A Semi-analytical Approach To Gravity Field Error Analysis From Satellite Formations

Past and current gravimetric satellite missions have contributed drastically to our knowledge of the Earth's gravity field.Nevertheless,Many geoscience disciplines,such as terrestrial water storage changes,ice-mass variations,ocean bottom pressure changes and sea-level variations push for ever higher requirements on accuracy,homogeneity and time-and spatial-resolution of the Earth's gravity field.Apart from better instruments or new ob-servables,alternative satellite formations,such as pendulum formation,cartwheel formation and Bender constellation,could improve the signal and error structure compared to GRACE.With respect to other methods,one significant advantage of the semi-analytical approach is its effective pre-mission error assessment for gravity field missions.One possibility to increase sensitivity and isotropy by adding cross-track information and radial direction information is a pair of satellites flying in a pendulum formation and cartwheel formation.The pendulum formation contains two satellites which have different ascending nodes and arguments of latitude but have the same orbital height and inclination.The cartwheel formation is formed by two satellites on elliptic orbits in the same plane with a 180° separation in perigee.The Bender constellation is constituted by two pairs of satellite formations with different inclinations,then it can improve the time-and spatial-resolution at the same time.In this study,the semi-analytical approach for efficient pre-mission error assessment is presented.This approach builds a linear relationship between Fourier spectrum of observa-tions and the spherical harmonic spectrum of the geo-potential.This spectral link is given by the transfer coefficients,which constitute the design matrix of the observation model.Each observable corresponds to a certain transfer coefficient.In connection with a stochastic model,it can be employed for pre-mission error assessment of gravity satellite mission.In this work,the transfer coefficients of range,range-rate and range-acceleration grav-itational perturbations are derived analytically for the pendulum formation considering a set of opening angles and also for cartwheel formation with different initial argument of perigee.For the pendulum formation,the new challenge is the time variations of the open-ing angle and the range,leading to temporally variable transfer coefficients.This is solved by Fourier expansion of the sine/cosine of the opening angle and the central angle.For the cartwheel formation,the eccentricity function is introduced for eccentric orbit,and the time dependent ranging is also considered in the transfer coefficients via convolution like pen-dulum formation.The transfer coefficients are further applied to assess the error patterns which are caused by different orbital parameters.Based on the semi-analytical approach,a series of simulations are designed for the pendulum,Bender and cartwheel formations.The simulation results indicate that a signifi-cant improvement in accuracy and isotropy is obtained for small and medium initial opening angles of single polar pendulums,compared to GRACE.The optimal initial opening angles are 40° and 10° for accuracy and isotropy,respectively.The error level is lower for lower orbit height and longer inter-satellite distance,but the improvement for longer inter-satellite distance is not obvious,especially for pavg>100 km.For a Bender configuration,which is constituted by a polar GRACE and an inclined pendulum in this paper,the behaviour of results is dependent on the inclination(prograde vs.retrograde)and on the relative baseline orientation(left or right leading).The simulation for a sun-synchronous orbit shows better results for the left leading case.For the classical Bender constellation,which is constituted by a polar GRACE and an inclined GRACE,the inclination I = 125° case provides the best results for error level and isotropy,respectively.Moreover,the error level and isotropy are worse for the classical Bender constellation.For the cartwheel formation,simulation is designed for different relative orientations.There is an improvement both in error level and isotropy,compared to GRACE-like mission.The simulation results still need more investigations.