Non-Gaussian noise quadratic estimation for linear discrete-time time-varying systems

This study deals with the input noise quadratic polynomial estimation problem for linear discrete-time non-Gaussian systems. The design of the non-Gaussian noise quadratic deconvolution filter and fixed-lag smoother is firstly converted into a linear estimation problem in a suitable second-order polynomial extended system. By employing the Kronecker algebra rules, the stochastic characteristics of the augmented noise in the augmented system are discussed. Then a solution to the non-Gaussian noise quadratic estimator is obtained through applying the projection formula in Kalman filtering theory. In addition, the stability is proved by constructing an equivalent state-space model with uncorrelated noises. Finally, a numerical example is given to show the effectiveness of the proposed method.