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目的:设计较现有方法鲁棒性更佳、效率更高的周期分析方法,从稀疏且含有噪声的周期事件观测数据中估算周期。创新点:本文首次将最大公因子逼近算法应用于周期估算问题。该算法在处理稀疏且含有噪声的数据方面具有效率高、性能稳定、鲁棒性好的特点。方法:首先,确定观测数据的噪声空间。本文根据观测数据自适应获取噪声上下限。然后,对观测数据进行预处理,消除其中包含的未知相位参数,并对预处理后的数据逐对以噪声穷举方式搜索所有可能的最大公因子,即采用公因子逼近的方法搜索候选周期,同时统计这些候选周期在整个搜索过程中出现的频率。搜索完成后,根据候选周期出现频率估算周期值,即选择出现频率最高的候选周期为估算周期。最后,采用仿真数据验证AGCD方法在处理稀疏且含有噪声的观测数据方面的鲁棒性和高效性。结论:(1)AGCD算法效率高,因其以穷举搜索噪声空间方式估算周期。而现有方法是以穷举周期的方式估算周期,噪声空间相比周期的取值空间小很多。所以,AGCD方法在效率上有很大提升。(2)AGCD能以更少的观测数据获得与其他方法近似或更高的准确率。(3)AGCD性能(准确性和效率)较其他方法更加稳定且受周期值影响更小。(4)AGCD方法无需利用有关周期取值区间的先验知识,相比于其他方法适用性更强。
OBJECTIVE: To design a more robust and efficient periodic analysis method than the existing methods, and estimate the period from the sparse and noisy periodic event observation data. Innovation: This article for the first time the maximum common factor approximation algorithm applied to the period estimation problem. The algorithm has the characteristics of high efficiency, stable performance and good robustness in dealing with sparse and noisy data. Method: First, determine the noise space of the observed data. In this paper, the upper and lower limits of noise are adaptively obtained based on the observed data. Then, the observed data are pre-processed to eliminate the unknown phase parameters contained therein, and the preconditioned data is searched for all the possible greatest common factors on a noise-exhaustive basis pair by pair, that is, the common-cycle approach is used to search for candidate cycles, At the same time statistics these candidate cycles in the search frequency of occurrence. After the search is completed, the cycle value is estimated according to the frequency of the appearance of the candidate cycle, that is, the cycle of the selection with the highest frequency of occurrence is the estimation cycle. Finally, simulation data are used to verify the robustness and efficiency of the AGCD method in dealing with sparse and noisy observations. Conclusion: (1) The AGCD algorithm is efficient because it estimates the cycle by exhaustive search of noise space. However, the existing method estimates the period by means of exhaustive cycle, and the noise space is much smaller than the period value space. Therefore, AGCD method has greatly improved in efficiency. (2) The AGCD can obtain the accuracy of similar or higher than other methods with less observational data. (3) AGCD performance (accuracy and efficiency) is more stable than other methods and less affected by the cycle value. (4) The AGCD method is more applicable than other methods without using the prior knowledge about the period value interval.