附加约束条件的井下控制网变参数序贯平差

Variable Parameter Sequential Adjustment with Constrained Condition of Underground Control Network

为了精确建立井下空间位置基准,针对井下控制网分期布设的特点,提出了一种附加约束条件的井下控制网变参数序贯平差模型。首先根据虚拟观测值法及最小二乘原理推导了井下控制网变参数序贯平差模型,并顾及井下陀螺定向边可作为坚强边的情况,利用无限权理论将约束条件转化为变参数序贯平差模型的观测方程,该模型不仅可以将陀螺边方向观测值作为限制条件处理,也可以作为普通观测值参与计算;然后,为了避免法方程病态,分析了定权系数的合理取值并通过工程实例对该模型的正确性进行了验证。结果表明:1当定权系数m=1时,陀螺边方位角的平差值与已知值之差最大达到5.1″,随着定权系数m的增大,其差值迅速减小;2当m=10时,其差值均小于0.1″;3当m=20时,陀螺边方位角的平差值与坐标平差值在有效位数范围内均与真值一致,方位角差值均小于0.01″,坐标差值均小于0.03 mm。所提出的平差模型具有思路简单、易于编程的特点,无需前期观测数据,适用于井下分期布设的控制网整体平差。

In order to establish the spatial position-reference accurately,and aiming at the characteristics of multi-period control network underground, the variable parameters sequential adjustment model of underground control network with con-strained condition is presented. Firstly,based on the virtual observation law and the least square method,the sequential adjust-ment model of underground control network is deduced. Considering the gyro direction edges as strong sides,the constrained conditions can be converted into the observation equation of the variable parameters sequential adjustment based on infinite weight theory. The new model can be used for processing gyro-side observation as constraint condition. Also,it can be employed to calculate the gyro-side observation as general observation values. Then,in order to avoid the ill-condition of normal equation, the reasonable values of weight coefficient are discussed. Besides that,the rationality of the model is verified by a project case. The results show that：①when the weight coefficient m=1,the maximum difference between adjusted value and true value of gyro azimuth is 5. 1″,with the increasing of weighting coefficient m, the difference decreases rapidly; ②when m=10,the difference is less than 0. 1″;③when m=20,the adjusted values of gyro-side azimuth and coordinates are consistent with the true value within the scope of effective number of bits,the azimuth difference is less than 0. 01″,and the coordinates of the difference is less than 0. 03 mm. The adjustment model proposed in this paper has the characteristics of simple idea,easy pro-gramming and no preliminary observation data needed,it is applicable to the integrated adjustment of the underground multi-pe-riod control network.