## 1 Introduction  
HaiYang-2B (HY-2B) is the second marine dynamic environment satellite of China [1]. It was launched on 25 October 2018, with an altitude and inclination of about 973 km and 99.3\({}^{\circ}\), respectively. The major objective of the HY-2B is to monitor and investigate the marine environment. It carries various instruments, including a dual-frequency altimeter in the Ku and C-bands, a scatterometer, and a microwave imager. The HY-2B mission undertakes routine measurements of sea surface height. Its precise orbit provides a good reference for an altimetry satellite, which is very important for long-term Earth observation missions [2, 3, 4]. Moreover, the precise orbit determination (POD) function of the altimetry satellite is the basis of various oceanographic applications based on altimetry technology [5, 6], such as the determination of global and regional mean sea level changes, the modeling of the mean sea height, ocean tide simulations, etc. [7, 8, 9]. To support this mission, the HY-2B spacecraft hosts a POD package, including an onboard Global Positioning System (GPS) receiver and a laser retroreflector (LRR) for satellite laser ranging (SLR). Based on Global Navigation Satellite System (GNSS) measurements and dynamical models of satellites, three different orbit determination methods were developed, which are known as kinematic, dynamic, and reduced-dynamic. To optimize the advantages of purely geometric observations and dynamic methods, pseudo-stochastic parameters are employed to compensate for potential deficiencies of dynamic models based on reduced-dynamic concepts [5; 10]. At present, the reduced-dynamic POD based on onboard GNSS observations has been widely used for most low-Earth orbit (LEO) geodetic [11; 12; 13] and remote sensing missions [14; 15; 16]. The precise orbits of GRACE [17], with an uncertainty of less than 3 cm in SLR residuals, are supported using onboard GPS data. Overall SLR validation better than 2 cm for GOCE missions can be obtained for GPS-based orbits [18]. The reduced-dynamic Swarm Precise Science Orbits (PSO) showed an accuracy of better than 2 cm by independent SLR validation [19; 20]. However, the dynamic background models of the satellites involved and their data processing strategies differ slightly, and there is no unified POD strategy. Empirical accelerations have been successfully used in LEO POD as an inherent strategy. Along with the initial state vector of LEO satellites and the scaling factors for individual force model constituents, empirical acceleration parameters are estimated in reduced-dynamic POD. The performance of this technique in high-precision orbit determination has been widely investigated by the LEO POD community [21; 22; 23]. A refined non-gravitational force model of a LEO satellite will reduce the amount of empirical acceleration [13; 23; 24], and many scholars have set their sights on model refinement. Some analysis has indicated the direction and the time variability of the remaining deficit [18; 22]. From the perspective of spectral analysis, the potential perturbation frequency of unmodeled acceleration information can be extracted and analyzed. Better orbit determination results may be obtained when the empirical acceleration is consistent with the spectral analysis. Therefore, spectral analysis of the remaining empirical acceleration of POD was performed, and an optimized piece-wise empirical acceleration (PEA) model is proposed in this article. The accurate known location of the GPS receiver antenna relative to the center of mass (CoM) is the premise of precise orbit determination [25; 26]. This location is typically provided by the spacecraft manufacturer, with a nominal accuracy of millimeters or better, but the experience of past geodetic missions has shown that there may be inconsistencies at the level of 2-3 cm [28; 16; 27]. Therefore, offset calibration of the GPS antenna phase center and empirical phase center variations (PCV) corrections were performed to eliminate the systematic errors in the HY-2B POD.