternatively, bathymetric sidescan sonar systems are applied [1, pp. 266–267], [2]. Both technologies are limited by the along-track (azimuth) resolution, given by the physical trans- ducer array size. Synthetic aperture sonar (SAS) has emerged as an attractive technique to improve along-track resolution [3]. While synthetic aperture radar (SAR) interferometry has grown to a mature high-resolution terrain mapping tool [4], [5], the corresponding underwater technology, interferometric SAS [6], [7], has yet to be explored to its full potential. Manuscript received March 30, 2006; revised October 10, 2006 and February 28, 2007; accepted March 2, 2007. The work of A. Hanssen was supported by the Research Council of Norway under Project 162831. Associate Editor: A. Trucco. T. O. Sæbø is with the Norwegian Defence Research Establishment (FFI), Kjeller NO-2027, Norway and the University of Tromsø, Tromsø NO-9037, Norway (e-mail: torstein-olsmo.sabo@ffi.no). R. E. Hansen is with the Norwegian Defence Research Establishment (FFI), Kjeller NO-2027, Norway (e-mail: roy-edgar.hansen@ffi.no). A. Hanssen is with the Department of Physics and Technology, University of Tromsø, Tromsø NO-9037, Norway (e-mail: alfred.hanssen@phys.uit.no). Digital Object Identifier 10.1109/JOE.2007.895244 The standard height-estimation technique based on SAR interferometry consists of utilizing the phase differences in complex images collected from different aspect angles [8]. This technique, often referred to as direct phase-differencing or interferometry, requires a strict coregistration of the images. In addition, phase ambiguities have to be resolved [9], [10]. To ease these problems, one can use cross correlations on range subswaths. Although this leads to a lowpass filtering of the estimated height, the accuracy can be retained by using the phase of the correlation function [11], [12]. In November 2000, a series of trials named InSAS-2000 were conducted at Elba Island in Island with the NATO Un- dersea Research Centre (NURC, La Spezia, Italy, formerly SACLANTCEN), Qinetiq (Hampshire, U.K., formerly DERA), and Norwegian Defence Research Establishment (FFI, Kjeller, Norway) as participants [13]. The basis of the experiment was to perform controlled motion of an interferometric SAS with a high-grade inertial navigation system (INS). The experimental data we apply in this paper are from the InSAS-2000 experi- ment. Cross-correlation-based methods on data collected from a 3-D geometry are often limited by geometrical decorrelation [8, p. 102]. In slant range, this causes a spectral shift, which can be reduced by using only the overlapping part of the two spectra [14]. The disadvantage with this filtering is that it reduces the resolution of the interferometric images. To reduce the geometrical decorrelation and simultaneously retain the full resolution, we propose to beamform images in ground range (or near-ground range) instead of in the slant-range plane [5, pp. 369–371]. Monte Carlo simulations of synthetic SAS data show an increase of the correlation in ground-range images, compared to that of slant-range images. We have developed a new description of the imaging geometry for ground-range imaging, which is more suitable for sonars with an offset transmitter like the InSAS-2000 sonar. A limiting factor in complex-correlation-based delay estima- tion is an uncompensated shift of the effective center frequency of the data. This shift is due to uneven weighting of the received frequency components, and it degrades the delay estimate for high signal-to-noise ratios (SNRs). In this paper, we propose a new technique to reduce this effect. As shown, our technique successfully removes the degradation of the time-delay estima- tion accuracy for SNR up to 60 dB. We have implemented and tested our method on previously unpublished data from the InSAS-2000 experiment. Height maps estimated from real and synthetic aperture data are derived and compared, and we demonstrate that man-made objects with submeter heights can readily be discerned in the synthetic aperture height maps. Several different objective image quality metrics are introduced and applied to the SAS 0364-9059/$25.00 © 2007 IEEE