# An Effective Surrogate Ensemble Modeling Method for Satellite Coverage Traffic Volume Prediction
## 1 Introduction  
In recent decades, satellite constellation networks have been developed to provide multiple ground traffic services for continuous global coverage, which can effectively supplement the coverage-limited terrestrial networks, such as air traffic monitoring [1] and ship trajectory identification [2]. Since the traffic distribution is geographically non-uniform, e.g., aircraft traffic distribution is dense in population agglomeration while scarce in vast ocean regions, satellite coverage traffic volume (SCTV) changes drastically during the satellite movement. To better fulfill the ground traffic service task, it is necessary to predict SCTV in advance so that the resource-limited satellite network could allocate the onboard resources dynamically, e.g., provide more power for payloads to work with full capacity. With the auxiliary information of the predicted upcoming ground traffic, [PERSON] et al. [3] optimize the frequency reuse and onboard transmit power. Moreover, [PERSON] et al. [4] adaptively adjust the onboard receiverconfiguration to improve the overall signal detection probability. To predict SCTV, traditionally a global SCTV distribution data table is first statistically constructed on the ground according to historical data and uploaded to the satellite. Then SCTV is predicted onboard by the data table lookup. To update the table with dynamically accumulated data, the SCTV data table should be uploaded each time the satellite passes over the ground station. Moreover, for better SCTV prediction, more data is preferred to construct a table with fine resolution. Then large data transmission and storage are necessitated, which is prohibitive for satellite communication and onboard data handling. To solve these problems, this paper proposes to distill the data into a surrogate model to be uploaded to satellite, which can both save the valuable communication link resource (as much fewer surrogate model parameters need be uploaded only) and improve the SCTV prediction accuracy compared to table lookup. Recently, a surrogate modeling method, namely meta-modeling method, has been widely studied in data-driven modeling, mainly including Polynomial Response Surface (PRS) [5], Kriging [6; 7], Radial Basis Function (RBF) [8], Support Vector Regression (SVR) [9], etc. In the work of [PERSON] et al. [10], the performance of PRS, RBF, Kriging, and SVR are compared in the design optimization of foam-filled tapered structures, and the results show that no single model is the best for approximating all objective functions in the considered problems. [PERSON] and [PERSON] [11] review different meta-modeling methods used in surrogate-based optimization, and recommend that the choice of which surrogate to use should be based on the problem size, the expected complexity and the cost of the analyses. Similarly, [PERSON] et al. [12] investigate recent advances in the field of surrogate models for problems in modeling, feasibility analysis, and optimization. They conclude that the correct selection of surrogates should consider the type of problem at hand. From the previous research, the consensus is that each surrogate has its own superiorities and drawbacks, and different surrogates are suitable for approximating different objective functions [13]. For the SCTV prediction problem with geographically changing distribution features, as shown in the experimental study in Section 4, it is also observed that the single surrogate can hardly perform universally well in this problem. To increase the approximation quality of the surrogate model, much research has been conducted into integrating multiple surrogates into a single ensemble to exploit the advantages of different surrogates for better approximation accuracy and robustness. One popular ensemble method is using the weighted sum approach [14]. [PERSON] et al. [15] study the effectiveness of the weighted aggregation method for the approximation of helicopter vibrations. [PERSON] et al.