Position determination and measurement error analysis for the spherical proof mass with optical shadow sensing

To meet the very demanding requirements for space gravity detection, the gravitational reference sensor (GRS) as the key payload needs to offer the relative position of the proof mass with extraordinarily high precision and low disturbance. The position determination and error analysis for the GRS with a spherical proof mass is addressed. Firstly the concept of measuring the freely falling proof mass with optical shadow sensors is presented. Then, based on the optical signal model, the general formula for position determination is derived. Two types of measurement system are proposed, for which the analytical solution to the three-dimensional position can be attained. Thirdly, with the assumption of Gaussian beams, the error propagation models for the variation of spot size and optical power, the effect of beam divergence, the chattering of beam center, and the deviation of beam direction are given respectively. Finally, the numerical simulations taken into account of the model uncertainty of beam divergence, spherical edge and beam diffraction are carried out to validate the performance of the error propagation models. The results show that these models can be used to estimate the effect of error source with an acceptable accuracy which is better than 20%. Moreover, the simulation for the three-dimensional position determination with one of the proposed measurement system shows that the position error is just comparable to the error of the output of each sensor.