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.

Representation and De-interleaving of Mixtures of Hidden Markov Processes

De-interleaving of the mixtures of Hidden Markov Processes (HMPs) generally depends on its representation model. Existing representation models consider Markov chain mixtures rather than hidden Markov, resulting in the lack of robustness to non-ideal situations such as observation noise or missing observations. Besides, de-interleaving methods utilize a search-based strategy, which is time-consuming. To address these issues, this paper proposes a novel representation model and corresponding de-interleaving methods for the mixtures of HMPs. At first, a generative model for representing the mixtures of HMPs is designed. Subsequently, the de-interleaving process is formulated as a posterior inference for the generative model. Secondly, an exact inference method is developed to maximize the likelihood of the complete data, and two approximate inference methods are developed to maximize the evidence lower bound by creating tractable structures. Then, a theoretical error probability lower bound is derived using the likelihood ratio test, and the algorithms are shown to get reasonably close to the bound. Finally, simulation results demonstrate that the proposed methods are highly effective and robust for non-ideal situations, outperforming baseline methods on simulated and real-life data.

Online Parameter Estimation and Change Point Detection for Multi-function Radar Pulse Sequence Based on the Bayesian Non-parametric HMM

Multi-function radars (MFRs) are sophisticated types of sensors with the capabilities of complex agile inter-pulse modulation implementation and dynamic work mode scheduling. The developments in MFRs pose great challenges to modern electronic reconnaissance systems or radar warning receivers for recognition and inference of MFR work modes. To address this issue, this paper proposes an online processing framework for parameter estimation and change point detection of MFR work modes. At first this paper designed a fully-conjugate Bayesian non-parametric hidden Markov model with a designed prior (agile BNP-HMM) to represent the MFR pulse agility characteristics. The proposed model allows fully-variational Bayesian inference. Then, the proposed framework is constructed by two main parts. The first part is the agile BNP-HMM model for automatically inferring data on pulse parameter clusters and corresponding number of clusters from input pulse sequence. The second part utilizes the streaming Bayesian updating to facilitate computation, and designed a online work mode change detection framework based upon a family of one-ended sequential probability ratio test. We demonstrate that the proposed framework is consistently highly effective and robust to baseline methods on diverse simulated data-sets.