Simultaneous input and state smoothing and its application to oceanographic flow field reconstruction

Forward-backward smoothing of unknown inputs and states of a nonlinear system is studied in this paper, motivated by oceanographic flow field reconstruction using a swarm of buoyancy-controlled drogues. A Bayesian paradigm is developed first to provide a statistics based solution framework. A nonlinear maximum a posteriori (MAP) optimization problem is established within the framework as a means to achieve simultaneous input and state smoothing, which is solved by the iteration based Gauss-Newton method. Application of the proposed method to reconstruction of a complex three-dimensional flow field is investigated via simulation studies.