Bearing is one of the most important parts of rotating machinery with high failure rate, and its working state directly affects the performance of the entire equipment. Hence, it is of great significance to diagnose bearing faults, which can contribute to guaranteeing running stability and maintenance, thus promoting production efficiency and economic benefits. Usually, the bearing fault features are difficult to extract effectively, which results in low diagnosis performance. To solve the problem, this paper proposes a bearing fault feature extraction method and it establishes a bearing fault diagnosis method that is based on feature fusion. The basic idea of the method is as follows: firstly, the time-frequency feature of the bearing signal is extracted through Wavelet Packet Transform (WPT) to form the time-frequency characteristic matrix of the signal; secondly, the Multi-Weight Singular Value Decomposition (MWSVD) is constructed by singular value contribution rate and entropy weight. The features of the time-frequency feature matrix obtained by WPT are further extracted, and the features that are sensitive to fault in the time-frequency feature matrix are retained while the insensitive features are removed; finally, the extracted feature matrix is used as the input of the Support Vector Machine (SVM) classifier for bearing fault diagnosis. The proposed method is validated by data sets from the time-varying bearing data from the University of Ottawa and Case Western Reserve University Bearing Data Center. The results show that the algorithm can effectively diagnose the bearing under the steady-state and unsteady state. This paper proposes that the algorithm has better fault diagnosis capabilities and feature extraction capabilities when compared with methods that aree based on traditional feature technology.

The singular value decomposition package (SVDP) is often used for signal decomposition and feature extraction. At present, the general SVDP has insufficient feature extraction ability due to the two-row structure of the Hankel matrix, which leads to mode mixing. In this paper, an improved singular value decomposition packet (ISVDP) algorithm is proposed: the feature extraction ability is improved by changing the structure of the Hankel matrix, and similar signal sub-components are selected by similarity to avoid having the same frequency component signals being decomposed into different sub-signals. In this paper, the effectiveness of ISVDP is illustrated by a set of simulation signals, and it is utilized in fault diagnosis of bearing data. The results show that ISVDP can effectively suppress the model-mixing phenomenon and can extract the fault features in bearing vibration signals more accurately.

Global Navigation Satellite System (GNSS) can be applied for the navigation of the high-orbit satellites. The system observability will change due to the changes in the visible satellite numbers and the spatial geometry between the navigation satellites and the users in the navigation system. The influence of the observability changing is not considered in the traditional navigation filter algorithm. In this paper, an optimized navigation filter method based on observability analysis is proposed. Firstly, a novel criterion for the relative observable degree is proposed for each observation component by making use of observation data from previous and posterior time simultaneously. Secondly, according to the relationship between observability and navigation filter accuracy, a novel optimized navigation filter method is constructed by introducing an adjusting factor based on the relative observable degree. Through the comparative simulations with the traditional Extended Kalman Filter (EKF), the optimized navigation filter method can reduce the estimation error of position and velocity by about 36% and 44% respectively. Therefore, the superiority of the proposed filter optimization algorithm is verified.