Interferometric Synthetic Aperture Sonar Design and Performance Philip J. Barclay, B.E. (Hons) A thesis presented for the degree of Doctor of Philosophy in Electrical and Computer Engineering at the University of Canterbury, Christchurch, New Zealand. August 2006 ABSTRACT Synthetic aperture sonar (SAS) has become a well developed imaging technique for imaging shallow water environments. Aperture synthesis provides high along-track res- olution imagery, with range independent resolution. However, mapping of the seafloor using traditional SAS is limited to a two-dimensional surface. To provide the third dimension (height), an interferometric synthetic aperture sonar (InSAS) is formed, comprising of two or more vertically displaced hydrophone arrays. Each of the inter- ferometric receiver datasets are processed using standard SAS algorithms, with motion compensation and corrective processing applied equally to each channel, preserving the underlying interferometric time delays. By then estimating the time delay of the incoming wavefronts across the interferometric receiver array, the height of the seafloor can be inferred from the side-scan geometry of the system. The InSAS approach is sim- ilar to the radar equivalent (InSAR), however, significant differences in geometry and medium properties limit the applicability of InSAR algorithms to the sonar equivalent. A height estimate from interferometric data is formed by estimating the time dif- ference between the receiver elements of the interferometric array. Therefore, for an accurate estimate of the time-delay, the signals of the receivers must contain significant ‘common’ information. Presented in this thesis is an analysis of coherence as applica- ble to an InSAS system. The coherence of an InSAS system can be decomposed into five ‘coherence components’: additive acoustic noise, footprint misalignment, baseline decorrelation, temporal decorrelation, and processing noise. Of these, it is shown foot- print misalignment has the greatest effect for an InSAS system if it is not corrected for. The importance of maintaining high coherence between the receiver channels is presented; small losses in coherence from the ideal of unity will have a significant im- pact of the accuracy of the resulting height estimate. To reduce the sensitivity of the height accuracy losses, multiple estimates of the height can be formed from independent ‘looks’ of the scene. Combining all these estimates into one height estimate is shown to significantly improve the height estimate. The design and signal processing of an InSAS system is of high importance to the generation of high accuracy height estimates of the seafloor. Several parameters of design are explored, in particular the effect of aperture sampling. Low along-track aperture sampling rates are shown to cause a significant decrease in signal coherence, iv ABSTRACT caused by the generating of ‘grating lobes’ from the synthetic aperture processing. Substantial improvements can be made by careful selection of transmitter and receiver element sizes, relaxing the requirements of a highly sampled aperture. An analysis of interpolation schemes on interferometric quality is also presented. The effect of footprint misalignment can be reduced by first resampling the data from each receiver onto a common ground-plane. However, this requires prior knowl- edge of the seafloor height, an unknown parameter before an interferometric height estimate is made. One possible method to form an initial height estimate is through the use of belief propagation, a technique applied from the field of stereo imaging. Be- lief propagation is used to estimate an initial height surface, albeit at discrete height intervals. This initial low resolution height surface can then be used to remap the data, partially eliminating the detrimental effects of footprint misalignment. The combination of all the independent estimates of the scene can be combined us- ing maximum likelihood estimation. This framework allows the individual estimates to be combined into one overall cost function. Searching of the cost function for minimum cost yields a single interferometric time-delay estimate, from which a single height esti- mate can be inferred. This framework allows looks formed from many different sources to be combined, including multiple imaging frequency bands, and the use of more than one interferometric pair of receivers. ACKNOWLEDGEMENTS Thank you to everyone who has helped me throughout this thesis. To my supervisors, Dr. Michael Hayes and Prof. Peter Gough, thank you for your guidance and useful discussions along the way. Thank you to the rest of the Acoustic Research Group, in particular Hayden Callow, Steve Fortune, Alan Hunter, and Edward Pilbrow. Also, thanks to Chris Forne for help with the application of belief propagation algorithms. During my stay as a postgrad in the ECE department I have had much support from the department, both from students and staff. It is these fantastic people that make writing a thesis possible. The construction and operation of the KiwiSAS sonar system was an integral part of the early work conducted in this thesis. Much of the mechanical work for the KiwiSAS system was performed by the technical staff of the ECE Department, in particular thanks goes to Michael Cusdin, Peter Lambert, and Steve Downing. For sea-trials of the KiwiSAS system, the use of Peter’s yacht was of much help, I hope we didn’t scratch it too much dragging things back onboard. To my family, thank you for always believing in me, and being there for me through the hard times. A special thank you to Helen. Your love and support means a lot to me. Thank you also to all my friends, especially those who dragged me away into the hills to get away from it all for a while. PREFACE The work in this thesis originally began as a hardware based extension of the KiwiSAS- II sonar system to allow for interferometric operation. The idea was to re-wire the exist- ing 3×3 array of hydrophone elements into three vertically separated receivers, allowing interferometry to be performed. For this, the acquisition hardware was extended to six channels, allowing each hydrophone to operate within two separate frequency bands, centered on 30 kHz and 100 kHz. The hardware developed for this system is covered in [Barclay et al., 2002a], expanded in Appendix B. Sea-trials with this hardware were performed locally in Lyttelton Harbour [Barclay et al., 2001], and the Hauraki Gulf Auckland [Hayes et al., 2001]. Later, the hardware was completely redesigned and rebuilt since it was apparent additional hydrophones would be of benefit. Instead of sending the received wave- forms up the cable in an analogue form, all the conversion and storage electronics was moved into the towfish housing. This was necessitated by the large increase in overall datarate from the expanded sonar configuration. Central to this electronics package is a Pentium-III industrial computer, mounted within a Compact-PCI cage [Hayes et al., 2002]. Waveform generation and echo recording implemented as three custom Compact-PCI cards. This configuration allows the transmitter to be driven in vertical groups of three, allowing synthetic horizontal beam shaping. The new receiver hardware provides nine channels, allowing the 3 × 3 receiver array to be individually sampled, each with a bandwidth of ≈150 kHz. Post-processing is used to extract the two 20 kHz bandwidth signals. During initial interferometric processing, direct phase differences between the re- ceiver channels were used as the basis of the angle-of-arrival [Barclay et al., 2002b, Bar- clay et al., 2003b]. Direct phase differences between the receivers was found to give poor results; the coherence loss due to footprint shift being the primary problem. This is covered in more detail in Chapter 3. The coherence loss due to footprint shift was exploited by resampling the data onto a range of differing height ground-planes, with a surface mapped through the solution space. The fitting of the surface through the solution space was performed using belief propagation, a technique first developed in the computer graphics field. This technique provides a good first order approximation to the seafloor topography. The details of this application of belief propagation can be viii PREFACE found in [Barclay et al., 2003a], reproduced in Appendix A. After a more in-depth analysis of signal coherence between the receivers was per- formed (see Chapter 3), it became apparent multiple ‘looks’ of the scene would be required to provide a high accuracy height estimate. Through various techniques de- tailed in Chapter 4, multiple looks of the scene could be generated. However, the combination of all the looks into one overall height estimate proved difficult, especially when combining data from the two distinct frequency bands (30 and 100 kHz). To achieve this combination, a maximum likelihood approach was taken. The data from each look is formed such that a single parameter search can be made to find the most likely angle-of-arrival. This approach has shown to be highly successful, results pre- sented in several papers [Barclay et al., 2004, Barclay et al., 2005, Barclay et al., 2006]. One major problem with a maximum likelihood approach is the assumption of a single angle-of-arrival, an assumption violated by multipath from the sea-surface. Work on this problem has also been performed both using belief propagation [Hayes and Barclay, 2003] and maximum likelihood approaches [Barclay et al., 2006]. Papers prepared during this thesis are presented here in order of presentation. Barclay, P. J., Forne, C. J., Hayes, M. P., and Gough, P. T. (2003a). Reconstruct- ing seafloor bathymetry with a multi-frequency, multi-channel broadband InSAS using belief propagation. In Oceans 2003. IEEE, MTS. Barclay, P. J., Hayes, M. P., and Gough, P. T. (2001). Using a multi-frequency synthetic aperture sonar for bathymetry. In Image and Vision Computing New Zealand 2001, pages 63–68, University of Otago, Dunedin, New Zealand. Barclay, P. J., Hayes, M. P., and Gough, P.