交会测量中具有自适应权因子的最优无偏方法

在利用多台测量站对空中运动物体进行交会测量过程中，测量站两两交会得到的测量结果并不会完全一致，有时甚至会有很大差别。讨论了具有自适应权的最优无偏方法：首先利用最小二乘法的原理，推导出了最小二乘解的表达式。在求解最优无偏解的过程中，通过求条件极值的方法导出了最优无偏解的权因子。由于权因子中的某些因素与目标像在CCD像面上的位置有关，提出了“自适应权”的思想，即权因子随目标像点位置的不同而自动调整。与传统的方法相比，具有自适应权的最优无偏方法，在一定程度上更充分地利用了不同情况下来自不同测量站的测量信息，从而提高了测量精度。经实际计算表明，在低空目标定位时，具有自适应权的最优无偏方法的平均偏差为传统方法平均偏差的40％左右。

Optimal Unbiased Method with Adaptive Weights in Crossing Measurement

In the process of measuring the aerial object with measuring stations, the crossing measurement results of every two stations are not absolutely consistent. And sometimes there may exist distinct differences. An optimal unbiased method with adaptive weights is proposed. Based on the least square principle, the expression of the least square result is deduced. The optimal weights are given with the constrained optimization method. Considering that the weights are related to the position of the target image on the CCD plane, the idea of adaptive weights is introduced, i.e. the weights can be adjusted as the position of the target image changes. Compared with the traditional methods, this method utilizes the measurement information from different stations sufficiently, and improves the accuracy evidently. The test results show that the optimal method with adaptive weights can decrease the average error to 40% compared with the traditional methods.