全张量重力梯度仪测量方程及误差分析

Measurement equations and error analysis of full tensor gravity gradiometer

为了研究加速度计性能与全张量重力梯度仪测量精度之间的关系,从全张量重力梯度仪的测量原理出发,建立了重力梯度仪的测量方程,并根据坐标变换矩阵得到测量坐标系和惯性平台坐标系下全张量重力梯度仪的输出表达式.根据加速度计的输入输出数学模型,给出了包含加速度计性能参数的输出方程,并分析了加速度计性能对全张量重力梯度仪测量精度的影响.理论分析结果表明,当旋转圆盘中心存在加速度时,加速度计的零位偏置、标度系数的非一致性以及二阶非线性系数均产生重力梯度测量误差.通过采用高精度加速度计、高精度稳定平台及标度系数在线自动补偿技术,可以提高重力梯度仪的测量精度.

To study the relationship between the accelerometer performance and the measurement precision of a full tensor gravity gradiometer,measurement equations are derived according to the measurement principle of full tensor gravity gradiometers.The output expressions of the full tensor gravity gradiometer in a measuring coordinate system and in an inertial platform coordinate system are obtained,respectively,according to the coordinate transformation matrix.According to the input-output mathematical model of the accelerometer,the output equation including accelerometer performance parameters is presented,and the influence of the accelerometer performance on the measurement precision of the gravity gradiometer is analyzed.The theoretical analysis results show that when the rotating disc center is in acceleration,the accelerometer bias,scale-factor inconsistency and second order nonlinear terms result in the measurement errors of the gravity gradiometer.The measurement precision of the gravity gradiometer can be improved by using a high precision accelerometer,a high precision stable platform and a scale-factor online automatic compensation technique.