Phase Wrap Error Correction by Random Sample Consensus With Application to Synthetic Aperture Sonar Micronavigation

Accurate time delay estimation between signals is crucial for coherent imaging systems such as synthetic aperture sonar (SAS) and synthetic aperture radar (SAR). In such systems, time delay estimates resulting from the cross-correlation of complex signals are commonly used to generate navigation and scene height measurements. In the presence of noise, the time delay estimates can be ambiguous, containing errors corresponding to an integer number of phase wraps. These ambiguities cause navigation and bathymetry errors and reduce the quality of synthetic aperture imagery. In this article, an algorithm is introduced for the detection and correction of phase wrap errors. The random sample consensus (RANSAC) algorithm is used to fit 1-D and 2-D models to the ambiguous time delay estimates made in the time delay estimation step of redundant phase center (RPC) micronavigation. Phase wrap errors are then corrected by recalculating the phase wrap number using the best-fitting model. The approach is demonstrated using the data collected by the 270-330 kHz SAS of the NATO Centre for Maritime Research and Experimentation Minehunting unmanned underwater vehicle for Shallow water Covert Littoral Expeditions. Systems with lower fractional bandwidth were emulated by windowing the bandwidth of the signals to increase the occurrence of phase wrap errors. The time delay estimates were refined using both the RANSAC algorithms using 1-D and 2-D models and the commonly used branch-cuts method. Following qualitative assessment of the smoothness of the full-bandwidth time delay estimates after application of these three methods, the results from the 2-D RANSAC method were chosen as the reference time delay estimates. Comparison with the reference estimates shows that the 1-D and 2-D RANSAC methods outperform the branch-cuts method, with improvements of 29%-125% and 30%-150%, respectively, compared to 16%-134% for the branch-cuts method for this data set.

I. Introduction

Synthetic aperture radar (SAR) [1] and synthetic aperture sonar (SAS) [2] are coherent imaging techniques that produce high-resolution images of the Earth's surface above and below the water, respectively. Very precise estimation of time delays between coherent band-limited signals is essential for the formation of a wide variety of SAS and SAR data products, including platform navigation solutions and 3D terrain maps.