切比雪夫多项式在单台经纬仪记忆跟踪中的应用

Application of Chebyshev Polynomial in Memory Tracking with Sinle Theodolite

针对单台经纬仪对目标进行跟踪时,易出现目标短暂丢失的情况,使用拟合精度最好的切比雪夫多项式,对经纬仪观测的数据对目标的轨迹进行拟合与外推,并与传统的插值法进行了比较,精度高于传统的插值算法。通过残差比较得出六次多项式时拟合精度和计算速度最佳,误差约为8.226μm。在经纬仪脱靶量无效或者目标速度突变时,经纬仪能够按照预测的轨迹运动。通过实验验证,该方法可在较短时间范围内(3～4s)经纬仪跟丢目标的情况下对目标进行稳定跟踪。目前,该问题在国内外均处于理论研究阶段,尚未应用于工程实践。

Aiming at the case of target missing in a short time occurring frequently in target tracking with a single theodolite, Chebyshev polynomial is used to fit and extrapolate the trajectory of the target with the data observed by theodolite. Chebyshev polynomial has a better accuracy than the traditional method of interpolation by comparison. The results of residuals and standard deviation calculated through the least square method show that six-order polynomial has the best fitting accuracy with the error of about 8.226 μm. When the missing distance of theodolite is invalid or the target speed features suddenly changes, the theodolite is able to follow the trajectory of the predicted movement. Experimental results show that this method can be used to fulfill stable target tracking when the theodolite loses the targets within a short scope of time （3~4 s）. Recently, this problem is still under theoretical study and cannot be put into engineering practice in the near future.