Quadratic filtering for linear stochastic systems with dynamical bias under amplify-and-forward relays: Dealing with non-Gaussian noises

Abstract

In this paper, the recursive quadratic filtering problem is investigated for a class of linear non-Gaussian systems with dynamical bias and amplify-and-forward relays. The stochastic bias, characterized by a dynamical process with certain non-Gaussian noises, is incorporated into the system state equation. An amplify-and-forward relay is utilized in the sensor-to-filter network channel to enhance signal transmission performance. The transmission powers of the sensor and relay are governed by two sets of random variables. Particular attention is given to the design of a quadratic filter in the presence of the dynamical bias, the amplify-and-forward relay, and non-Gaussian noises. For this purpose, an augmented system is constructed by aggregating the augmented state (comprising the original state and the associated bias) and its second-order Kronecker power. Consequently, the addressed quadratic issue for the underlying non-Gaussian system is reformulated as a linear filtering problem for the augmented system. Using difference equations, the filtering error covariance is derived and subsequently minimized through the design of an appropriate gain matrix. Moreover, sufficient conditions are established to ascertain the existence of the lower and upper bounds on the filtering error covariance. Finally, the effectiveness of the designed quadratic filtering algorithm is demonstrated through a numerical example.