Infinite Factorial Linear Dynamical Systems for Transient Signal Detection

Accurately detecting the transient signal of interest from the background signal is one of the fundamental tasks in signal processing. The most recent approaches assume the existence of a single background source and represent the background signal using a linear dynamical system (LDS). This assumption might fail to capture the complexities of modern electromagnetic environments with multiple sources. To address this limitation, this paper proposes a method for detecting the transient signal in a background composed of an unknown number of emitters. The proposed method consists of two main tasks. First, a Bayesian nonparametric model called the infinite factorial linear dynamical system (IFLDS) is developed. The developed model is based on the sticky Indian buffet process and enables the representation and parameter learning of the unbounded number of background sources. This study also designs a parameter learning method for the IFLDS using slice sampling and particle Gibbs with ancestor sampling. Second, the finite moving average (FMA) stopping time is introduced to minimize the worst-case probability of missed detection, and the statistical performance of the stopping time is investigated. To facilitate the computation of the FMA stopping time, this study derives the factorial Kalman forward filtering (FKFF) method and designs a dependence structure for the underlying model, allowing the stopping time to be defined by a recursive function. Numerical simulations demonstrate the effectiveness of the proposed method and the validity of the theoretical results. The experimental results of the pulse signal detection under the condition of communication interference confirm the effectiveness and superiority of the proposed method.