# Combination Analysis of Future Polar-Type Gravity Mission and GRACE Follow-On
## 1 Introduction  
The Earth is undergoing complicated and continuous mass transport [1]. To better quantify the mass changes, the Gravity Recovery and Climate Experiment (GRACE) mission was launched in 2002, which consists of the twin satellites flying in the same near-polar orbit at about 500-km altitude and separated by 220 km [2]. The key technology that enables GRACE to observe large-scale mass variations near the Earth surface is the onboard K-band microwave ranging system (KBR), which delivers inter-satellite range measurements with an accuracy at micron level to precisely capture orbit perturbation differences between the two GRACE satellites caused by heterogeneous mass distribution of the Earth [2, 3]. Along with the KBR, other important sensors onboard GRACE satellites include Global Positioning System (GPS) receivers for precise orbit determination (POD), high-precision accelerometers for measuring non-gravitational forces and star cameras for attitude determination [4, 5, 6]. Based on the precise data collected by the above sensors, many scientific institutions have produced high-quality static and temporal gravity field models [7, 8, 9, 10, 11], which are successfully adopted for quantitative researches concerning the Earth's mass changes, such as global mean sea-level variations [12, 13], continental water balance [14, 15], and the Tibetan Plateau and Antarctic regional ice losses [16, 17]. In view of such a great success achieved by GRACE in terms of the Earth's mass change exploration, its successor GRACE Follow-On (GFO) was launched on 22 May 2018 to continue providing the geodetic observation records [18; 19]. As a demonstrator, GFO carries a laser ranging interferometer (LRI) for measuring inter-satellite ranges with an accuracy level of a few tens nanometers in addition to the sensors onboard the GRACE satellites [18; 19; 20]. However, even with such a dramatic accuracy improvement for the range observations, some full-scale pre-launch simulations indicated that only a moderate improvement on gravity field estimation can be reached by GFO as compared to GRACE [18; 21]. The dominant barrier to further improvement on gravity field determination by GFO is the temporal aliasing issue, which is more intractable than other limiting factors in the GFO error budget [18; 21]. From a digital signal processing aspect, aliasing is due to undersampling of the signal to be recovered. According to the Nyquist sampling theorem, when sampling frequency is smaller than twice of the original signal frequency, aliasing definitely occurs [22]. In terms of GRACE monthly gravity field recovery, temporal aliasing is mainly attributed to those high-frequency signals originating from the oceanic tidal variations at daily or sub-daily scale, as well as the short-term energy exchange process (generally within a few hours) between atmosphere and ocean [23; 24]. Because of the limited bandwidth for observations and sparse ground track of GRACE, most part of these signals typically need to be reduced by priori background models during gravity field recovery process [25], which are, however, subject to errors [26; 27]. Therefore, the remaining high-frequency signals result in the temporal aliasing errors in monthly-average gravity solutions, which manifest themselves as the typical north-south stripes in spatial pattern of unfiltered GRACE models [28; 29]. To mitigate the troublesome temporal aliasing effects, post-processing filtering techniques are generally applied as a standard procedure [28; 29; 30]. However, the fundamental solution should be based on the enhanced signal sampling and gravity field modelling strategy [31; 32; 33; 34]. One of the most straightforward and efficient ways is to increase the number of satellites in space for denser sampling of gravity signals. Thereby, many researchers have investigated novel concepts of satellite formation flight (SFF) or satellite constellations dedicated to gravity field recovery, including the cartwheel, pendulum, and Bender-type configurations [35; 36; 37; 38; 39].