经纬仪最佳一致逼近多项式速度实时求解

Real-time solution of optimal uniform approximation polynomial velocity for theodolite

利用经纬仪进行速度实时求解,一直是测控领域难题,为了提高经纬仪求解速度的实时性及高精度,激光测距光电经纬仪,在反复实验中,提出了一种最佳一致逼近多项式速度求解方法,即保证了速度实时性又保证了速度的精度。首先,利用单站经纬仪加激光测距获得目标空间位置,对激光测距信息采用改进的最小二乘法进行拟合滤波;然后根据求解速度模型,计算速度初值;在采用多项式逼近速度真值时,采用常规的表达形式会产生很大的计算误差,为了减少计算误差,多项式采用三次切比雪夫多项式组合的方式获得最佳一致逼近多项式计算速度函数;最佳一致逼近多项式速度函数使用三次有限差分方法识别速度野值,获得实时、高精度的目标速度值。激光测距经纬仪测速的指标包括实时性(延时<100 ms)和精度(误差<1 m/s)两个指标,把加载在无人机上的较高精度GPS的测速值作为比对值,采用多种算法计算目标速度,实验结果表明:高斯函数方法速度实时性好,但测量速度精度>1.5 m/s;卡尔曼方法求速度精度很好,但是因为用了大量的历史数据,速度值滞后;本文最佳一致逼近多项式法计算得到的速度,实时性好,延时50 ms;速度精度均方差为0.8 m/s,满足设备的指标要求。

The use of a theodolite for real-time velocity calculation has always been a challenge in the field of measurement and control.To improve the real time and high accuracy of theodolite solutions,the laser ranging optoelectronic theodolite project has proposed an optimal uniform approximation polynomial veloci⁃ty solution method through repeated experiments,which ensures both real-time and accurate velocity.First,a single station theodolite and laser ranging are used to obtain the spatial position of the target,and an improved least squares method is used to fit and filter distance measured by the laser.Then,by solving the velocity model,the initial velocity value is calculated.When using polynomials to approximate the true value of velocity,using conventional expressions can result in significant computational errors.To reduce computational errors,polynomials are combined with cubic Chebyshev polynomials to obtain the optimal uniform approximation polynomial for calculating the velocity function.The optimal uniform approxima⁃tion polynomial velocity function uses the cubic finite difference method to identify the velocity outliers and obtain real-time and high-precision target velocity values.The indicators of laser-ranging theodolite speed measurement include real time ability(delay<100 ms)and accuracy(error<1 m/s).The speed measure⁃ment value of GPS loaded on the UAV is taken as the true value,and multiple algorithms are used to cal⁃culate the target speed.The test results show that the Gaussian function method for speed calculation has good real-time performance;however,the speed measurement accuracy is>1.5 m/s.The Kalman meth⁃od has good accuracy in calculating velocity;however,owing to the use of a large amount of historical da⁃ta,the velocity value lags behind.The speed calculated by the optimal uniform approximation polynomial method in this study has good real-time performance and a delay of 50 ms.The mean square deviation of speed accuracy is 0.8 m/s,which meets the equipment’s indicator requirements.