正交基函数多项式实时拟合在轴角编码器测速中的应用

Application of real time polynomial fitting based on orthogonal basis function algorithm to encoder rate measurement

提出了一种基于正交基函数的多项式实时拟合方法,并应用于轴角编码器测速,解决了常规算法中拟合多项式阶数大于3阶时法方程组容易出现病态,进而使测速精度降低的问题。光电跟踪测量设备地面目标跟踪实验表明,该算法通过对拟合处理后的角度值进行微分运算得到角速率,能有效地降低编码器角度输出中随机误差对测速的影响。在典型实验条件下,与采用同阶拟合多项式的常规方法进行了比对,前者的测速误差标准偏差为0.013 43°/s,后者为0.028 15°/s,采用本算法提高了编码器的测速精度,适合在工程上应用。

A real time polynomial fitting algorithm based on orthogonal basis function was proposed to encoder angular rate measurement. The algorithm can avoid the ill conditioned status leading to degrading the rate-measuring precision in normal equation when the rank of fitting polynomial is more than three. The ground target tracking experiment with photoelectric tracking survey equipment shows that the algorithm is effective to decrease the effect of angular random errors on angular rate measureemnt when calculating the differential of the angular fitting output. Typically, the standard deviation of rate-measuring errors using this algorithm is 0. 01343°/s by contrast with the 0. 02815°/s using the normal method. Therefore the improved algorithm applied to engineering can improve the angular rate measurement precision obviously.