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This paper aims to propose Bayesian filtering based on solving the Fokker–Planck equation, to improve the accuracy of filtering in non-Gauss case. Nonlinear filtering plays an important role in many science and engineering fields for estimating the state of dynamic system, but the existing filtering algorithms are mainly used for solving the problem of Gauss system.

Under the Bayesian framework, the time update of this filtering is based on solving Fokker–Planck equation, while the measurement update uses the Bayes formula directly. Therefore, this novel algorithm can be applied to nonlinear, non-Gaussian estimation. To reduce the computational complexity due to standard meshing, an adaptive meshing algorithm proposed which includes the coarse meshing, significant domain determination that is generated using extended Kalman filtering and Chebyshev’s inequality theorem, and value assignment for significant domain. Simulations are conducted on a reentry body tracking problem to demonstrate the effectiveness of this novel algorithm.

In this way, finer grid points can be placed in the regions with high conditional probability density, while the grid points with low conditional probability density can be neglected. The simulation results indicate that the novel algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

A novel Bayesian filtering based on solving the Fokker–Planck equation using adaptive meshing is proposed, and the simulations show that algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

A novel nonlinear filtering based on solving the Fokker–Planck equation is proposed. The novel algorithm is suitable for non-Gauss system, and can achieve similar accuracy compared to the standard meshing with the significant reduction of computational burden.

A novel vision-based relative navigation system (VBRNS) plays an important role in aeronautics and astronautics fields, and the filter is the core of VBRNS. However, most of the existing filtering algorithms used in VBRNS are derived based on Gaussian assumption and disregard the non-Gaussianity of VBRNS. Therefore, a novel robust filtering named as cubature Huber-based filtering (CHF) is proposed and applied to VBRNS to improve the navigation accuracy in non-Gaussian noise case.

Under the Bayesian filter framework, the third-degree cubature rule is used to compute the cubature points which are propagated through state equation, and then the predicted mean and the associated covariance are taken. A combined minimum l₁ and l₂-norm estimation method referred as Huber’s criterion is used to design the measurement update. After that, the vision-based relative navigation model is presented and the CHF is used to integrate the line-of-sight measurements from vision camera with inertial measurement of the follower to estimate the precise relative position, velocity and attitude between two unmanned aerial vehicles. During the design of relative navigation filter, the quaternions are used to represent the attitude and the generalized Rodrigues parameters are used to represent the attitude error. The simulation is conducted to demonstrate the effectiveness of the algorithm.

By this means, the VBRNS could perform better than traditional VBRNS whose filter is designed by Gaussian filtering algorithms. And the simulation results demonstrate that the CHF could exhibit robustness when the system is non-Gaussian. Moreover, the CHF has more accurate estimation and faster rate of convergence than extended Kalman Filtering (EKF) in face of inaccurate initial conditions.

A novel robust nonlinear filtering algorithm named as CHF is proposed and applied to VBRNS based on cubature Kalman filtering (CKF) and Huber’s technique. The CHF could adapt to the non-Gaussian system effectively and perform better than traditional Gaussian filtering such as EKF.

The purpose of this paper is to develop a distributed task allocation method for cooperative mission planning of multiple heterogeneous unmanned aerial vehicles (UAVs) based on the consensus algorithm and the online cooperative strategy.

In this paper, the allocation process is conducted in a distributed framework. The cooperative task allocation problem is proposed with constraints and uncertainties in a real mission. The algorithm based on the consensus algorithm and the online cooperative strategy is proposed for this problem. The local chain communication mode is adopted to restrict the bandwidth of the communication link among the UAVs, and two simulation tests are given to test the optimality and rapidity of the proposed algorithm.

This method can handle both continuous and discrete uncertainties in the mission space, and the proposed algorithm can obtain a feasible solution in allowable time.

This study is only applied to the case that the total number of the UAVs is less than 15.

This study is expected to be practical for a real mission with uncertain targets.

The proposed algorithm can go beyond previous works that only deal with continuous uncertainties, and the Bayesian theorem is adopted for estimation of the target.

Penetrator plays an important role in the exploration of Moon and Mars. The navigation method is a key technology during the development of penetrator. To meet the high accuracy requirements of Moon penetrator, this paper aims to propose two kinds of navigation systems.

The line of sight of vision sensor between the penetrator and Moon orbiter could be utilized as the measurement during the navigation system design. However, the analysis of observability shows that the navigation system cannot estimate the position and velocity of penetrator, when the line of sight measurement is the only resource of information. Therefore, the Doppler measurement due to the relative motion between penetrator and the orbiter is used as the supplement. The other option is the relative range measurement between penetrator and the orbiter. The sigma-point Kalman Filtering is implemented to fuse the information from the vision sensor and Doppler or rangefinder. The observability of two navigation system is analyzed.

The sigma-point Kalman filtering could be used based on vision sensor and Doppler radar or laser rangefinder to give an accurate estimation of Moon penetrator position and velocity without increasing the payload of Moon penetrator or decreasing the estimation accuracy. However, the simulation result shows that the last method is better. The observability analysis also proves this conclusion.

Two navigation systems are proposed, and the simulations show that both systems can provide accurate estimation of states of penetrator.

Two navigation methods are proposed, and the observability of these navigation systems is analyzed. The sigma-point Kalman filtering is first introduced to the vision-based navigation system for Moon penetrator to provide precision navigation during the descent phase of Moon penetrator.

The purpose of this paper is to present a high accuracy path following method for low-cost fixed-wing UAVs.

The original vector field (VF) algorithm is condensed. A spatial integration mechanism is added to the existing VF and nonlinear guidance law, aiming to decrease steady-state cross-track-error and cope with long-term disturbance.

Numerical simulations show the proposed method could diminish steady-state cross-track-error effectively. Test flights show the proposed method is applicable on low-cost fixed-wing UAVs.

The path following accuracy shown in simulations and test flights indicates the proposed method could be deployed in scenarios including inflight rendezvous, formation, trafficway take-off and landing.

This paper provides an improved high-accuracy path following method for low-cost fixed-wing UAVs.

In daily life, some special systems are difficult to handle, such as indistinct systems (the reverse of explicit systems), history systems, future systems, infinite systems, etc. It is one of the more important topics of broad-spectrum philosophy to give these systems observo-controllable and -manipulatable forms from the angle of epistemology and methodology. The paper aims to discuss these issues.

The author conducted a broad-spectrum analysis of some typical mechanisms of general object systems and general cognition systems through a generalized quantification method and a dynamic structure method.

Through generalized quantification and dynamic structure methods, the author can draw some new conclusions about these special systems: for example, the indistinct system has certain relations and structures, but these relations and structures cannot be observo-controlled directly under certain conditions; further, the indistinct system and explicit system are interdependent, and therefore people can transform an indistinct system into an explicit one.

Through the study of special systems, the author may find a new perspective and research topic for broad-spectrum philosophy, which may provide a new concept and study frame for future analysis of these special systems.

The behavior of joints has a significant effect on the stability of water conveyance tunnel. The purpose of this paper is to study the contact and friction at the joint of the tunneling segment lining and establish its contact friction model. At the same time, the stress and deformation characteristics at the joint of the segment under hydrostatic load are analyzed.

In this study, the contact and friction in a bolted joint are examined using shear testing. The feasibility of the proposed model is verified by a numerical simulation of tests and a theoretical analysis. Accordingly, the effect of joints on the lining is explored under internal hydrostatic loading.

The results show that the openings of tunnel segments in joints gradually expand from the positions of the inner and outer edges to the location of the bolt. Moreover, the stress concentration zone is formed at the bolt. Under hydraulic loading, the opening displacement at the joint increases as the water pressure increases; nevertheless, it does not exceed engineering requirements. When the water pressure of the tunnel lining joint reaches 0.5 MPa, the opening of the joint slowly increases. When the water pressure exceeds 0.7 MPa, the opening of the joint rapidly and significantly increases.

Contact and friction in a bolted joint were examined using shear testing. A cohesive zone model of bolted joints was proposed based on test results. The influence of joint behavior on the stability of water conveyance tunnel was studied.

The time delay would occurs when the measurements of multiple unmanned aerial vehicles (UAVs) are transmitted to the date processing center during cooperative target localization. This problem is often named as the out-of-sequence measurement (OOSM) problem. This paper aims to present a nonlinear filtering based on solving the Fokker–Planck equation to address the issue of OOSM.

According to the arrival time of measurement, the proposed nonlinear filtering can be divided into two parts. The non-delay measurement would be fused in the first part, in which the Fokker–Planck equation is utilized to propagate the conditional probability density function in the forward form. The time delay measurement is fused in the second part, in which the Fokker–Planck is used in the backward form approximately. The Bayes formula is applied in both parts during the measurement update.

Under the Bayesian filtering framework, this nonlinear filtering is not only suitable for the Gaussian noise assumption but also for the non-Gaussian noise assumption. The nonlinear filtering is applied to the cooperative target localization problem. Simulation results show that the proposed filtering algorithm is superior to the previous Y algorithm.

In this paper, the research shows that a better performance can be obtained by fusing multiple UAV measurements and treating time delay in measurement with the proposed algorithm.

In this paper, the OOSM problem is settled based on solving the Fokker–Planck equation. Generally, the Fokker–Planck equation can be used to predict the probability density forward in time. However, to associate the current state with the state related to OOSM, it would be used to propagate the probability density backward either.

This study aims to construct a double layer heat insulation coating based on hollow glass microspheres (HGMs) and to investigate the effect of particle size on barrier property and heat insulation performance.

The waterborne double layer coating was composed of an anticorrosive epoxy ester primer and an HGM-containing silicone acrylic topcoat. With varied HGM sizes (20 μm, 40 μm, 60 μm and a 1:3 w/w mixture of 20 and 60 μm particles), the coating was immersed in 3.5 wt% NaCl solution for 28 days and was then subjected to a salt spray test for 450 h. The barrier properties of the coating were evaluated through electrochemical impedance spectroscopy. Heat insulation performance was examined using a self-made device.

The addition of HGMs decreased the barrier properties of the coating by creating particle/resin interfaces for water penetration. In the HGMs-containing coatings, the use of larger HGMs showed relatively good barrier properties because of the lower particle density. The coating with smaller particles yielded a higher heat insulating capacity as indicated by lower equilibrium temperatures.

Future work will be focused on improving the barrier properties of the coating. Field exposure tests should also be performed to assess the long-term performance of the coating.

The mechanical properties of the coatings in this study also implied that HGMs can be used to develop scratch-resistant and impact-resistant coatings. Other potential applications for further studies include the uses of HGMs for coatings with improved fire retardancy and electromagnetic interference shielding.

A double layer coating was developed to provide balanced performance on both anticorrosion and heat insulation. The effects of HGM size were particularly highlighted.

The purpose of this paper is to assess the immediate and lagged effects of founder's turnover on firm performance, and test the moderating effects of enterprise scale and founders' tenure on enterprise performance.

The paper selects 307 listed companies founded by founder from the Listed Company's Financial Database provided by the China Center for Economic Research. Based on 1,535 observations, this paper tests the relationship between founder turnover and performance by using the random effect model and the fixed effect model.

It is found that founders' turnover will have a significant immediate and negative effect on firm performance. There exists a lagged effect of founders' turnover, but this lagged effect is not as strong as immediate effect. It is also found that the effect of founders' turnover has been moderated by firm size and founders' characteristics.

Founders should choose an appropriate time of leaving when the firm's performance has reached a level high enough for the successor to have a better chance of improving its future operations.

Although some scholars have recognized the special role of founders and that enterprises' performances are mainly determined by the founders, few have studied founders' turnover on firm performance directly and empirically. This paper expands understanding of the founders' departure behavior on firm performance.