## 1 Introduction  
The Earth Rotation Parameters (ERP), encompassing polar motion (PM) and its rates, along with UT1-UTC and its rate (length of day, LOD), describe the spatiotemporal variations in the Earth's rotation vector [1]. These parameters play a crucial role in defining a global reference frame and are determined through space geodetic techniques such as Very-Long-Baseline Interferometry (VLBI), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), Satellite Laser Ranging (SLR), and Global Navigation Satellite System (GNSS) [2]. Due to the characteristics of the different techniques, these techniques are sensitive to different aspects of the Earth system [3]. The GNSS technology is predominant in PM estimates because of the dense and uniform global distribution of the observing network, the continuous and high-precision observations, as well as the wide and stable satellite constellation [4; 5]. The latest IGS Repro3 ERP products, contributing to the most recent ITRF2020, were generated without incorporating data from the Beidou Navigation Satellite System (BDS). [6; 7]. The global BDS, namely BDS-3, has completed its construction which consists of hybrid constellations including Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites [8]. It is worth noting that the BDS-3 MEO satellites were made by two entities including the China Academy of Space Technology (CAST) and the Shanghai Engineering Center for Microsatellites (SECM) [9; 10]. The network of ground observing stations for BDS-3 are evenly distributed globally now. The five open service signals of BDS-3 satellites include B1I, B3I, B1C, B2a, and B2b [11]. Notably, B1I and B3I signals are also transmitted by the regional BDS (BDS-2). The B1C, B2a, and B2b signals, unique to BDS-3, are designed to be compatible and interoperable with signals from other GNSSs [12]. For the usage of an ionosphere-free combination, the official interface control document recommends B1C/B2a and B1I/B3I frequency combinations [13; 14]. This research aims to assess the ERP derived from observations based on both BDS-3 B1I/B3I and B1C/B2a frequency combinations and seeks to identify the optimal dual-frequency combination for BDS-3 ERP estimates for the future ITRF definition with a consideration of BDS-3. Many studies related to ERP derived by BDS-3 are based on B1I/B3I dual-frequency combination because most of BDS station receivers only support this frequency couple at the initial stage [9; 15; 16]. [PERSON] et al. investigated the influence of the solar radiation pressure (SRP) model on BDS orbit, geocenter motion, and ERP estimation as well as estimated the box-wing parameters based on B1I/B3I combination observations, concentrating on BDS satellites with a maximum PRNs of C37 due to receiver limitations from Multi-GNSS Experiment (MGEX) stations at the outset [9]. Afterwards, [PERSON] et al. enhanced ERP estimates from BDS satellites, incorporating box-wing models estimated based on B1I/B3I observations with PRNs extending up to C46 [15]. [PERSON] et al. showcased the advantages of hybrid constellation construction for ERP determination, utilizing IGSO and MEO satellites from BDS with B1I/B3I observations [16]. [PERSON] et al. further investigated the benefits of hybrid BDS constellation construction, considering GEO, IGSO, and MEO satellites, along with a hybrid SRP model [17]. Moreover, [PERSON] et al. compared the ERP estimated by BDS, GPS, and Galileo and analyzed the features of their systematic bias in ERP [18]. In addition, [PERSON] et al. studied the ERP-obtained discontinuous VLBI observations and BDS-3 based on B1I/B3I measurements [19]. However, these studies for ERP derived from BDS-3 only utilized B1I/B3I observations without a consideration of using BDS-3 B1C/B2a observations. Recently, many researchers studied the superiority of the BDS-3 B1C/B2a combination on the usage of Precise Point Positioning (PPP), clock offset, and orbit estimation. [PERSON] et al.