This paper considers a group of drogues whose objective is to estimate the physical parameters that determine the dynamics of ocean nonlinear internal waves. Internal waves are important in oceanography because, as they travel, they are capable of displacing small animals, such as plankton, larva, and fish. These waves are described by models that employ trigonometric functions parameterized by a set of constants such as amplitude, wavenumber, and temporal frequency. While underwater, individual drogues do not have access to absolute position information and only rely on inter-drogue measurements. Building on this data and the study of the drogue dynamics under the flow induced by the internal wave, we design two strategies, referred to as the Vanishing Derivative Method and the Passing Wave Method, that are able to determine the wavenumber and the speed ratio. Either of these strategies can be employed in the Parameter Determination Strategy to determine all the remaining wave parameters. We analyze the correctness of the proposed strategies and discuss their robustness against different sources of error. Simulations illustrate the algorithm performance under noisy measurements as well as the effect of different initial drogue configurations.
A group of drifters underwater are driven by the dynamics induced by an internal wave. Collecting only relative motion measurements, they can determine the wave's physical parameters.