Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for unknown complicated systems subjected to stochastic sensor noise. The proposed methodology assimilates the benefits of conventional optimal control procedure with the advantages of maximum likelihood approaches to deliver a novel iterative trajectory optimization paradigm to be called as Stochastic Optimal Control – Expectation Maximization (SOC-EM). This trajectory optimization procedure exhibits theoretical results which prove that the optimal policy parameters produced by the maximum likelihood technique produce better performance in terms of reduction of cumulative cost-to-go and less stochasticity in the states and actions. Furthermore, the paper provides empirical results which support the superiority of the new technique when applied to a system in presence of measurement noise, compared to some of widely known and extensively employed methodologies.