An expectation maximization (EM) algorithm-based simultaneous state and input estimator for nonlinear systems is developed. This study uses a Bayesian solution to estimate the states and unknown inputs simultaneously. It was assumed that a joint distribution between states and inputs exists. The joint distribution was estimated sequentially using an EM algorithm. The EM algorithm has two steps: expectation step (E-step) and maximization step (M-step). In the E-step, a particle filter was used to estimate the conditional probability of states. The conditional distribution of the measurements conditioned on the estimated states was maximized with respect to inputs in the M-step, and inputs were estimated. These two steps were performed alternatively until both states and inputs converge to steady values. The effectiveness of the proposed method was demonstrated using simulation and experimental case studies.