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In the estimation of distributed sensor networks, process noise and measurement noise may have outliers which have heavy-tailed characteristics. To solve this problem, this paper proposes a distributed consensus estimating method for sensor networks based on Student-t distribution. In the state space model, both process noise and measurement noise are modeled as Student-t distributions with heavy-tailed characteristics. First, for the assumption that the process noise and measurement noise have the same degree of freedom parameters, an exact distributed consensus Student-t filtering algorithm is derived. In practical applications, this assumption is often not true, and due to the increasing degrees of freedom, the method will quickly converge to the traditional distributed consensus Kalman filter. Therefore, it is necessary to relax the assumption of the same degree of freedom and keep the degree of freedom unchanged within a certain range. Based on this, an approximate distributed consensus Student-t filter algorithm is proposed. Simulation results verify the effectiveness of the proposed algorithm.

The paper studies the consensus of event-triggered for second-order multi-agent systems (MASs) with or without input time delay. Based on the designed triggering function, a distributed event-triggered control strategy is presented to drive the system to achieve consensus. For each agent, controller update only needs the neighbor’s information communication and its own error value, thus continuous communication among agents is not necessary. Communication energy can be saved as the agents send their state information only at infrequent event instants. To demonstrate the asymptotical stability of the closed-loop error system, S-procedure approach is used by combing Lyapunov stability theories with linear matrix inequality (LMI) technique. Two sufficient conditions are derived by solving LMIs for achieving second-order consensus under the cases of with or without input time delay, respectively.Numerical examples are presented to verify the effectiveness of the proposed controllers.

The coverage control problem of mobile directional sensor networks (DSNs) via a steam function approach, is investigated in the paper. A novel coverage strategy is proposed to coordinate the sensors to cover the designated area. Then, based on the requirement of the proposed coverage network topology, a potential-based sensor placement algorithm is further developed, the superposition of stream function and dipole flow function are applied to achieve formation coverage control and obstacle avoidance. It is shown that the proposed potential-based sensor placement algorithm is convergent based on stability theory. Furthermore, when the mobile sensors reach the intended positions, a rotation strategy is given, the 1-coverage of sensors is realized. Finally, some simulation results demonstrate the effectiveness of the proposed algorithms.

In multi-target tracking (MTT), the imprecise model for sensor characteristics might result in poor performance. The Variational Bayesian labeled multi-Bernoulli (VB-LMB) filter based on Gamma distribution can handle this problem. However, the predictive likelihood of the existing VB-LMB filter is simply treated as a Gaussian, which is inaccurate. In this paper, a VB-LMB filter with inverse Wishart distribution is presented to perform MTT under the unknown sensor characteristics. The measurement noise covariance is modeled as an inverse Wishart (IW) distribution. This distribution has potential to deal with the full noise covariance matrix compared with the Gamma distribution. Since the state and the measurement noise covariance are coupled, the updated equation can be solved by variational Bayesian (VB) method. The predictive likelihood is calculated via minimizing the Kullback-Leibler divergence by the VB lower bound. A MTT scenario is used to evaluate the proposed method. Simulation results show that our approach has better performance than the existing VB-LMB filter with the Gamma distribution.

The event-based leader-following consensus problem for multi-agent systems with input saturation is stud­ied in this paper. The control input update is event-driven, and the triggering function is linear, under the given trigger function and trigger condition. At first, a sufficient condition of the leader-following consensus for multi-agent systems without input saturation is presented. Furthermore, under the constraint of input saturation and communication time delay, the leader-following consensus control is achieved through designing control protocol and choosing suitable pa­rameters of control input. Lyapunov function in combination with S-procedure method is adopted to prove the consensus stability for multi-agent systems with input saturation and communication time delay. Moreover, the Zeno-behavior is excluded for the triggering time sequence. Finally, simulations are present to illustrate the effectiveness of the proposed consensus control protocols.

The implementation of new course standard of mathematics is one of the significant changes of our educational business. Through our analysis of the present mathematics education to discuss the new idea of mathematics education under the new curriculum standard, the new ways of mathematics classroom teaching under the new curriculum standard are given in the paper.

The paper has put forward an idea about the teaching reformation to course of probability and statistics in agriculture and forestry universities. We have paid attention to the theory contact with practice. We also present a new teaching method that the idea of mathematical modeling is applied in the teaching process of application cases to reform teaching methods and seek new teaching modes. Students' ability on applying and innovation will be trained by strengthening the practice of students.

The implementation of new course standard of mathematics is one of the significant changes of our educational business. Through our analysis of the present mathematics education to discuss the new idea of mathematics education under the new curriculum standard, the new ways of mathematics classroom teaching under the new curriculum standard are given in the paper.