Joint Maximum a Posteriori Smoother for State and Parameter Estimation in Nonlinear Dynamical Systems

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In this paper, we propose and demonstrate the direct use of optimization to search for the mode of the joint posterior state distribution of stochastic nonlinear dynamical systems. That is accomplished by forming a very large but sparse nonlinear optimization problem with the states in all time instants as decision variables. The proposed method generalizes well for parameter estimation without the need for treating them as augmented states and the introduction of artificial dynamics. It is also possible to estimate parameters such as the noise variances, which are assumed known in traditional methods.