In a satellite navigation system, high-precision prediction of satellite clock bias directly determines the accuracy of navigation, positioning, and time synchronization and is the key to realizing autonomous navigation. To further improve satellite clock bias prediction accuracy, we establish a satellite clock bias prediction model by using long short-term memory (LSTM) that can accurately express the nonlinear characteristics of the navigation satellite clock bias. Outliers in the original clock bias should be preprocessed before using the clock bias for prediction. By analyzing the working principle of the traditional median absolute deviations method, the ambiguity of the mathematical model of that method was improved. Experimental results show that the improved method is better than the traditional method at detecting gross errors. The single difference sequence of the preprocessed satellite clock bias was taken as the research object. First, a quadratic polynomial model was fit to the trend term of the single difference sequence. Second, based on the LSTM neural network model and the basic principles of supervised learning, a supervised learning LSTM network model (SL-LSTM) was proposed that models cyclic and random terms. Finally, the prediction function of the satellite clock bias was realized by extrapolating the model by adding a trend term. We adopt the GPS precision satellite clock bias of International GNSS Service data forecast experiments and apply wavelet neural network (WNN), autoregressive integrated moving average (ARIMA), and quadratic polynomial (QP) models to compare their prediction effects. The average prediction RMSE for 3 h, 6 h, 12 h, 1 d, and 3 d based on the SL-LSTM improved by approximately −21.80, −1.85, 8.57, 2.27, and 40.79%, respectively, compared with the results of the WNN. The average prediction RMSE based on the SL-LSTM improved by approximately 38.23, 65.48, 80.22, 85.18, and 94.51% compared with the ARIMA results. The average prediction RMSE based on the SL-LSTM improved by approximately 82.37, 75.88, 67.24, 45.71, and 58.22% compared with the QP results. Compared with the WNN, the SL-LSTM method has no obvious advantages in the prediction accuracy and stability in short-term prediction but achieves a better long-term prediction accuracy and stability. With an increased prediction duration, the SL-LSTM method is clearly better than the other three methods in terms of the prediction accuracy and stability. The results indicated that the quality of satellite clock bias prediction by the SL-LSTM method is better than that of the above three methods and is more suitable for the middle- and long-term prediction of satellite clock bias.
Aiming at the problem of road network multi-scale matching, a multi-scale road matching method under the constraint of road mesh of small-scale data has been proposed. First, two road meshes with different scale data are constructed; Secondly, under the constraint of the small-scale road mesh, the composite mesh composed of several road meshes in the large-scale road is extracted, and the mesh matching with the small-scale road mesh is completed; Then, many-to-many matching of road meshes with different scales is realized; finally, the matching relationship between composite mesh and small-scale road mesh is transformed into the matching between multi-scale road mesh boundary roads and internal roads, and the matching of the whole road network is completed. The experimental results show that this method can better realize the matching of multi-scale road network.
Building simplification is an important research area in automatic map generalization. Up to now, many approaches have been proposed by scholars. However, in the continuous transformation of scales for buildings, keeping the main shape characteristics, area, and orthogonality of buildings are always the key and difficult points. Therefore, this paper proposes a method of progressive simplification for buildings based on structural subdivision. In this paper, iterative simplification is adopted, which transforms the problem of building simplification into the simplification of the minimum details of building outlines. Firstly, a top priority structure (TPS) is determined, which represents the smallest detail in the outline of the building. Then, according to the orthogonality and concave–convex characteristics, the TPS are classified as 62 subdivisions, which cover the local structure of the building polygon. Then, the subdivisions are divided into four simplification types. The building is simplified to eliminate the TPS continuously, retaining the right-angle characteristics and area as much as possible, until the results satisfy the constraints and rules of simplification. A topographic dataset (1:1K) collected from Kadaster was used for our experiments. In order to evaluate the algorithm, many tests were undertaken, including tests of multi-scale simplification and simplification of typical buildings, which indicate that this method can realize multi-scale presentation of buildings. Compared with the existing simplification methods, the comparison results show that the proposed method can simplify buildings effectively, which has certain advantages in keeping shape characteristics, area, and rectangularity.
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