一种基于Hermite函数约束的光学经纬仪多站定位方法研究

Research on the Positioning Method of Multi-optical Theodolites Based on Hermite Function Restriction

传统光学几何交会方法中采用的方向余弦定位法因其算法简单清晰一直广泛应用于工程实践,但该方法受空间几何关系影响较大,对测元误差抑制能力差,因此定位精度并不理想,而且不能多站同时定位计算。为此提出一种基于Hermite函数约束的光学经纬仪多站定位解算方法,称为函数约束误差模型弹道最佳估计(EMBET)方法。该方法首先在采用Hermite函数表征目标定位参数以压缩待估参数数量的基础上进而实现对光学经纬仪测元的数学表征,然后将多站多测元观测数据组成联合测量方程,最后依据最小二乘准则优化解算方程获取目标定位参数,并具有对测元系统误差校准的能力。结合仿真实例计算,对方向余弦定位方法和函数约束EMBET方法进行了比较分析,验证了函数约束EMBET方法在光学经纬仪多站定位中具有更高的定位精度和更强的实用性,为工程应用提供了参考依据。

The direction cosine location method which is used in traditional optical geometric intersection is simple,so it is widely used in engineering practice.But this method is greatly influenced by the geometric relationship,and cannot inhibit the measuring error,so its positioning accuracy is unsatisfactory.In addition,it cannot be used to compute the locations with more than three stations at a time.A new positioning method with multi-optical theodolites is proposed based on Hermite function restriction.This method can be called function restricted EMBET method.This method uses Hermite function to express the positioning parameters to compress the number of parameters to be estimated,and meanwhile the measuring elements of optical theodolite can be expressed.The measuring equation can be formed by measuring data of multiple measuring elements.Based on least square criterion,the positioning parameters are obtained by computing the combined equation,and the system errors of measuring elements are calibrated.Through the calculation of simulated example,the function restricted EMBET method is compared with the direction cosine location method.The result shows that the function restricted EMBET method is more accurate and more practical.