Investigation and Enhancement for Optimal Smoothing and Filtering of Chaotic and Noisy Dynamical Systems

Adaptive kalman filtering method is based on generating a separable variational model for estimating joint posterior distribution of states in dynamical system and noise parameters on each time step separately. in this article we present a gaussian approximation based framework for optimal smoothing of non-linear stochastic state space models, and also time-varying noisy measurements of the system are obtained at discrete instances of time. it is also shown how the method can be applied to a class of models. the result is a recursive algorithm, where on each step the state is estimated with kalman filter and the sufficient statistics of the noise variances are estimated. we also numerically compare accuracies and error performance of the algorithm with different simulated data.