This paper studies the problem of simultaneous input and state estimation (SISE) for nonlinear dynamical systems with and without direct input output feedthrough. We take a Bayesian perspective to develop a sequential joint input and state estimation approach. Our scheme gives rise to a nonlinear Maximum a Posteriori optimization problem, which we solve using the classical Gauss Newton method. The proposed approach generalizes a number of SISE methods presented in the literature. We illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously. (C) 2013 Elsevier Ltd. All rights reserved.