Coherence-Induced Bias Reduction in Synthetic Aperture Sonar Along-Track Micronavigation

Abstract

Subwavelength motion estimation is vital for the production of focused synthetic aperture sonar (SAS) imagery. The required precision is obtainable from the sonar data itself through a process termed micronavigation. Along-track micronavigation is achieved by a similar technique to that used in correlation velocity logs (CVLs), where sparse estimates of the spatial coherence function are interpolated to estimate the location of the peak coherence and hence estimate the interping vehicle motion. However, along-track micronavigation estimates made using this technique are biased, which limits the utility of these measurements for long-term navigation of autonomous underwater vehicles (AUVs). Three sources of along-track motion estimation bias are considered in this article. First, imperfect temporal registration between the signals results in coherence estimates that are negatively biased as a function of the temporal offset. Second, the sparse estimates of the spatial coherence function are obtained by cross-correlation of complex baseband signals, a process which is known to result in positively biased coherence estimates, especially when the true coherence is low. Finally, mismatches between the underlying spatial coherence function and the interpolation kernel used to estimate the peak coherence location also result in along-track micronavigation bias. In this article, we describe and evaluate three methods for reducing along-track micronavigation bias. We introduce a temporal registration of the signals before coherence estimation, which reduces the impact of negative coherence bias due to temporal offsets. The remaining coherence estimation bias is reduced by combining multiple coherence estimates in a Bayesian coherence estimator. Additionally, an improved interpolation kernel is derived with a significantly improved fit compared to the current gold standard Gaussian interpolation kernel. The improvements in along-track micronavigation accuracy are demonstrated using two simulated data sets, which both allow comparison with ground truth. The first involves direct simulation of the spatial coherence from a given interping geometry using the pulse-echo formulation of the van Cittert–Zernike theorem, while the second involves simulation of raw sonar echo data using a point-scatterer model. Using these simulations, a reduction in along-track micronavigation bias of 48.5%–99.5% is demonstrated, with reductions in along-track micronavigation error standard deviation of up to 34%. This improvement expands the potential for SAS-equipped AUVs to reduce their long-term navigation drift, facilitating longer underwater transits, improved target localization, and reduced track misalignment in repeat-pass operations.