Title: Filtering and smoothing for nonlinear simultaneous input and
state estimation

Abstract: The unknown external inputs and the states of a nonlinear
dynamic system often need to be estimated simultaneously from the
output measurements in various applications such as disturbance
rejection, fault detection, oceanographic exploration. We treat the
problem of nonlinear simultaneous input and state estimation (NL-SISE)
from a Bayesian perspective. We then develop both filtering and
smoothing algorithms for NL-SISE via Maximum a Posteriori estimation
within a proposed Bayesian framework. We apply the algorithms to
oceanographic flow field reconstruction, where the measurements
(acceleration and position) collected by a group of drogues deployed
in an ocean domain are assimilated to estimate the flow velocities
(unknown inputs) and the drogues' trajectories and velocities
(states). The results are validated via simulation studies.