Robust, Distributed Estimation of Internal Wave Parameters via Inter-Drogue Measurements

Internal waves are important to oceanographers because, as they travel, they are capable of displacing mass, such as plankton and small fish. This paper considers a group of drogues estimating the physical parameters that determine the dynamics of an ocean linear internal wave. While underwater, individual drogues do not have access to absolute position information and can only rely on inter-drogue measurements. Building on this data and the knowledge of the drogue dynamics under the flow induced by the internal wave, we propose the Vanishing Distance Derivative Detection Strategy to allow individual drogues to determine the wave parameters. We analyze the correctness and robustness of this strategy under noiseless and noisy measurements, respectively. We also introduce a general methodology, termed pth-Order Parameter Fusion, for combining the parameter estimates obtained at different times and characterize its error. Simulations illustrate our results.