捷联惯组误差系数的分形特征及插值算法

Fractal characteristic and interpolation method for SIMU error coefficients

针对传统模型难以描述捷联惯组误差系数的复杂性、突变性和非线性特征这一问题,研究了其多重分形特征,并提出了一种自适应分形插值算法。利用盒维数和MF-DFA方法分析得出捷联惯组误差系数具有明显的多重分形特征。改进了适用于非等间隔数据的垂直比例因子求取算法,根据测试数据间隔大小赋予每个仿射变换不同的概率和使用次数,按照无放回抽样原则进行随机分形插值,在不增加迭代次数的条件下解决了分形插值点分布不均匀的问题。利用加权平均法得到指定时间的标定值。结果表明,所提算法插值准确性比常规分形插值至少提高了3倍。

Traditional model can’t describe the complexity,mutability and non-linearity of test data in strapdown inertial measurement unit（SIMU）.To solve this problem,the multi-fractal characteristics were discussed,and a self-adaptive fractal interpolation algorithm was proposed.The analysis was made by using box counting dimension and MF-DFA method,and the results indicate that SIMU error coefficients have obvious multi-fractal feature.The computing method of vertical scaling factor applied to unequal-interval data was improved,and according to the interval size of test data,each affine transformation was endued with different probability and used times.The stochastic fractal interpolation was processed based on the principle of un-replaced sampling,and the problem of the unequal distribution of fractal interpolation points was solved with no increasing of iteration number.The calibration value in appointed time was obtained using weighted average method.The result indicates that the interpolation accuracy of the proposed algorithm is at least three times higher than that of traditional integration methods.