光学精密工程2023，Vol.31Issue(24)：3549-3558,10.DOI:10.37188/OPE.20233124.3549
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
摘要
Abstract
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.关键词
最佳一致逼近速度求解/高斯速度求解/卡尔曼滤波速度求解/有限差分法Key words
Optimal Uniform Approximation(OUA)/Gaussian velocity solving/Kalman filtering speed solution/finite difference分类
计算机与自动化引用本文复制引用
赵立荣,袁光福,吴冬,高群,王潇洵..经纬仪最佳一致逼近多项式速度实时求解[J].光学精密工程,2023,31(24):3549-3558,10.基金项目
国家自然科学基金资助项目(No.6210031610) （No.6210031610）
