In this article, we propose a dual set membership filter for nonlinear dynamic systems with additive unknown but bounded noises, and it has three distinct advantages. First, the nonlinear system is translated into the linear system by leveraging a semi-infinite programming, rather than linearizing the nonlinear function. The semi-infinite programming is to find an ellipsoid bounding the nonlinear transformation of an ellipsoid, which aims to compute a tight ellipsoid to cover the state. Second, the duality result of the semi-infinite programming is derived by rigorous analysis; then, a first-order Frank–Wolfe method is developed to efficiently solve it with a lower computation complexity. Third, the proposed filter enjoys stability for some special nonlinear dynamic systems and succeeds the advantages of the classic linear set membership filter. Finally, two illustrative examples in the simulations reveal the effectiveness of the dual set membership filter.

Extreme public health interventions play a critical role in mitigating the local and global prevalence and pandemic potential. Here, we use population size for pathogen transmission to measure the intensity of public health interventions, which is a key characteristic variable for nowcasting and forecasting of COVID-19. By formulating a hidden Markov dynamic system and using nonlinear filtering theory, we have developed a stochastic epidemic dynamic model under public health interventions. The model parameters and states are estimated in time from internationally available public data by combining an unscented filter and an interacting multiple model filter. Moreover, we consider the computability of the population size and provide its selection criterion. With applications to COVID-19, we estimate the mean of the effective reproductive number of China and the rest of the globe except China (GEC) to be 2.4626 (95% CI: 2.4142–2.5111) and 3.0979 (95% CI: 3.0968–3.0990), respectively. The prediction results show the effectiveness of the stochastic epidemic dynamic model with nonlinear filtering. The hidden Markov dynamic system with nonlinear filtering can be used to make analysis, nowcasting and forecasting for other contagious diseases in the future since it helps to understand the mechanism of disease transmission and to estimate the population size for pathogen transmission and the number of hidden infections, which is a valid tool for decision-making by policy makers for epidemic control.

This paper considers the distributed group target tracking (DGTT) problem under sensors with limited and different field of views (FoVs). Usually, for the tracking of groups, targets within groups are closely spaced and move in a coordinated manner. These groups can split or merge, and the numbers of targets in groups may be large, which lead to more challenging issues related to data association, filtering and computational complexities. Particularly, these challenges may be further complicated in distributed fusion system architectures. To deal with these difficulties, we propose a consensus-based DGTT method within the belief propagation (BP) framework, which introduces undetected targets inside the FoV or new targets outside the FoV and performs the probabilistic track association via BP. Meanwhile, the obtained track association probabilities make it possible to exploit a probabilistic consensus fusion scheme for fusing local target densities. Furthermore, the proposed method exhibits computational scalability scaling only linearly on the numbers of group partitions, local measurements and neighboring sensors, and scaling quadratically on the number of targets. Numerical results validate the performance of the proposed method.

Directional motion toward a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the prediction and filtering performance of system models. This article focuses on the reconstruction and state filtering of a linear dynamic system model with destination constraints in the set-valued framework. We treat destination constraints as inherent information in the state evolution process and employ convex optimization techniques to construct a coherent and robust state model. This model effectively captures the influence of destination constraints on state evolution at each time step. To enhance the continuity of the target trajectory generated by the process model, we design an optimal weight matrix for the reconstructed model. Furthermore, we propose a destination-constrained set-valued filtering algorithm, which ensures that the center of the estimated bounded ellipsoid consistently satisfies the destination constraint. Finally, simulation experiments verify its superiority over unconstrained and other state-constrained filtering methods under the set-valued framework.