IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 35, NO. 4, OCTOBER 2010 887 Model-Based Sonar Motion Compensation for Bottom Reverberation Coherence Jinyun Ren, Student Member, IEEE, and Rodney G. Vaughan, Fellow, IEEE Abstract—Much signal processing in sonar takes advantage of ping-to-ping bottom reverberation coherence. However, bottom re- verberation coherence is degraded owing to environment varia- tions including unknown sonar sensor motions from platform in- stability. In this paper, an algorithm is described to compensate small-scale motion of high-frequency sonar sensors which is for enhancing ping-to-ping bottom reverberation coherence. The al- gorithm is based on sonar modeling of bottom reverberation. It comprises three steps: template selection, footprint matching, and phase rotation. Simulations using the sonar modeling indicate that the algorithm can correct for sensor motion of up to several wave- lengths for two pings using the data from only one element of the sonar receiver. The algorithm achieves a significant coherence im- provement over a large region ensonified by the sonar beam. Index Terms—Bottom reverberation coherence, motion compen- sation, sonar sensor motion, sonar signal processing. I. INTRODUCTION B OTTOM reverberation (bottom scattering of the sonar pulse) in shallow water is reported to exhibit coherence from ping to ping [1], [2]. The ping-to-ping coherence means that if the same waveform is transmitted via the water bottom many times from a given transducer position and orientation, the signals scattered from a particular area on the bottom will be similar from ping to ping. This implies that the acoustic nature of the propagation medium and the scatterers do not change significantly during transmissions. Many sonar applications take advantage of ping-to-ping bottom reverberation coherence. For example, synthetic aper- ture sonar (SAS) [3] forms a virtual sensor array using a predetermined number of pings. SAS implicitly assumes that the bottom reverberation during these pings is the same as that seen by an actual sensor array. Successful applications [4] of SAS have proven bottom reverberation to be coherent during an operationally useful period of time. In [5], ping-to-ping bottom reverberation coherence was used for underwater ve- hicle positioning. In [2], this coherence property was used for the detection of small, slow-moving targets in shallow water. Variations in the propagation medium and unknown sonar sensor motions degrade the coherence, and therefore degrade the performance of the above applications. Extensive research has been directed at correcting these errors. Direct position mea- Manuscript received April 06, 2009; accepted September 15, 2010. Date of publication November 11, 2010; date of current version November 30, 2010. Associate Editor: D. Knobles. The authors are with the School of Engineering Science, Simon Fraser University, Burnaby, BC V5A 1S6 Canada (e-mail: jren@alumni.sfu.ca; rodney_vaughan@sfu.ca). Digital Object Identifier 10.1109/JOE.2010.2079610 surement (DPM) [6] using navigation systems is the most intu- itive approach. However, DPM can only handle large-scale plat- form motions whereas small-scale motion can be sufficient to spoil the coherence. The displaced phase center array (DPCA) technique estimates along-track 1 motion of a moving vehicle by using the colocated phase centers of a transducer array. DPCA also estimates the cross-track 2 motion of the vehicle by using multiple pings. These estimates can be used for motion compen- sation, and work when the vehicle cross-track motion is small from ping to ping (e.g., less than several wavelengths at a few hundreds of kilohertz) [1]. Phase gradient autofocus (PGA) is perhaps the most popular method for focusing blurred targets in a given area for a spotlight-mode synthetic aperture radar (SAR) image [7]. It can correct small phase errors caused by uncom- pensated cross-track vehicle motions, medium inhomogeneity, and other noisy sources. PGA has been adapted to sonar applica- tions for the same purpose [6], [8], but it is restricted to spotlight imaging geometries and requires many pings of data collected from the different view angles of the target. Stripmap phase gradient autofocus (SPGA) is an improved PGA algorithm de- signed for Stripmap-mode SAS [9]. It requires data only from a small number of pings to focus blurred targets, but it considers only the area where the object of interest is present. This paper describes a relatively simple algorithm that can compensate small-scale sensor motion caused by platform mo- tion during the collection of pings, which is suitable for most of the far-field region ensonified by a high-frequency (i.e., a few hundreds of kilohertz) sonar sensor. Moreover, the algo- rithm requires the data from only one element of the receiver, which simplifies the deployment of some sonar systems such as shallow-water sonar surveillance systems described in [10]. The proposed motion compensation algorithm is based on the signal modeling of bottom reverberation, which is presented in the companion paper [11]. Compared with the DPCA technique in SAS [1], the tech- niques presented in this paper are for fundamentally different sonar systems. DPCA has the advantage of using a sonar array and addresses large along-track motion for moving vehicles and small cross-track motion for areas at the far range; and that presented here, using a static sonar with a single element, ad- dresses small cross-track motion for wide-area coverage. A mo- tion compensation algorithm, proposed in [12], is similar to that proposed here in the sense that it compensates the sensor mo- tions for two pings through the sample shift and the phase rota- tion. However, the techniques here offer a different insight be- 1 Along track is the heading direction of the vehicle carrying the transducer array. 2 Cross track is the direction perpendicular to the heading direction of the ve- hicle. 0364-9059/$26.00 © 2010 IEEE