Cooperative Estimation to Reconstruct the Parametric Flow Field Using Multiple AUVs

This article investigates the cooperative estimation problem to recover the parametric flow field through sensor measurements from an autonomous underwater vehicle (AUV) team. We establish the parametric flow model that incorporates the concept of incompressibility to provide a physical property. Then, considering the influence of unknown flow field on AUVs’ trajectories while submerged, we define: 1) the deviation between actual and predicted relative positions between each vehicle and its neighbors as an relative motion-integration error, which is available using local measurement and 2) the deviation between the actual and predicted position of each vehicle as an absolute motion-integration error, which is available from global positioning system (GPS) when the AUVs are on the sea surface. Based on relative and absolute motion-integration errors, we formulate a set of nonlinear equations to present the deterministic and continuous relationship between the above errors and the parametric flow model. To reconstruct the flow field, an iterative algorithm is proposed to estimate the model parameters by solving an inverse problem for these nonlinear equations. Moreover, a detailed convergence analysis of the proposed algorithm is given. Finally, simulations are conducted to illustrate the effectiveness of the proposed algorithm in a simulated and real dataset of the flow field.