Kalman type filter under stationary noises

In this paper, we are interested in finding an explicit solution to the filtering problem for a dd-dimensional autoregressive signal observed through a linear channel when the noises are stationary Gaussian with the same covariance. We represent the signal–observation pair in terms of a 2×d2×d-dimensional autoregressive process driven by a white Gaussian noise. Simulations are given for fractional Gaussian noises (fGn), autoregressive noises (AR(1)) and moving average noises (MA) in order to analyze the performance of the filtering algorithm compared to other approaches in the literature.