Estimation-Based Ocean Flow Field Reconstruction Using Profiling Floats

This note considers ocean flow field monitoring using profiling floats and investigates a foundational estimation problem underlying flow field reconstruction, which is known as simultaneous input and state estimation. We take a Bayesian perspective to develop the needed estimation approaches. With this perspective, we first build Bayesian estimation principles for input and state estimation for both the cases of filtering and smoothing. Then, we formulate maximum a posteriori estimation problems and solve them using the classical Gauss-Newton method, leading to a set of algorithms. The proposed algorithms represent a new development of the Bayesian estimation theory to address joint input and state estimation and generalize a number of relevant methods in the literature. We illustrate the effectiveness of our approach in addressing an oceanographic flow field estimation problem based on profiling floats that measure position intermittently and acceleration continuously.