光学经纬仪多站交会的整体最小二乘算法

Total least square algorithm applied in multi-station intersection of optical theodolite

靶场多台光学经纬仪获取空中炸点坐标时,所采用的水平投影法存在未能充分利用冗余观测值以及难以从多组解算结果中选出最精确结果的问题。而基于最小二乘的交会算法,虽然能解决上述问题,但是受初值影响较大、迭代速度慢甚至可能发散。提出了一种基于整体最小二乘的交会算法,该方法在迭代计算的过程中,对权矩阵不断进行调整,直到满足一定的精度要求为止。结合仿真数据对算法进行了验证。结果表明:该算法在初值较大的情况下,不容易发散,进行10次以内的迭代计算,即可得到较好的结果,当站点至目标距离为1 500m时,精度可达到0.3m以内,满足靶场要求。该算法同时考虑了观测值误差和模型线性化误差,大大降低了初值的影响,提高了收敛速度,能够精确地解算出炸点的三维坐标。

Horizontal projection method, which is applied in calculating coordinates of aerial bursting points, has major problem in exploiting redundancy observations and in filtrating optimal results from multi-group solutions. Intersection algorithm based on least square, although able to solve the above problems, is influenced by initial value of a larger, iterative slow or even divergent. An intersection algorithm based upon total least square is proposed. In the process of iterative computation, weight matrix is adjusted continuously until a certain precision requirement is satisfied. This algorithm is validated by combining simulation data. Results show that proposed algorithm can obtain better results when initial value is larger, and it is not easy to diverge. It can get better results by 10 iterations or less, and precision can reach 0.3 m when distance from station to target is 1 500 m. This algorithm takes into account both observation error and model linearization error, which greatly reduces influence of initial value and improves convergence speed, and can accurately calculate three-dimensional coordinates of aerial bursting points.