Optimal strategies for the control of autonomous vehicles in data assimilation

We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for the locally optimal control algorithm presented here, with objective formed from the variance trace of the expected posterior distribution. We present results for linear flows near hyperbolic fixed points. Keywords: Bayesian inverse problem, Lagrangian data assimilation, Optimal control, Ocean glider 2010 MSC: 49M, 62F, 62L, 93C, 65C 1. Introduction The need for a more accurate and better resolved estimate of oceanic flows is being driven by a number of pressing global issues, including the crisis facing many species of fish and waterborne organisms, the mitigation of pollutants resulting from spills and offshore contamination, and the important role played by ocean dynamics on climate change. Scientific efforts to estimate ocean flow began in the 1980s with the work of Robinson [1], but has enjoyed limited success due to a lack of observational data. In an effort to improve the current state of understanding of the world's oceans, autonomous vehicles (AVs) are being deployed for the collection of physical oceanography data in a growing number of projects around the globe.