Hidden state estimation in the state space model with first-order autoregressive process noise

In this article, the discrete time state space model with first-order autoregressive dependent process noise is considered and the recursive method for filtering, prediction and smoothing of the hidden state from the noisy observation is designed. The explicit solution is obtained for the hidden state estimation problem. Finally, in a simulation study, the performance of the designed method for discrete time state space model with dependent process noise is verified.