ESTIMATING SYSTEM-LEVEL UNCERTAINTY FOR UNDERWATER NAVIGATION INCORPORATING ACOUSTIC RANGING AND DEAD RECKONING

摘要

The challenge of underwater positioning continues to limit our capability to explore, understand and operate in the marine environment. Positioning solutions that use time-of-flight acoustic range measurements have been a standard for underwater navigation for over thirty years. Advances in estimation techniques and the increased performance of navigation instrumentation have improved our ability to localize underwater assets, but a reliance on acoustic time-of-flight range measurements persists. Modern navigation solutions provide a real time six degree-of-freedom state estimate, fusing observations from a variety of complementary and redundant proprioceptive sensors. Designing such an integrated navigation system requires an analytical framework for predicting the system-level performance based on the precision and configuration of the individual components. We present an analytical tool for predicting the quality of the overall navigation solution based on the uncertainty in all the constituent measurements and the geometry of the acoustic elements in the system. This solution is applicable to a wide variety of acoustic ranging applications, including basin-scale positioning of drifting floats based on time-of-arrival measurements, long baseline (LBL) positioning and compact, short baseline solutions. This estimation framework is based on the Cramer Rao lower bound (CRLB) combined with the notion of dilution of precision, adopted by the global positioning system community, to quantify these tradeoffs. The advantage of this approach is that it incorporates all the navigation sensors as information sources, allowing for quantitative tradeoffs based on how the individual components impact the overall system performance. The result is a general purpose predictive tool for designing integrated navigation solutions. To illustrate this general tool, we present quantifiable answers to a few pertinent questions for the design of modern, multi-instrument navigation solutions which include acoustic time-of-flight range observations: 1 How does the geometry (constellation) of acoustic elements affect the overall positioning uncertainty? 2 When using odometry instruments, such as a Doppler velocity log (DVL), what is the sensitivity of the overall positioning precision with respect to the uncertainty in velocity, range and survey measurements? 3 How does the temporal update rate for each instrument in the navigation solution affect the system-level localization performance? 4 What is the relative importance of heading, odometry and range precision for overall performance? Finally, we validate our estimation framework with controlled field tests using a next generation high-precision LBL sensor. This instrument provides sub-centimetre timing precision over ranges in excess of 300 metres and provides an ideal test case for verifying the results of our predictive model.