# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 1 Introduction  
Continuously changing of global ice, ocean and atmosphere, the core-mantle interaction torques, and the gravitational attraction of the sun, moon, and planets [1, 2] give rise to the variations of earth rotation. These effects can be comprehensively described by defining a set of parameters, namely, Earth rotation parameters (ERP), which consist of pole coordinates and universal time 1--universal time coordinated (UT1-UTC) or its first derivative in time, denoted as length-of-day (LOD). The ERP series, along with nutation and precession, characterize the varying orientation of the Earth in space [34]. Obtaining the accurate knowledge of the Earth's rotation and its evolution in time is one of the fundamental goals for the geodesy community. Considerable efforts have been made to achieve this goal by many researchers [5, 6, 7] and organizations, such asInternational Earth Rotation and Reference Systems Service (IERS), based on different space geodetic techniques. Among the key techniques of ERP estimation is satellite laser ranging (SLR), which measures the round-trip time-of-flight of laser light pulses between the satellite and ground stations. The International Laser Ranging Service (ILRS) [8] has routinely generated the ERP product using the SLR data that were collected by a global distributed network for many years. Although a number of low Earth orbit (LEO) satellites carry retroreflectors for tracking and navigation purposes, Laser Geodynamics Satellites (LAGEOS) and Etalons are the satellites that are most commonly used to determine the Earth rotation parameters, which only contribute to 9% of all the SLR observations [9]. This means that a large number of SLR observations for LEO satellites are neglected while generating geodetic parameter products, and only used for orbit validation or space navigation [10]. Generally, the LEO satellites, which are usually not considered in the ERP estimation, can be classified into the following two distinct categories: passive geodetic LEO satellites and Earth observation LEO satellites. Similarly to LAGEOS and Etalons, most passive geodetic LEO satellites are specifically designed and launched to study the geodetic properties of the Earth. However, these satellites are excluded from the ERP product generation, due to many factors, for instance, sparse observations, deficiencies in the force model, and inferior accuracy of orbit, etc. [11; 12]. Many studies have been carried out to overcome these limitations and improve the contribution of these geodetic LEO satellites to the realization of a reference frame [13; 14; 15]. The other type, namely, Earth observation LEO satellite, refers to the satellites that are dedicated to observing, exploring and understanding the Earth system. A well-known example is the Gravity Recovery and Climate Experiment (GRACE), whose primary objective is to map the time-variable and mean gravity field of the Earth [16]. Different from the spherical geodetic LEO satellites, the Earth observation LEO satellites are usually equipped with a geodetic-grade Global Navigation Satellite Systems (GNSS) receiver to fulfill the requirement of the high-accuracy orbit information. For most space missions, a laser ranging retroreflector (LRR) is also accommodated on the satellite platform, for assessing the quality of GNSS-based precise orbit determination solutions. The potential of these satellites for generating geodetic parameters is neglected because of their irregular geometry shape, large area-to-mass ratio, and complicated force models, which eventually leads to the deficiencies in precise orbit determination (POD) processing. However, thanks to the development of the onboard GNSS technique and advances in dynamical modeling, the quality of LEO orbits has been improved significantly. The SLR validation in the previous studies indicates that the orbit accuracy at the level of 5-10 mm (1D) is achievable for these satellites [17; 18; 19].