Ensemble-Based Adaptive Observation

Authors: Muhan Zhao, and Thomas R. Bewley

Submitted to: Automatica (2025)

Abstract:
This paper presents an effective mathematical framework to optimize the feasible trajectories of sensor vehicles moving through a given physical domain, in order to minimize a relevant measure of the uncertainty of an ensemble-based estimate of a PDE system evolving in the same domain. A pair of continuous-time (CT) adjoint analyses is used in this optimization framework, one related to the motion of the M sensor vehicles, and one related to the evolution of the N ensemble members representing both the estimate, and the estimation uncertainty, of the evolving PDE system. It is assumed that the sensor vehicles take local measurements of the PDE system in discrete time (DT), at t_k=k/h for k=1,2,..., which are used to develop the state estimate. The resulting hybrid CT/DT Ensemble-Based Adaptive Observation (EBAO) framework is extensible to a broad range of systems; we illustrate its use here by applying EBAO to a simple model of an environmental plume.