基于切比雪夫多项式的旋变轴角快速解调算法  

Rapid resolver angle demodulation algorithm based on chebyshev polynomial

作　　者：杨辉[1] 赵剡[1] 野超[1] 王志龙[1] 

机构地区：[1]北京航空航天大学仪器科学与光电工程学院,北京100191

出　　处：《中国惯性技术学报》2013年第4期530-535,共6页Journal of Chinese Inertial Technology

基　　金：航空基金(20110112007;20100818018)

摘　　要：双通道旋转变压器在定点汇编层实现轴角解调时,传统方法运算量大、占用存储空间多。文中根据粗(精)测角所对应的正余弦值大小及其符号,依据反正切函数的性质将求角的定义域从[,]转化到[0,1],设计了在[0,1]区间上基于切比雪夫多项式快速逼近arctan(x)的低阶分段多项式,用来解决其解调问题;提出了一种通过粗测角,在其附近寻找最佳粗精组合角值的轴角组合及纠错方法;最后在某型号导引头系统的内场试验中进行了测试。试验结果表明,应用本文方法比调用反正切函数法的计算时间减少了50%,比应用查表法的计算精度提高了103倍;该方法具有较好的解码速度和精度,能够用于某些既需要综合考虑功能、体积、重量等要求,又需要快速在定点汇编层实现反正切求角解调的导航系统。In using two-channel multiple resolver to realize axle-angle demodulation on fixed-point assembly layer, traditional methods would cost large amount of calculation and take too much storage space. In order to solve these problems, the angle defined-region is changed from [-∞,＋∞] to [0,1] according to the measured coarse （fine） angle sine-cosine value and the arctan（x）＇s property, and the piecewise low order polynomial which approximate to arctan（x） quickly during [0,1] is designed based on the Chebyshev multinomial. The method of combination and error-correct is put forward, which looks for the resolver fine combination angle of coarse and fine code around the coarse angle. Finally, infield experiments on a particular model seeker system is made which indicate that the calculation time of the proposed method is 50% less than that of calling arctan（x）, and the calculation precision is 103 higher than that of checking tables. The decoding speed and accuracy is high enough to be applied in such precise navigation guidance system as it not only needs to consider the volume, weight, functional requirements, but also needs to use assembly language to solve the arctan（x） and finish the resolver demodulation.

关 键 词：双通道旋转变压器 轴角解调 切比雪夫逼近 反正切 粗精组合 纠错 

分 类 号：U666.1[交通运输工程—船舶及航道工程]