基于分形的捷联惯组历次测试数据混合插值算法

摘要

Aiming at the problem of small sample size, unequal-interval, and non-linearity of the SIMU successive test data, a three-time-hybrid-interpolation algorithm based on fractal interpolation is presented to deal with this problem. The first interpolation (fractal interpolation) can keep the changing trend of original test data, the second interpolation (spline function interpolation) can implement the accuracy of interpolation in order to get equal interval original test data, and the third interpolation (piecewise-linear-interpolation) can enlarge the sample size, while the statistic characteristic of original test data will not be changed. The illustration shows that this algorithm can effectively achieve the equal interval quantization and sample size enlargement of the original test data, and provide a better foundation for the small sample modeling and forecasting.%针对捷联惯组历次测试数据小样本、非等间隔、非线性的问题,提出了一种基于分形插值的三次混合插值算法.通过第一次分形插值保证原始测试数据的变化趋势;通过第二次样条函数插值保证了插值的准确性,实现原始测试数据等间隔化;通过第三次分段线性插值,扩大样本容量,同时保证了原有测试序列的统计特性不变.实例分析表明,该算法很好的实现了对捷联惯组历次测试数据的等间隔处理和样本容量扩大,为捷联惯组历次测试数据小样本建模分析提供良好的基础.