Article Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO

Xingxing Li, Hongmin Zhang, Keke Zhang *, Yongqiang Yuan, Wei Zhang and Yujie Qin

School of and , Wuhan University, 129 Luoyu Road, Wuhan 430079, ; [email protected] (X.L.); [email protected] (H.Z.); [email protected] (Y.Y.); [email protected] (W.Z.); [email protected] (Y.Q.) * Correspondence: [email protected]

Abstract: Earth rotation parameters (ERP) are one of the key parameters in realization of the Interna- tional Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the laser ranging (SLR)-based ERP products only using SLR observations to Laser Satellite (LAGEOS) and Etalon satellites. Apart from these geodetic satellites, many low Earth (LEO) satellites of Earth observation missions are also equipped with laser retroreflector arrays, and produce a large number of SLR observations, which are only used for orbit validation. In this study, we focus on the contribution of multiple LEO satellites to ERP estimation. The SLR and Global (GPS) observations of the current seven LEO satellites (-A/B/C, Gravity Recovery and Experiment (GRACE)-C/D, and Sentinel-3A/B) are used. Several schemes are designed to investigate the impact of LEO orbit improvement, the ERP quality of the single-LEO solutions, and the contribution of multiple LEO combinations. We find that ERP es-  using an ambiguity-fixed orbit can attain a better result than that using ambiguity-float  orbit. The introduction of an ambiguity-fixed orbit contributes to an accuracy improvement of 0.5%, Citation: Li, X.; Zhang, H.; Zhang, 1.1% and 15% for X pole, Y pole and station coordinates, respectively. In the multiple LEO satellite K.; Yuan, Y.; Zhang, W.; Qin, Y. Earth solutions, the quality of ERP and station coordinates can be improved gradually with the increase in Rotation Parameters Estimation the involved LEO satellites. The accuracy of X pole, Y pole and length-of-day (LOD) is improved by Using GPS and SLR Measurements to 57.5%, 57.6% and 43.8%, respectively, when the LEO number increases from three to seven. Moreover, Multiple LEO Satellites. Remote Sens. the combination of multiple LEO satellites is able to weaken the orbit-related signal existing in the 2021, 13, 3046. https://doi.org/ single-LEO solution. We also investigate the combination of LEO satellites and LAGEOS satellites 10.3390/rs13153046 in the ERP estimation. Compared to the LAGEOS solution, the combination leads to an accuracy improvement of 0.6445 ms, 0.6288 ms and 0.0276 ms for X pole, Y pole and LOD, respectively. In Academic Editor: Pietro Tizzani addition, we explore the feasibility of a one-step method, in which ERP and the orbit parameters are

Received: 4 June 2021 jointly determined, based on SLR and GPS observations, and present a detailed comparison between Accepted: 27 July 2021 the one-step solution and two-step solution. Published: 3 August 2021 Keywords: onboard GPS; SLR; LEO; Earth rotation parameters; ambiguity fixing Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published and institutional affil- iations. 1. Introduction Continuously changing of global ice, ocean and atmosphere, the core–mantle inter- action torques, and the gravitational attraction of the sun, , and planets [1,2] give rise to the variations of earth rotation. These effects can be comprehensively described by Copyright: © 2021 by the authors. defining a set of parameters, namely, Earth rotation parameters (ERP), which consist of Licensee MDPI, Basel, Switzerland. pole coordinates and universal time 1—universal time coordinated (UT1-UTC) or its first This article is an open access article derivative in time, denoted as length-of-day (LOD). The ERP series, along with nutation distributed under the terms and and precession, characterize the varying orientation of the Earth in space [3,4]. conditions of the Creative Commons Obtaining the accurate knowledge of the Earth’s rotation and its evolution in time Attribution (CC BY) license (https:// is one of the fundamental goals for the geodesy community. Considerable efforts have creativecommons.org/licenses/by/ been made to achieve this goal by many researchers [5–7] and organizations, such as 4.0/).

Remote Sens. 2021, 13, 3046. https://doi.org/10.3390/rs13153046 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 3046 2 of 23

International Earth Rotation and Reference Systems Service (IERS), based on different space geodetic techniques. Among the key techniques of ERP estimation is (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 (LEO) satellites carry retroreflectors for tracking and 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 estima- tion, 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 [13–15]. 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 ob- jective is to 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 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 [17–19]. In recent years, more attention has been paid to the Earth observation satellites for the purpose of ERP estimation and even the realization of a reference frame. Guo et al. [20] found that the GRACE-A satellite, as the co-location of SLR and GNSS techniques, allowed the precise estimation of SLR station coordinates, with a consistency at the level of 2–3 cm with respect to Satellite Laser Ranging Frame 2014 (SLRF2014). Using two years of SLR data from Sentinel-3 satellites, Strugarek et al. [9] investigated the possibility of estimating geodetic parameters, only based on LEO observations. The result showed that it is feasible to solely use the SLR observations of LEO satellites for the determination of ERP and geocenter motion, and the combination of LAGEOS and Sentinel satellites can provide high-accuracy geodetic parameters. Bloßfeld et al. [21] used SLR observations to Jason satellites to derive SLR station coordinates using the preprocessed observation-based attitude of Jason satellites. A posteriori variance factor of the estimation of SLR station coordinates improved by about 10% for Jason-1 and Jason-3, and almost 20% for Jason-2, when compared to that using a nominal yaw-steering model. The previous studies demonstrate the feasibility of ERP estimation based on the SLR observations to some Earth observation satellites. However, they only focus on a single LEO satellite or single LEO satellite mission, which leads to sparse SLR observations for Remote Sens. 2021, 13, 3046 3 of 23

ERP estimation. Considering that, currently, a number of LEO satellites are equipped with an LRR, the great potential of multiple LEO satellites from different missions for ERP estimation has not been fully explored. The goal of this study is to investigate the contribution of multiple LEO satellites to the ERP estimation with seven LEO satellites flying at different orbits. The combination of multiple LEO satellites and LAGEOS satellites is highlighted and investigated in detail. In addition, we also discuss the possibility of the joint processing of SLR and GPS observations to determine ERP and the orbits parameters simultaneously in this study. The paper is organized as follows: Section2 addresses the data set and describes the detailed processing strategies. In Section3, we validate the GPS-derived LEO orbit and evaluate the performance of ERP based on the single-LEO solutions. Subsequently, in Section4, the ERP estimation, based on multiple LEO satellites, and the combination of LEO satellites and LAGEOS satellites is analyzed. Additionally, the two-step method and one-step method are compared. In Section5, a discussion about the results obtained in this study is given. Finally, in Section6, a summary of the results and corresponding discussions are presented.

2. Data Set and Processing Strategy In order to evaluate the performance of LEO satellites for ERP determination, one-year onboard SLR and GPS data in 2019, from seven LEO satellites, including Sentinel-3A, Sentinel-3B, Swarm-A, Swarm-B, Swarm-C, GRACE-C, and GRACE-D, are used in this study. Table1 gives the orbit information of these satellites, and the types of LRR and GPS receivers they carried. Two types of LRR, with different basic designs, are carried by the satellites we selected. The LRR with seven-prism, made by the Institute of Precision Instruments Engineering (IPIE), is mounted on the Sentinel-3 satellites, while the gravity recovery and climate experiment follow-on (GRACE-FO) and Swarm are equipped with a four-prism LRR, manufactured by the GeoForschungsZentrum (GFZ). The Swarm and Sentinel-3 onboard GPS receivers are developed by RUAG Space, and have eight channels that are available for dual-frequency tracking of GPS satellites. While GRACE-FO is equipped with the Jet Propulsion Laboratory (JPL) TriG receiver, which can observe the GPS signal at L1/L2 and track up to 16 GPS satellites. In addition to the LEO observations, we also process SLR observations of LAGEOS-1/-2 satellites, to obtain a LAGEOS-based solution for a reference.

Table 1. Overview of LEO mission used in this study.

Satellite Perigee Altitude/km Inclination/deg LRR GPS Receiver Sentinel-3A 814 98.65 7-prism RUAG Sentinel-3B 814 98.65 7-prism RUAG Swarm-A 462 87.35 4-prism RUAG Swarm-B 511 87.35 4-prism RUAG Swarm-C 462 87.35 4-prism RUAG GRACE-C 500 89.00 4-prism TriG GRACE-D 500 89.00 4-prism TriG LAGEOS-1 5860 109.90 426 corner cubes —- LAGEOS-2 5620 52.67 426 corner cubes —-

In this study, we adopt two methods to estimate the ERP from the SLR and GPS observations of LEO satellites, namely, the two-step method and one-step method. Figure 1 gives the flowchart of these two methods. In the two-step method, the orbits of the LEO satellites are firstly estimated, using the onboard GPS observations. Here, we choose to independently perform POD for the seven LEO satellites, rather than directly using the external precise orbit products; this is because the external LEO orbit products are Remote Sens. 2021, 13, x FOR PEER REVIEW 4 of 23

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satellites are firstly estimated, using the onboard GPS observations. Here, we choose to independently perform POD for the seven LEO satellites, rather than directly using the generatedexternal precise based orbit on differentproducts; processing this is because strategies, the external software LEO platformsorbit products and are GPS gener- products, andated thesebased inconsistencies on different processing may introduce strategies, additional software errors platforms to the and final GPS ERP products, solutions. and After thethese LEO inconsistencies POD processing, may introduce we estimate additional ERP from errors SLR to observations the final ERP with solutions. the LEO After orbit the fixed. LEO InPOD the processing, one-step method, we estimate the GPSERP andfrom SLR SLR observations observations arewith jointly the LEO processed orbit fixed. to simul- taneouslyIn the estimateone-step method, the LEO the orbit GPS and and ERP SLRin observations a common are least-squares jointly processed adjustment. to sim- The pseudorange,ultaneously estimate carrier the phase LEO observations,orbit and ERP andin a SLRcommon observations least-squares are weightedadjustment. according The pseudorange, carrier phase observations, and SLR observations are weighted according to the ratio of about 1:15,000:15,000. It should be noted that, in the two-step method, the to the ratio of about 1:15,000:15,000. It should be noted that, in the two-step method, the orbits are only determined based on GPS observations, while in the one-step method, the orbits are only determined based on GPS observations, while in the one-step method, the orbits are calculated using GPS and SLR observations simultaneously. In order to avoid orbits are calculated using GPS and SLR observations simultaneously. In order to avoid the possible accuracy degradation of the estimated LEO orbit in an orbit arc with a longer the possible accuracy degradation of the estimated LEO orbit in an orbit arc with a longer lengthlength (such (such as as 7 7 days), days), in in this this study study we we select select a 3 a-day 3-day arc arclength length with with 2-day 2-day overlaps overlaps betweenbetween two two adjacent adjacent consecutive consecutive orbit orbit arcs. arcs.

FigureFigure 1. FlowchartFlowchart of of two two-step-step method method and and one one-step-step method. method.

In the the LEO LEO POD POD processing, processing, we we use use undifferenced undifferenced ionosphere-free-free GPSGPS observations observations withwith 30-s30-s sampling, and and the the cutoff cutoff elevation elevation angle angle is set is setto 1°. to 1The◦. The GPS GPS phase phase center center offset offset (PCO)(PCO) and phase phase center center variation variation (PCV) (PCV) are are corrected corrected with with igs14.atx igs14.atx [22]. [ 22For]. the For LEO the LEO satellitesatellite antennas, antennas, the the PCO PCO corrections corrections from from ground ground calibration calibration are areemployed, employed, while while the the PCVPCV values are are computed computed using using the the in in-flight-flight calibrated calibrated model model estimated estimated by the by residual the residual method [23,24]. The GPS orbit, products, and wide-lane satellite biases products method [23,24]. The GPS orbit, clock products, and wide-lane satellite biases products from from the Centre National d’Études Spatiales/Collecte Localisation Satellites (CNES/CLS) the Centre National d’Études Spatiales/Collecte Localisation Satellites (CNES/CLS) are are used to enable the single-receiver ambiguity fixing [25]. used to enable the single-receiver ambiguity fixing [25]. Table 2 summarizes the force model for the POD of the LEO satellites. The N-body Table2 summarizes the force model for the POD of the LEO satellites. The N-body gravitation of LEO satellites refers to the gravitational attraction from the sun, the moon, gravitationand other planets. of LEO The satellites radiation refers to pressure the gravitational of LEO satellites attraction is computed from the base sun,d on the the moon, andbox-wing other model planets. with The simplified solar radiation geometric pressure model and of LEOpanel satellites information. is computed In terms of based at- on themospheric box-wing drag, model the atmosphere with simplified density geometric is computed model by the and NRLMSISE00 panel information. model and In a terms ofdrag atmospheric scale coefficient drag, is theadditionally atmosphere estimated density as a is piecewise computed constant by the parameter NRLMSISE00 to com- model andpensate a drag for the scale mismodeled coefficient atmospheric is additionally force. estimated The interval as aof piecewisethis coefficient constant varies parameter with tothe compensate specific satellite, for i. thee., 90 mismodeled minutes for GRACE atmospheric-FO and force. Swarm The satellites, interval and of 100 this minutes coefficient variesfor Sentinel with-3 the satellites. specific Additionally, satellite, i.e., in 90order minutes to absorb for GRACE-FOthe unmodeled and or Swarmmismodeled satellites, andforce 100 errors, minutes a set forof cycle Sentinel-3-per-revolution satellites. empirical Additionally, accelerations in order in to the absorb along the-track unmodeled and orcross mismodeled-track directions force are errors, introduced. a set of cycle-per-revolution empirical accelerations in the along-track and cross-track directions are introduced.

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Table 2. Force model for the POD of LEO satellites.

Dynamics Model Earth gravity EGM08 (120 × 120) N-body JPL DE405 [26] Ocean tide FES 2004 (30 × 30) [27] Relativity IERS 2010 [28] Solid tide and pole tide IERS 2010 Earth radiation pressure Not considered Solar radiation pressure Box-wing model for LEO satellites [29] Atmospheric density NRLMSISE00 [30] Estimated Parameters Satellite initial state Position and velocity at initial GRACE-FO and Swarm: one constant scale Atmospheric drag parameter per 90 min Sentinel-3: one constant scale parameter per 100 min GRACE-FO and Swarm: piecewise periodic accelerations in cross-track and along-track Empirical accelerations directions per 90 min Sentinel-3: piecewise periodic accelerations in cross-track and along-track directions per 100 min Receiver clock error Each epoch as white noise

In the step of ERP estimation, we process the available SLR observations that were collected by all the SLR stations. In the SLR observation modelling, the relativity effects, due to the presence of the Earth’s gravitational field, are taken into consideration [28]. We use the zenith delay model proposed by Mendes and Pavlis [31], as well as the mapping function FCULa proposed by Mendes et al. [32], to correct the range delay caused by the troposphere. In addition, the azimuth- and elevation-dependent range correction patterns of laser retroreflector arrays (LRA), derived from Neubert [33] and Montenbruck and Neubert [34], are adopted for the four-prism arrays of GRACE-FO and Swarm, and the seven-prism array of Sentinel-3, respectively. The estimated parameters that are related to the SLR observations from the LAGEOS and LEO satellites are illustrated in Table3. We use SLRF2014 (ILRS [ 35]) to provide a priori reference frame. The no net rotation minimum condition is imposed in order to define the datum. The station coordinates and range biases are estimated as one set of parameters for each three-day solution, with priori constraints of 1 m and 100 m, respectively. It should be noted that in the LAGEOS-involved solutions, only range biases for selected stations are estimated according to the ILRS data handling file. For the ERP, a piecewise linear (PWL) parametrization is applied in order to achieve a better estimation [36]. Since UT1-UTC is correlated with the node of the satellite, it is not possible to independently determine UT1- UTC from any satellite tracking technique, such as SLR or GNSS measurements. Hence, we adopt a similar strategy to that used by the ILRS Analysis Standing Committee, in which UT1-UTC are strongly constrained to the finals2000A.data series published by IERS, and a constraint of 1 m is imposed on the remaining ERPs. In addition, for the LAGEOS-involved solutions, we also estimate the LAGEOS orbit apart from the ERP and station-specific parameters. Remote Sens. 2021, 13, 3046 6 of 23

Table 3. Parameter estimated related with SLR observations for LAGEOS and LEO satellites in two-step method.

Parameter LAGEOS-1/2 LEO SLR station coordinate One set for three-day arc One set for three-day arc Range bias Estimated for selected sites Estimated for all sites Earth rotation parameters PWL daily PWL daily Satellite orbits Position and velocity at initial Satellite initial state — epoch One constant scale parameter Atmospheric drag — the whole arc One constant and two periodic accelerations in the Empirical accelerations — cross-track and along-track directions

All computations are performed on the GNSS+ Research, Application and Teaching (GREAT) software, which is designed and developed at the School of Geodesy and Geo- matics of Wuhan University (WHU). The software can support multiple applications, such as multi-technique geodetic parameter estimation, GNSS real-time orbit, and clock determi- nation, PPP-RTK (real-time kinematic) [37], multi-GNSS bias estimation [38], multi-sensor integration navigation, etc.

3. ERP Estimation Based on the Single LEO Satellite In this section, the quality of the LEO orbit that we calculated is assessed, firstly, by comparison with external products and SLR validation. Then, the influence of LEO orbit improvement on the ERP estimation is assessed. After that, we compare and analyze the ERP solutions based on the different LEO observations, and highlight the differences between these single-LEO solutions.

3.1. Orbit Validation The capacity of generating high-quality orbit for LEO satellites is a vital prerequisite for the recovery of ERP. Hence, before the ERP estimation, we firstly assess the accuracy of the following two types of LEO orbit solutions that we generated: ambiguity-float solutions and ambiguity-fixed solutions. Table4 lists the average root-mean-square (RMS) value of orbit differences, with respect to the external product in the along-track, cross-track and radial components for the ambiguity-float solutions and ambiguity-fixed solutions. Thanks to the additional geometric constraint offered by the ambiguity fixing, the ambiguity-fixed solution shows a smaller RMS value compared to the ambiguity-float solution, and the most distinct improvement is observed in the along-track component. Meanwhile, we can find that GRACE-FO satellites achieve the largest improvement compared to the other missions, and the improvement with respect to the ambiguity-float orbit in the along-track, cross-track and radial components can reach 40%, 13% and 18%, respectively. This can be easily understood by the fact that the GRACE-FO product delivery by JPL is an ambiguity-fixed solution. In the case of Swarm, the benefits of ambiguity fixing are not as evident as they are in the GRACE-FO mission, since the reference orbits are produced with carrier phase ambiguities treated as float values. However, a better consistency to the reference orbits is still visible for the ambiguity-fixed solutions. When referred to Sentinel-3, the consistency with the orbit product is improved for the along-track and radial components in the ambiguity- fixed solution when compared to the ambiguity-float solution. Since the orbit product of Sentinel-3 is based on GPS and Doppler Orbitography by radiopositioning integrated on Remote Sens. 2021, 13, 3046 7 of 23

satellite (DORIS) observations, this result indicates that the ambiguity fixing processing can weaken the inconsistency between the LEO orbit based on different techniques.

Table 4. Average RMS of orbit difference with respect to the external orbit products of seven LEO satellites (GRACE-C/D, Swarm-A/B/C, Sentinel-3A/B).

Satellite Orbit Type Along (mm) Cross (mm) Radial (mm) Product Source Solution Type

Ambiguity-float 12.4 9.9 8.0 National GRACE-C Ambiguity-fixed 7.3 8.6 6.6 Aeronautics and Ambiguity- Space fixed Ambiguity-float 13.4 10.5 7.4 Administration GRACE-D orbit Ambiguity-fixed 8.2 9.2 5.9 (NASA) JPL [39] Ambiguity-float 15.3 14.3 7.1 Swarm-A Ambiguity-fixed 11.5 13.3 6.0

Ambiguity-float 16.2 14.7 7.4 European Space Ambiguity- Swarm-B float Ambiguity-fixed 12.6 13.4 6.0 Agency (ESA) [40] orbit Ambiguity-float 15.9 14.7 7.3 Swarm-C Ambiguity-fixed 12.0 13.8 6.0 Ambiguity-float 13.7 8.8 9.6 Sentinel-3A Ambiguity-fixed 10.9 9.3 8.7 Ambiguity- CNES [25] fixed Ambiguity-float 15.2 9.3 10.3 orbit Sentinel-3B Ambiguity-fixed 12.1 9.6 9.1

Table5 summarizes the mean bias and standard deviation (STD) of SLR residuals for seven LEO satellites. Here, the SLR validation is performed based on a subset of 12 high-quality core stations (Graz, Greenbelt, Haleakala, Hartebeesthoek, Herstmonceux, Matera, Mt Stromlo, Potsdam, Wettzell (two stations), Yarragadee, and Zimmerwald) [10]. The SLR residuals over ±0.2 m are regarded as outliers and are excluded from the result statistics. As shown in Table5, an evident reduction of 1–3 mm in STD of SLR residuals of ambiguity-fixed solutions indicates the better orbit accuracy enabled by the ambiguity- fixing processing. These improved orbits will naturally facilitate the estimation of geodetic parameters, such as ERP.

Table 5. Mean bias and STD of SLR residuals for the ambiguity-float solutions and ambiguity-fixed solutions.

SLR Residuals (mm) Satellite Ambiguity-Float Ambiguity-Fixed Mean STD Mean STD GRACE-C 2.2 14.6 1.3 11.8 GRACE-D 3.0 15.9 3.2 12.8 Swarm-A −0.4 20.9 0.5 19.5 Swarm-B 1.0 21.7 1.2 20.5 Swarm-C 1.0 21.5 1.0 20.1 Sentinel-3A 1.2 18.0 1.5 16.9 Sentinel-3B 2.6 20.4 2.2 19.1

3.2. Impact of Using Ambiguity-Fixed Orbit on the ERP Estimation Considering the relationship between the quality of the estimated ERP and LEO orbit accuracy, the contribution of ambiguity-fixed orbit to the ERP estimation is investigated Remote Sens. 2021, 13, 3046 8 of 23

based on the two-step method in this subsection. Taking GRACE-D as an example, Figure2 Remote Sens. 2021, 13, x FOR PEER REVIEWtypically presents the pole coordinate and LOD differences between the finals2000A.data8 of 23 series and the ERP solutions, based on different orbits. It can be observed that the orbit improvement derived from the ambiguity fixing contributes an evident improvement to theimprovement ERP estimation. to the ComparedERP estimation. with Compared the ambiguity-float with the orbitambiguity solution,-float the orbit ambiguity-fixed solution, orbitthe ambiguity solution- exhibitsfixed orbit a smaller solution variation, exhibits whicha smaller indicates variation, a better which consistency indicates a with better respect toconsistency the finals2000A.data with respect products. to the finals2000A.data With the application products. of With the ambiguity-fixed the application of orbit, the the RMSambiguity values-fixed of X orbit, pole andthe RMS Y pole values differences of X pole are and reduced Y pole bydifferences 12 uas and are 22 reduced uas, respectively, by 12 butuas slightand 22 accuracy uas, respectively, degradation but slight is observed accuracy in degradation LOD. is observed in LOD.

FigureFigure 2. 2. TimeTime series series of pole of pole coordinates coordinates and the and length the-of length-of-day-day differences differences with respect with to respect to fi- nals2000A.datafinals2000A.data series series forfor thethe GRACE-DGRACE-D solutions solutions based based on on the the ambiguity ambiguity-float-float orbit orbit and and ambiguity- fixedambiguity orbit.-fixed Values orbit. in Values the top in right the top corner right indicate corner indicate the mean the andmean RMS and ofRMS differences of differences for thesefor two these two schemes. schemes.

The benefit benefit of of ambiguity ambiguity fixing fixing is is also also visible visible in inthe the coordinates coordinates of SLR of SLR stations. stations. Table Table 6 6 presents the station coordinate differences between SLRF2014 and the different GRACE- presents the station coordinate differences between SLRF2014 and the different GRACE-D D solutions. On average, the interquartile range (IQR) of SLR station coordinates in the solutions. On average, the interquartile range (IQR) of SLR station coordinates in the east, north and up components are reduced by 18%, 14%, and 13%, respectively, when east, north and up components are reduced by 18%, 14%, and 13%, respectively, when introducing the ambiguity-fixed orbit. Particularly, the better accuracy is achieved by the introducing the ambiguity-fixed orbit. Particularly, the better accuracy is achieved by core stations, due to the large amount of SLR data they collected. Meanwhile, we can find thethat corethe applicat stations,ion due of the to theambiguity large amount-fixed orbit of SLRyields data a smaller they collected.median of core Meanwhile, station we cancoordinate find that differences the application with respect of the ambiguity-fixedto the SLRF2014. orbit From yields the above a smaller results, median we can of core stationconclude coordinate that the ERP differences estimation with based respect on the to ambiguity the SLRF2014.-fixed FromLEO orbit the above can obtain results, a we canbetter conclude result. Therefore, that the ERP all LEO estimation-involved based ERP onsolutions the ambiguity-fixed hereafter are performed LEO orbit based canobtain on a betterthe ambiguity result. Therefore,-fixed orbit. all LEO-involved ERP solutions hereafter are performed based on the ambiguity-fixed orbit. Table 6. Coordinate differences of SLR stations w.r.t. SLRF2014 for the GRACE-D solutions based Tableon the 6.ambiguityCoordinate-float differences orbit and ambiguity of SLR stations-fixed w.r.t.orbit. SLRF2014 for the GRACE-D solutions based on the ambiguity-float orbit and ambiguity-fixedE (mm) orbit. N (mm) U (mm) Station Orbit Type MedianE (mm)IQR Median N (mm)IQR Median U (mm)IQR StationAll AmbiguityOrbit Type-float 1.4 20.2 0.0 23.9 1.6 16.9 Median IQR Median IQR Median IQR stations Ambiguity-fixed –0.2 16.6 1.0 20.5 2.6 14.7 Ambiguity-float 1.4 20.2 0.0 23.9 1.6 16.9 CoreAll Ambiguity-float 1.2 17.7 –3.2 23.0 –0.6 12.5 stations stations AmbiguityAmbiguity-fixed-fixed –−0.10.2 14.9 16.6 –0.6 1.0 19.6 20.5 –0.5 2.6 10.814.7 Core Ambiguity-float 1.2 17.7 −3.2 23.0 −0.6 12.5 stations Ambiguity-fixed −0.1 14.9 −0.6 19.6 −0.5 10.8

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3.3. ERP Estimation with Different LEO Satellites 3.3.Figure ERP Estimation 3 typically with presents Different LEOthe number Satellites of SLR observations (normal points, NPs) of each Figure 3-day 3solution typically for presents GRACE the- numberD, Sentinel of SLR-3A, observations Swarm-A, (normalSwarm- points,B, and NPs) LAGEOS satellites.of each 3-day An evident solution difference for GRACE-D, between Sentinel-3A, LEO and Swarm-A, LAGEOS Swarm-B, satellites and can LAGEOS be noted. In general,satellites. the An average evident number difference of SLR between observations LEO and used LAGEOS for a satellites3-day solution can be is noted. 213, 204, In 129, 437,general, and 317 the averagefor GRACE number-D, ofSentinel SLR observations-3A, Swarm used-A, forSwarm a 3-day-B and solution LAGEOS, is 213, 204,respectively. 129, The437, largest and 317 number for GRACE-D, of SLR observations Sentinel-3A, Swarm-A, is achieved Swarm-B by Swarm and-B, LAGEOS, which is respectively. even over three timesThe largest more numberthan that of of SLR Swarm observations-A. The is observation achieved by Swarm-B,number of which most is LEO even overcannot three reach a similartimes morelevel thanto that that of of LAGEOS, Swarm-A. because The observation there are number two LAGEOS of most LEO satellites cannot and reach LAGEOS a aresimilar calibration level to satellites that of LAGEOS, for SLR becausestations, there hence are most two LAGEOSstations track satellites them. and In LAGEOS addition, we are calibration satellites for SLR stations, hence most stations track them. In addition, we can see that the core stations contribute to almost 70% of the SLR observations for LEO can see that the core stations contribute to almost 70% of the SLR observations for LEO and andLAGEOS LAGEOS satellites. satellites.

FigureFigure 3. 3. NumberNumber of observationsobservations in in 3-day 3-day solution solution for for GRACE-D, GRACE Sentinel-3A,-D, Sentinel Swarm-A,-3A, Swarm Swarm-B,-A, Swarm- B,and and LAGEOS LAGEOS (LAGEOS-1 (LAGEOS +-1 LAGEOS-2) + LAGEOS collected-2) collected by all by stations all stations (left) and (left) core and stations core stations (right). (right).

TableTable 77 presentspresents the the statistical statistical data data of ERPof ERP based based on SLRon SLR observations observations to seven to seven LEO LEO satellite ambiguity-fixed orbits, respectively. The LAGEOS-based solution is also listed satellite ambiguity-fixed orbits, respectively. The LAGEOS-based solution is also listed here to provide a reference. In the case of a single-LEO solution, the estimated ERP become heremore to sensitive provide toa reference. the number In of the SLR case observations, of a single since-LEO only solution, one LEO the satellite estimated is used. ERP We become morecan find sensitive that the to quality the number of ERP exhibitsof SLR aobservations, strong dependence since ononly the one observation LEO satellite numbers. is used. WeAmong can findthe LEO-based that the quality solutions, of the ERP Swarm-B exhibits solution a strong exhibits dependence the best consistency on the observation with numbers.the IERS product, Among thanks the LEO to its-based obviously solutions, largest number the Swarm of available-B solution observations, exhibits and the best consistencyRMS value forwith X pole, the YIERS pole andproduct, LOD isthanks 1.9286 ms,to its 1.6634 obviously ms and 0.0673largest ms, number respectively. of available It obsershouldvations, be noted and that, the though RMS thevalue nearly for comparable X pole, Y amountpole and of SLRLOD observations is 1.9286 mas is achieved, 1.6634 mas andfor GRACE-FO 0.0673 mas, and respectively. Sentinel-3 satellites, It should the beSentinel-3 noted solution that, though shows thean evidently nearly comparable worse ERP result than that of GRACE-FO solutions. The main reason for this phenomenon is amount of SLR observations is achieved for GRACE-FO and Sentinel-3 satellites,◦ the Sentinelthat the-3 specific solution sun-synchronous shows an evidently orbit of Sentinel-3, worse ERP with the result orbital than inclination that of of GRACE 98.6 , -FO results in a low sensitivity for [41]. On the other hand, the relatively lower solutions. The main reason for this phenomenon is that the specific sun-synchronous orbit orbit accuracy of Sentinel-3 also accounts for their degraded ERP result (see Table5). It can ofbe Sentinel seen that-3, the with accuracy the orbital of single-LEO inclination solutions of 98.6 is not◦, comparableresults in a to low that sensitivity of the LAGEOS for polar motisolution,on [4 even1]. On for the Swarm-B other hand, solution. the The relatively superior lower performance orbit accuracy of the LAGEOS of Sentinel solution-3 also accountsis resulted for from their their degraded simple satellite ERP result structure, (see the Table uncomplicated 5). It can be force seen model, that and the enoughaccuracy of singleobservations.-LEO solutions is not comparable to that of the LAGEOS solution, even for the Swarm-B solution. The superior performance of the LAGEOS solution is resulted from their simple satellite structure, the uncomplicated force model, and enough observations.

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Table 7. Mean biases and RMS values of pole coordinates and the length-of-day in seven single-LEO Table 7. Mean biases and RMS values of pole coordinates and the length-of-day in seven single- satellite solutions and LAGEOS satellite solution w.r.t the finals2000A.data series. LEO satellite solutions and LAGEOS satellite solution w.r.t the finals2000A.data series.

X Pole(mas)X Pole (ms)Y Pole(mas) Y Pole (ms)LOD(ms) LOD (ms) SatelliteSatellite Mean MeanRMS RMSMean MeanRMS RMSMean MeanRMS RMS GRACEGRACE-C-C –0.1694− 0.16942.00622.0062 0.0043 0.00431.8425 1.8425–0.0050− 0.00500.0650 0.0650 GRACEGRACE-D-D –0.0622− 0.06222.34692.3469 0.1280 0.12801.8840 1.88400.0018 0.001800579 00579 SWARM-A –0.0343 2.9698 –0.0413 2.1253 –0.0048 0.0770 SWARM-A −0.0343 2.9698 −0.0413 2.1253 −0.0048 0.0770 SWARM-B –0.0492 1.9286 0.0619 1.6634 0.0039 0.0673 − SWARMSWARM-B-C –0.0932 0.04922.85651.9286 –0.0519 0.06191.9805 1.66340.0139 0.00390.0719 0.0673 SENTINELSWARM-C- −0.0932 2.8565 −0.0519 1.9805 0.0139 0.0719 0.0636 2.7018 –0.0757 2.1211 –0.0178 0.0675 SENTINEL-3A3A 0.0636 2.7018 −0.0757 2.1211 −0.0178 0.0675 SENTINEL- SENTINEL-3B–0.0137− 0.01373.12213.1221 –0.0012− 0.00122.1866 2.1866–0.0287− 0.02870.0829 0.0829 3B LAGEOS −0.0475 1.0686 0.0871 0.9449 −0.0088 0.0424 LAGEOS –0.0475 1.0686 0.0871 0.9449 –0.0088 0.0424

FigureFigure 44 typically typically gives gives the the spectral spectral analysis analysis results results for four for foursingle single-LEO-LEO solutions solutions and and thethe LAGEOS LAGEOS solution. solution. It can It can be beseen seen that that the theLEO LEO solutions solutions apparently apparently have havemore morenoisy noisy signalssignals with with the the period period up up to to50 50days days than than the theLAGEOS LAGEOS solution. solution. No evident No evident semiannual semiannual signalsignal is is visible visible in in all all the the solutions. solutions. However, However, a adistinct distinct signal, signal, with with a 119 a 119-day-day period period in in the thepole pole coordinates, coordinates, can can be be observed observed in inthe the Sentinel-3A Sentinel-3A solution. solution. This This signal signal may may be be related relatedwith the with perigee the perigee revolution revolution of 122 ofdays 122 days forthe for Sentinel-3the Sentinel satellite.-3 satellite.

FigureFigure 4. 4. SpectralSpectral analysis analysis for for GRACE GRACE-C,-C, Sentinel Sentinel-3A,-3A, LAGEOS LAGEOS (LAGEOS (LAGEOS-1-1 and and LAGEOS LAGEOS-2),-2), Swarm- SwarmC and-C Swarm-B and Swarm solutions.-B solutions.

FigureFigure 55 gives gives the the differences differences of ofthe the estimated estimated station station coordinates coordinates w.r.t w.r.tSLRF2014 SLRF2014 for for thethe different different satellite satellite solutions, solutions, and and summarized summarized data data are shown are shown in Table in Table 8. For8. all For the all the LEOLEO solutions, solutions, the the positioning positioning of ofall all the the SLR SLR stations stations obtains obtains the the accuracy accuracy at the at thelevel level of of 20 20mm–30 mm–30 mm. mm. While While for for the the corecore stations,stations, thethe accuracy level can can reach reach about about 10 10 mm mm–20–20 mm. mm.Although Although there there is the is largest the largest number number of available of available observations observations for Swarm-B, for Swarm the-B, Swarm-B the Swarmsolution-B is solution inferior, is with inferior, an IQR with of an 29 mm,IQR 23of mm29 mm, and 23 24 mm in and three 24 componentsmm in three for all componthe stations,ents for which all the is stations, probably which due tois probably the relatively due to poor the precisionrelatively poor of the precision Swarm-B of orbits the(see Swarm Table-5B). orbits Among (see these Table LEO 5). Among satellite these solutions, LEO satellite the GRACE-C solutions, and the GRACE-DGRACE-C solutionsand GRACEcan obtain-D solutions better results can obtain than better other results solutions, than withother ansolutions, IQR of with about an 15–20 IQR of mm abo inut the E, N, U components for all the stations, thanks to their high-accuracy ambiguity-fixed orbit. These results illustrate that the accuracy of station coordinates are more sensitive to the

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Remote Sens. 2021, 13, 3046 11 of 23 15–20 mm in the E, N, U components for all the stations, thanks to their high-accuracy ambiguity-fixed orbit. These results illustrate that the accuracy of station coordinates are more sensitive to the quality of the LEO orbit, under the condition that enough SLR observationsquality of the to LEO the orbit, LEO undersatellite the can condition be obtained. that enough SLR observations to the LEO satellite can be obtained.

FigureFigure 5. Differences of of all all SLR SLR station station and and core core station station coordinates coordinates w.r.t. w.r.t. SLRF2014. SLRF2014.

TableTable 8.8. DifferencesDifferences in in estimated estimated SLR SLR station station coordinates coordinates w.r.t. SLRF2014w.r.t. SLRF2014 in seven in single-LEO seven single satellite-LEO satellitesolution solution and LAGEOS and LAGEOS satellite solution satellite decomposed solution decomposed into E, N, U components.into E, N, U components.

EE (mm) (mm) N (mm)N (mm) U (mm)U (mm) StationStation SatelliteSatellite MedianMedian IQRIQR MedianMedian IQR IQR Median Median IQR IQR GRACE-CGRACE-C 0.60.6 19.019.0 1.31.3 21.221.2 0.70.7 16.8 16.8 GRACE-DGRACE-D −0.2–0.2 16.616.6 1.01.0 20.520.5 2.62.6 14.7 14.7 SWARM-ASWARM-A 0.60.6 17.317.3 0.90.9 26.726.7 4.84.8 19.8 19.8 All SWARM-BSWARM-B −2.4–2.4 29.429.4 −0.1–0.1 22.622.6 7.77.7 23.7 23.7 Allstations stations SWARM-CSWARM-C −3.6–3.6 24.024.0 −0.3–0.3 28.928.9 4.64.6 21.1 21.1 SENTINEL-3ASENTINEL-3A 7.17.1 21.821.8 −0.3–0.3 21.8 21.8 −3.0–3.0 14.1 14.1 SENTINEL-3BSENTINEL-3B 10.510.5 32.432.4 −0.1–0.1 26.5 26.5 −0.2–0.2 21.8 21.8 LAGEOSLAGEOS 1.21.2 23.123.1 −4.9–4.9 25.6 25.6 −5.6–5.6 24.9 24.9 GRACE-CGRACE-C 0.40.4 14.214.2 0.50.5 21.1 21.1 −1.0–1.0 11.1 11.1 GRACE-DGRACE-D −0.1–0.1 14.914.9 −0.6–0.6 19.6 19.6 −0.5–0.5 10.8 10.8 SWARM-A –0.3 16.9 –0.8 23.9 5.1 16.7 SWARM-A −0.3 16.9 −0.8 23.9 5.1 16.7 SWARM-B –1.5 24.8 –0.8 22.1 5.0 16.8 CoreCore stations SWARM-B −1.5 24.8 −0.8 22.1 5.0 16.8 SWARM-C –6.6 18.8 1.7 30.2 2.2 15.3 stations SWARM-C −6.6 18.8 1.7 30.2 2.2 15.3 SENTINEL-3A 6.2 16.3 0.9 20.5 –3.9 10.7 SENTINEL-3A 6.2 16.3 0.9 20.5 −3.9 10.7 SENTINEL-3B 9.0 27.4 2.2 27.3 –3.0 16.7 SENTINEL-3B 9.0 27.4 2.2 27.3 −3.0 16.7 LAGEOS 0.2 14.4 –1.6 19.0 –4.3 14.5 LAGEOS 0.2 14.4 −1.6 19.0 −4.3 14.5 As shown in Table 8, the LAGEOS solution achieves a station coordinate with worse accuracy than some single-LEO solutions, such as GRACE-C, GRACE-D and Sentinel-3A solutions, when considering all the SLR stations. In order to explain this phenomenon, here we give Figure 6, which shows the percentage of observations from core stations and non-core stations for LAGEOS satellites, and the number of core stations and non-core

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Remote Sens. 2021, 13, x FOR PEER REVIEWAs shown in Table8, the LAGEOS solution achieves a station coordinate with worse12 of 23 accuracy than some single-LEO solutions, such as GRACE-C, GRACE-D and Sentinel-3A solutions, when considering all the SLR stations. In order to explain this phenomenon, here we give Figure6, which shows the percentage of observations from core stations and stations.non-core stationsWe can for see LAGEOS that the satellites, non-core and stations the number account of core for a stations large part and non-core of the stations trackingstations. LAGEOS, We can see but that only the contribute non-core stations to about account 30% of for SLR a largeobservations part of the to LAGEOS. stations The smalltracking amount LAGEOS, of observations but only contribute for non to- aboutcore stations 30% of SLR weaken observations the solution to LAGEOS. strength The for the stationsmall amount coordinates, of observations and lead for to non-core a degraded stations positioning weaken the accuracy solution for strength non-core for the stations. Thisstation may coordinates, explain the and larger lead to average a degraded RMS positioning values with accuracy an IQR for non-coreof nearly stations. 25 mm This for the E, Nmay, and explain U components the larger average for all RMSthe stations. values with For an the IQR core ofnearly stations, 25 mm LAGEOS for the E,and N, some and LEO solutionsU components can achieve for all the a comparable stations. For thepositioning core stations, accuracy, LAGEOS and and the some GRACE LEO-C solutions and GRACE- can achieve a comparable positioning accuracy, and the GRACE-C and GRACE-D solutions D solutions even present a smaller RMS value in the up component, with an IQR decrease even present a smaller RMS value in the up component, with an IQR decrease of nearly of4 mm.nearly These 4 mm. analyses These suggest analyses that suggest it is tenable that to it achieve is tenable a desirable to achieve station a desirable coordinate station coordinateresult based result on the based LEO orbit on the of highLEO accuracy. orbit of high accuracy.

FigureFigure 6.6. ((aa)) Percentage Percentage of of observations observations to LAGEOS to LAGEOS satellites satellites from core from stations core stations and non-core and stations;non-core stations(b) number; (b) of n coreumber stations of core and stations non-core and stations non-core in 3-day stations solutions. in 3-day solutions. 4. ERP Estimation Based on the Combination of Multiple LEO Satellites 4. ERP Estimation Based on the Combination of Multiple LEO Satellites In this section, we focus on the ERP estimation using the onboard data from multiple LEOIn satellites. this section, The quality we focus of ERP on the solutions, ERP estimation based on the using different the onboard combinations data from of LEO multiple LEOsatellites, satellites. is firstly The investigated. quality of Then,ERP solutions, we perform based a combined on the solution different with combinations LAGEOS and of LEO satellites,LEO satellites is firstly in order investigated. to explore theThen, contribution we perform of LEO a combined satellites. solution Finally, awith comparison LAGEOS and LEObetween satellit thees one-step in order solution to explore and two-step the contribution solution is of presented. LEO satellites. Finally, a comparison between the one-step solution and two-step solution is presented. 4.1. Impact of LEO Number on the ERP Estimation 4.1. ImpactIn order of LEO to investigate Number on the the impact ERP Estimation of LEO number on the ERP estimation, three combination solutions with 3-, 5- and 7-LEO satellites have been performed. The design of theseIn schemes order is to on investigate the basis of the maximizing impact the of LEOdiversity number of orbit on type, the which ERP isestimation, beneficial three combinationfor eliminating solutions the LEO-related with 3 orbit-, 5- signalsand 7- inLEO ERP satellites estimation. have The been 3-LEO performed. scheme includes The design ofGRACE-C, these schemes Swarm-A, is and on Sentinel-3A. the basis of The maximizing 5-LEO scheme the indicates diversity the ofsolution orbit generated type, which is beneficialusing GRACE-C, for eliminating GRACE-D, the Swarm-A, LEO-related Swarm-B, orbit and signals Sentinel-3A in ERP satellites. estimation. The 7-LEO The 3-LEO scheme includes GRACE-C, Swarm-A, and Sentinel-3A. The 5-LEO scheme indicates the solution generated using GRACE-C, GRACE-D, Swarm-A, Swarm-B, and Sentinel-3A satellites. The 7-LEO scheme is with all the LEO satellites mentioned in Section 2, which maximizes the number of LEO observations and further strengthens the observation geometry. The results from the 3-LEO, 5-LEO and 7-LEO solutions are illustrated in Figure 7. Figure 7 shows that the scatter distributions of the 7-LEO solution are much denser near the zero line than those of the 3-LEO and 5-LEO solutions. The ERP RMSs of the 3-LEO solution are the largest, and the best result occurs in the 7-LEO solution with the RMSs of

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scheme is with all the LEO satellites mentioned in Section2, which maximizes the number Remote Sens. 2021, 13, x FOR PEER REVIEWof LEO observations and further strengthens the observation geometry. 13 of 23

The results from the 3-LEO, 5-LEO and 7-LEO solutions are illustrated in Figure 7. Figure7 shows that the scatter distributions of the 7-LEO solution are much denser near the zero line than those of the 3-LEO and 5-LEO solutions. The ERP RMSs of the 0.7530 mas, 0.4486 mas and 0.0223 mas for X pole, Y pole and LOD, respectively. It 3-LEO solution are the largest, and the best result occurs in the 7-LEO solution with the indicatesRMSs of 0.7530that more ms, 0.4486LEO satellites ms and 0.0223 included ms forin the X pole, estimation Y pole andlead LOD, to a smaller respectively. ERP ItRMS. Thisindicates improvement that more can LEO be satellites attributed included to the in significant the estimation increase lead toin aSLR smaller observations, ERP RMS. and theThis enhanced improvement observation can be attributed geometry to the with significant more increase LEO satellit in SLRes. observations, Moreover, and the the 7-LEO solutionenhanced performs observation better geometry than the with LAGEOS more LEO solution satellites. (see Moreover, Table 7) the for 7-LEO ERP solution estimation, whichperforms indicates better than that the for LAGEOS the ERP solution estimation (see Tableunder7) forthe ERPshort estimation, arc condition, which the indicates multiple- LEOthat forsolution the ERP can estimation reach a undersimilar the or shorteven arc better condition, accuracy the multiple-LEOcompared with solution the LAGEOS can solution.reach a similar or even better accuracy compared with the LAGEOS solution.

FigureFigure 7. 7. Time series series of of pole pole coordinates coordinates and and the thelength-of-day length-of- differencesday differences with respect with respect to fi- to finals2000A.datanals2000A.data series series for for the the 3-LEO, 3-LEO, 5-LEO 5-LEO and and 7-LEO 7-LEO solutions. solutions. Values Values in the in topthe righttop right corner corner indicateindicate the meanmean andand RMS RMS of of differences differences for for these these three three schemes. schemes.

Figure8 8 gives gives the the spectral spectral analysis analysis for for the the 3-LEO, 3-LEO, 5-LEO 5-LEO and and 7-LEO 7-LEO solutions. solutions. It can It can bebe clearly observedobserved thatthat the the 119-day 119-day period period for for Sentinel-3A, Sentinel-3A, mentioned mentioned in Sectionin Section 3.3, is3.3, is eliminated in the 3-LEO solution, which suggests that the ERP estimation with multiple eliminated in the 3-LEO solution, which suggests that the ERP estimation with multiple LEO satellites can mitigate the orbit-related signal of single LEO in ERP solutions. Moreover, LEO satellites can mitigate the orbit-related signal of single LEO in ERP solutions. the amplitude of the 5-LEO solution is smaller than that of the 3-LEO solution for X pole, Y Moreover,pole, and LOD. the amplitude This indicates of the that 5- theLEO inclusion solution of is Swarm-B smaller andthan GRACE-D that of the improves 3-LEO solution the forbitor X diversification,pole, Y pole, and which LOD. can This further indicates improve that the the ERP inclusion solution. of Additionally, Swarm-B and the GRACE 7-LEO -D improvessolution obtains the orbit the smallest diversification, amplitude within which the can period further less than improve 120 days. the ERP solution. Additionally, the 7-LEO solution obtains the smallest amplitude within the period less than 120 days.

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Figure 8. Spectral analysis for the 3-LEO, 5-LEO and 7-LEO solutions. Figure 8. Spectral analysis for the 3-LEO, 5-LEO and 7-LEO solutions. Figure9 shows the differences in all the stations’ coordinates w.r.t SLRF2014 for the 3-LEO,Figure 5-LEO, 9 shows and the 7-LEO differences solutions. in all The the correspondingstations’ coordinates statistics w.r.t areSLRF2014 severally for the listed in 3Table-LEO,9. 5 With-LEO, more and LEO7-LEO satellites solutions. included The corresponding in, more observations statistics canare severally be used for listed estimating in Tablestation 9. coordinates. With more ForLEO core satellites station included solutions, in, a more notable observations improvement can can be beused seen for in the estimating station coordinates. For core station solutions, a notable improvement can be north component. Compared with the 3-LEO solution, the 7-LEO solution improves by seen in the north component. Compared with the 3-LEO solution, the 7-LEO solution 32% in the north component. For the non-core stations, we can find that the combination improves by 32% in the north component. For the non-core stations, we can find that the of more LEO satellites can lead to an obvious improvement in all three components for combination of more LEO satellites can lead to an obvious improvement in all three non-core stations. The best results for non-core stations are in the 7-LEO solution, with IQRs components for non-core stations. The best results for non-core stations are in the 7-LEO solution,of 19.6 mm, with 13.6 IQRs mm, of and 19.6 25.6 mm, mm 13.6 in the mm, east, and north, 25.6 and mm up in component, the east, north, respectively. and up This component,is because morerespectively. LEO satellites This is because bring moremore LEO observations satellites bring and strengthenmore observations the observation and strengthengeometry, the which observation is especially geometry, vital which for the is especially estimation vital of for these the non-coreestimation stationsof these with nonless-core observations. stations with In addition, less observations. there are In some addition, stations, there such are some as SVEL stations, and BEIL, such as whose SVELcoordinates and BEIL, are unavailablewhose coordinates in the 3-LEOare unavailable solution, in due the to 3- theLEO lack solution, of observations. due to the However,lack Remote Sens. 2021, 13, x FOR PEER REVIEW 15 of 23 ofwe observations. can get a relatively However, reliable we can coordinate get a relatively solution reliable for such coordinate stations in sol theution 5-LEO for andsuch 7-LEO stationssolutions. in Thisthe 5 further-LEO and confirms 7-LEO thesolutions. advantage This offurther the combination confirms the of advantage LEO satellites. of the combination of LEO satellites.

FigureFigure 9. 9. DifferencesDifferences in inall all estimated estimated SLR SLR station station coordinates coordinates w.r.t. w.r.t. SLRF2014 SLRF2014 for the for 3- theLEO, 3-LEO, 5- 5-LEO LEOand and 7-LEO 7-LEO solutions. solutions.

Table 9. Differences in estimated SLR station coordinates w.r.t. SLRF2014 for the 3-LEO, 5-LEO and 7-LEO solutions with core stations and non-core stations decomposed into the east, north, and up components (in mm).

E (mm) N (mm) U (mm) Station Solution Median IQR Median IQR Median IQR 3LEO 1.9 14.8 2.5 15.6 –1.7 9.8 Core stations 5LEO 1.3 17.7 –0.8 11.4 –0.2 12.0 7LEO –3.4 15.0 0.4 10.6 2.8 11.3 3LEO –1.5 22.7 1.3 18.7 14.3 30.5 Non-core 5LEO 1.5 23.4 –0.6 15.2 12.1 24.3 stations 7LEO –1.1 19.6 0.2 13.6 12.9 25.6

4.2. Combination of LEO Satellite and LAGEOS The routine ERP product from ILRS is majorly based on LAGEOS. Hence, the investigation of the contribution of LEO satellites and LAGEOS combination to ERP estimation is especially meaningful. Figure 10 shows the ERP differences w.r.t the finals2000A.data series of the LAGEOS solution, the 7-LEO solution, and the combined solutions. The combined solution characterized by more concentrated blue dots reflects that the stability of the ERP solution is notably improved. In contrast to the LAGEOS solution, the combined solution shows RMS reductions of 0.644 mas, 0.629 mas and 0.028 mas for X pole, Y pole and LOD, respectively, since the involvement of seven LEO satellites offers a large number of observations. Besides, from the spectrum in Figure 11, it can be seen that the correlations between the LOD and LAGEOS satellite orbital parameters are weakened when LEO satellites are included. The 118-day period signal in LOD, which is related to the 112.5-day eclipsing period of LAGEOS-2, is visibly mitigated in the combination solution. When compared with the 7-LEO solution, the combination of LAGEOS and seven LEO satellites also attains a superior result, with a distinct decrease in the RMS of ERP.

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Table 9. Differences in estimated SLR station coordinates w.r.t. SLRF2014 for the 3-LEO, 5-LEO and 7-LEO solutions with core stations and non-core stations decomposed into the east, north, and up components (in mm).

E (mm) N (mm) U (mm) Station Solution Median IQR Median IQR Median IQR 3LEO 1.9 14.8 2.5 15.6 −1.7 9.8 Core stations 5LEO 1.3 17.7 −0.8 11.4 −0.2 12.0 7LEO −3.4 15.0 0.4 10.6 2.8 11.3 Non- 3LEO −1.5 22.7 1.3 18.7 14.3 30.5 core 5LEO 1.5 23.4 −0.6 15.2 12.1 24.3 stations 7LEO −1.1 19.6 0.2 13.6 12.9 25.6

4.2. Combination of LEO Satellite and LAGEOS The routine ERP product from ILRS is majorly based on LAGEOS. Hence, the investi- gation of the contribution of LEO satellites and LAGEOS combination to ERP estimation is especially meaningful. Figure 10 shows the ERP differences w.r.t the finals2000A.data series of the LAGEOS solution, the 7-LEO solution, and the combined solutions. The combined solution characterized by more concentrated blue dots reflects that the stability of the ERP solution is notably improved. In contrast to the LAGEOS solution, the combined solution shows RMS reductions of 0.644 ms, 0.629 ms and 0.028 ms for X pole, Y pole and LOD, respectively, since the involvement of seven LEO satellites offers a large number of observa- tions. Besides, from the spectrum in Figure 11, it can be seen that the correlations between the LOD and LAGEOS satellite orbital parameters are weakened when LEO satellites are included. The 118-day period signal in LOD, which is related to the 112.5-day eclipsing period of LAGEOS-2, is visibly mitigated in the combination solution. When compared Remote Sens. 2021, 13, x FOR PEER REVIEW 16 of 23 with the 7-LEO solution, the combination of LAGEOS and seven LEO satellites also attains a superior result, with a distinct decrease in the RMS of ERP.

FigureFigure 10. 10. TimeTime series series of of pole pole coordinates coordinates and and the the length length-of-day-of-day differences differences with with respect respect to to fi- finals2000A.datanals2000A.data series series for for the the LAGEOS LAGEOS solution, solution, 7-LEO 7-LEO solution solution and combined and combined solution. solution. Values Valuesin in thethe top top right right corner corner indicate indicate the themean mean and andRMS RMS of differences of differences for these for thesethree threeschemes. schemes.

Figure 11. Spectral analysis for the LAGEOS solution, the 7-LEO solution and the combined solution.

Figure 12 depicts the differences in all the estimated SLR station coordinates w.r.t. SLRF2014, and the statistical data are presented in Table 10. For all the stations, the combination of seven LEO satellites and LAGEOS satellites can obtain a superior coordinate result, with an IQR below 10 mm in the east and north components, which improves notably when compared with the LAGEOS solution and 7-LEO solution. It is visible that the estimated coordinates of the core stations are further improved when the LEO data are included. The results for the core station with the combination of LEO satellites and LAGEOS can reach the accuracy level below 10 mm in all three components.

Remote Sens. 2021, 13, x FOR PEER REVIEW 16 of 23

Figure 10. Time series of pole coordinates and the length-of-day differences with respect to Remote Sens. 2021, 13, 3046 16 of 23 finals2000A.data series for the LAGEOS solution, 7-LEO solution and combined solution. Values in the top right corner indicate the mean and RMS of differences for these three schemes.

Figure 11. 11. SpectralSpectral analysis analysis for for the the LAGEOS LAGEOS solution, solution, the the 7-LEO 7-LEO solution solution and and the thecombined combined solution. solution. Figure 12 depicts the differences in all the estimated SLR station coordinates w.r.t. SLRF2014,Figure 1 and2 depicts the statistical the differences data arein all presented the estimated in Table SLR station10. For coordinates all the stations, w.r.t. the SLRF2014,combination and of seventhe statistical LEO satellites data are and presented LAGEOS in satellites Table 10. can For obtain all thea superior stations, coordinate the combinationresult, with an of IQRseven below LEO 10 satellites mm in and the LAGEOS east and north satellites components, can obtain which a superior improves coordinatenotably when result, compared with an IQR with below the LAGEOS10 mm in solutionthe east and and north 7-LEO components, solution. Itwhich is visible Remote Sens. 2021, 13, x FOR PEER REVIEWimprovesthat the estimated notably when coordinates compared of with the corethe LAGEOS stations solution are further and improved 7-LEO solution. when17 of It the23 is LEO

visibledata are that included. the estimated The results coordinates for the of corethe core station stations with are the further combination improved of when LEO satellitesthe LEO data are included. The results for the core station with the combination of LEO and LAGEOS can reach the accuracy level below 10 mm in all three components. The satellites and LAGEOS can reach the accuracy level below 10 mm in all three components. Thecombination combination solution solution is is improved improved by 7 7 mm, mm, 3 3mm, mm, and and 3 mm 3 mm compared compared to the to 7- theLEO 7-LEO solution.solution.

FigureFigure 12. 12. DifferencesDifferences in all in estimated all estimated SLR station SLR station coordinates coordinates w.r.t. SLRF2014 w.r.t. SLRF2014 for the LAGEOS for the LAGEOS solution, the 7-LEO solution and the combined solution. solution, the 7-LEO solution and the combined solution. Table 10. Differences in estimated SLR station coordinates w.r.t. SLRF2014 for the LAGEOS solution, the 7-LEO solution and the combined solution. The statistical data are classified into all SLR stations and core stations decomposed into the east, north, and up components (in mm).

E (mm) N (mm) U (mm) Station Solution Median IQR Median IQR Median IQR LAGEOS 1.2 23.1 –4.9 25.6 –5.6 24.9 All 7LEO 1.9 16.4 0.3 11.5 1.9 17.1 stations 7LEO+LAGEOS 3.9 9.7 –0.9 7.8 0.1 13.5 LAGEOS 0.2 14.4 –1.6 19.0 –4.3 14.5 Core 7LEO 3.0 15.0 0.4 10.6 –0.4 11.3 stations 7LEO+LAGEOS 4.5 8.1 –1.2 7.0 –3.0 8.7

Additionally, the LEO observations can serve as a supplement in the case where the high-quality LAGEOS data are missing. Figure 13 gives the time series of 7110 station coordinates. It can be observed that the coordinate solution of the station is unavailable from DOY 10 to DOY 20, and from DOY 40 to DOY 50 in the LAGEOS solution, due to the lack of observations. When the LEO data are used, the station coordinates’ time series can be more continues, with denser red dots. It indicates that the combination of LEO satellites and LAGEOS can maximize the number of solved stations and strengthen the continuity of the station coordinate solutions.

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Table 10. Differences in estimated SLR station coordinates w.r.t. SLRF2014 for the LAGEOS solution, the 7-LEO solution and the combined solution. The statistical data are classified into all SLR stations and core stations decomposed into the east, north, and up components (in mm).

E (mm) N (mm) U (mm) Station Solution Median IQR Median IQR Median IQR LAGEOS 1.2 23.1 −4.9 25.6 −5.6 24.9 All stations 7LEO 1.9 16.4 0.3 11.5 1.9 17.1 7LEO + LAGEOS 3.9 9.7 −0.9 7.8 0.1 13.5 LAGEOS 0.2 14.4 −1.6 19.0 −4.3 14.5 Core stations 7LEO 3.0 15.0 0.4 10.6 −0.4 11.3 7LEO + LAGEOS 4.5 8.1 −1.2 7.0 −3.0 8.7

Additionally, the LEO observations can serve as a supplement in the case where the high-quality LAGEOS data are missing. Figure 13 gives the time series of 7110 station coordinates. It can be observed that the coordinate solution of the station is unavailable from DOY 10 to DOY 20, and from DOY 40 to DOY 50 in the LAGEOS solution, due to the lack of observations. When the LEO data are used, the station coordinates’ time series can be more continues, with denser red dots. It indicates that the combination of LEO satellites Remote Sens. 2021, 13, x FOR PEER REVIEW 18 of 23 and LAGEOS can maximize the number of solved stations and strengthen the continuity of the station coordinate solutions.

Time series of 7110 station coordinates 0.2 two-step(7LEO+LAGEOS) LAGEOS 0.1 0 -0.1 -0.2 0.2 0.1 0 -0.1 -0.2 0.2 0.1 0 -0.1 -0.2 0 50 100 150 200 250 300 350 FigureFigure 13. TimeTime series series of of station station coordinate coordinate of a ofstation a station in Monument in Monument Peak (7110) Peak (7110)from LAGEOS from LAGEOS solutionssolutions and and the the combination combination solutions. solutions.

4.3.4.3. Comparison of of One One-Step-Step and and Two Two-Step-Step Methods Methods Based on on the the observations observations of of LAGEOS LAGEOS and and seven seven LEO LEO satellites, satellites, the one the- one-stepstep method method isis implemented and and compared compared with with the the two two-step-step method. method. Figure Figure 14 shows 14 shows the comparison the comparison ofof the ERP results derived derived from from the the two two-step-step and and one one-step-step methods. methods. When When the one the-step one-step methodmethod is implemented, implemented, with with the the combination combination of seven of seven LEO LEO satellites satellites and andLAGEOS, LAGEOS, an an evidentevident accuracy accuracy degradation degradation is is visible visible in inthe the ERP ERP result. result. Especially Especially for the for LOD the parameter, LOD aparameter, factor of 2.0 a factor increase of 2.0 in RMS increase is observed. in RMS is The observed. similar Thedegradation similar degradation in simultaneously in estimatingsimultaneously the orbitestimating and ERP the alsoorbit occurs and ERP in thealso ERP occurs series in the derived ERP series from derived SLR observations from toSLR GNSS observations satellites, to asGNSS reported satellites, by as So´snicaet reported al.by [Sośnica42]. This et al is. [ possibly42]. This is because possibly of the because of the introduction of orbit parameters. In the one-step solution, the orbit introduction of orbit parameters. In the one-step solution, the orbit parameters of LEO parameters of LEO satellites, such as the initial positions and velocities of LEO satellites, satellites, such as the initial positions and velocities of LEO satellites, atmospheric drag atmospheric drag scale parameter and empirical accelerations, have to be additionally scale parameter and empirical accelerations, have to be additionally estimated, which estimated, which substantially increases the degree of freedom and weakens the stability substantially increases the degree of freedom and weakens the stability of the solution. of the solution.

Figure 14. Time series of pole coordinates and the length-of-day differences with respect to finals2000A.data series for the two-step solution and one-step solution. Values in the top right corner indicate the mean and RMS of differences for these two methods.

Remote Sens. 2021, 13, x FOR PEER REVIEW 18 of 23

Time series of 7110 station coordinates 0.2 two-step(7LEO+LAGEOS) LAGEOS 0.1 0 -0.1 -0.2 0.2 0.1 0 -0.1 -0.2 0.2 0.1 0 -0.1 -0.2 0 50 100 150 200 250 300 350 Figure 13. Time series of station coordinate of a station in Monument Peak (7110) from LAGEOS solutions and the combination solutions.

4.3. Comparison of One-Step and Two-Step Methods Based on the observations of LAGEOS and seven LEO satellites, the one-step method is implemented and compared with the two-step method. Figure 14 shows the comparison of the ERP results derived from the two-step and one-step methods. When the one-step method is implemented, with the combination of seven LEO satellites and LAGEOS, an evident accuracy degradation is visible in the ERP result. Especially for the LOD parameter, a factor of 2.0 increase in RMS is observed. The similar degradation in simultaneously estimating the orbit and ERP also occurs in the ERP series derived from SLR observations to GNSS satellites, as reported by Sośnica et al. [42]. This is possibly because of the introduction of orbit parameters. In the one-step solution, the orbit parameters of LEO satellites, such as the initial positions and velocities of LEO satellites, Remote Sens. 2021, 13, 3046 atmospheric drag scale parameter and empirical accelerations, have to be additionally18 of 23 estimated, which substantially increases the degree of freedom and weakens the stability of the solution.

Figure 14. TimeTime series series of of pole pole coordinates coordinates and and the the length length-of-day-of-day differences differences with with respect respect to to fi- Remote Sens. 2021, 13, x FOR PEER REVIEWnals2000A.datafinals2000A.data series series for forthe the two-step two-stepsolution solution and and one-step one-step solution. solution. Values Values in in the the top top19 right ofright 23 corner

indicatecorner indicate the mean the mean and RMS and RMS of differences of differences for these for these two two methods. methods.

FFigureigure 1 515 presents presents the the differences differences of all of the all theestimated estimated SLR station SLR station coordinates coordinates w.r.t. w.r.t.

SLRF2014SLRF2014 for for the the two two-step-step method method and and one one-step-step method. method. Statistical Statistical data are data shown are shown in in TableTable 11. 11 .When When the the one one-step-step method method is compared is compared with with the two the- two-stepstep method, method, the results the results forfor al alll the the stations stations become become worse, worse, with with an IQR an IQR of 15 of mm, 15 mm, 14 mm, 14 mm,and 20 and mm 20 in mm the ineast, the east, northnorth and and up up components, components, respectively. respectively. Such Such degradation degradation possibly possibly occurs occurs because because the the orbit orbitdeficiencies deficiencies are are propagated propagated into into the the obtained obtained station station coordinate, coordinate, while the the LEO LEO orbit orbit and andstation station coordinates coordinates are estimated are estimated simultaneously simultaneously in the one-step in the method. one-step Additionally, method. in Additionally,one-step method in one the-step GPS method observations the GPS observations are also processed, are also inprocessed, which the in SLRwhich results the are SLRpossibly results affected are possibly by errors affected in the by GPSerrors data in the and GPS data data processing. and data processing.

FigureFigure 15. 15. DifferencesDifferences in all in estimated all estimated SLR station SLR station coordinates coordinates w.r.t. SLRF2014 w.r.t. SLRF2014 for the two for-step the two-step solutionsolution and and one one-step-step solution. solution.

Table 11. Differences in estimated SLR station coordinates w.r.t. SLRF2014 using two-step method and one-step method classified into all SLR stations and core stations (in mm).

E (mm) N (mm) U (mm) Station Solution Median IQR Median IQR Median IQR Two-step 3.9 9.7 –0.9 7.8 0.1 13.5 All stations One-step 0.3 15.9 –0.8 14.4 1.0 20.1 Two-step 4.5 8.1 –1.2 7.0 –3.0 8.7 Core stations One-step 0.8 12.6 –1.9 12.7 –1.6 11.6

In addition, we also assess the quality of the LEO orbit derived from the two-step and one-step methods. Here, we take Sentinel-3A as an example, since the orbit product of Sentinel-3 from CNES is based on DORIS and GPS observations. Figure 16 shows the average RMS of orbit difference with respect to the orbit product of Sentinel-3A. This figure shows that, compared with the two-step solution, the orbit of the one-step solution can achieve a slight accuracy improvement at the level of sub-millimeter. A similar benefit is also reported by Guo et al. [43], Jäggi et al. [44], and Wirnsberger et al. [45]. Such improvement can be attributed to the increased observations and strengthened observation geometry that benefit from additional SLR observations in the one-step method. It demonstrates that the inclusion of SLR observations can eliminate the inter- technique inconsistency between the GPS-only orbit and GPS–DORIS-based orbit product to some extent.

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Table 11. Differences in estimated SLR station coordinates w.r.t. SLRF2014 using two-step method and one-step method classified into all SLR stations and core stations (in mm).

E (mm) N (mm) U (mm) Station Solution Median IQR Median IQR Median IQR All Two-step 3.9 9.7 −0.9 7.8 0.1 13.5 stations One-step 0.3 15.9 −0.8 14.4 1.0 20.1 Core Two-step 4.5 8.1 −1.2 7.0 −3.0 8.7 stations One-step 0.8 12.6 −1.9 12.7 −1.6 11.6

In addition, we also assess the quality of the LEO orbit derived from the two-step and one-step methods. Here, we take Sentinel-3A as an example, since the orbit product of Sentinel-3 from CNES is based on DORIS and GPS observations. Figure 16 shows the average RMS of orbit difference with respect to the orbit product of Sentinel-3A. This figure shows that, compared with the two-step solution, the orbit of the one-step solution can achieve a slight accuracy improvement at the level of sub-millimeter. A similar benefit is also reported by Guo et al. [43], Jäggi et al. [44], and Wirnsberger et al. [45]. Such improvement can be attributed to the increased observations and strengthened observation geometry that benefit from additional SLR observations in the one-step method. It demonstrates that the inclusion of SLR observations can eliminate the inter-technique Remote Sens. 2021, 13, x FOR PEER REVIEW 20 of 23 inconsistency between the GPS-only orbit and GPS–DORIS-based orbit product to some extent.

FigureFigure 16. 16. AverageAverage RMS RMS of Sentinel of Sentinel-3A-3A orbit orbit difference difference with respect with respect to the CNES to the product CNES product for the for the twotwo-step-step solution solution and and one one-step-step solution. solution. Values Values in the in thetop topright right corner corner indicate indicate the mean the mean of RMS of RMS for for the whole processing period. the whole processing period.

5.5. Discussion Discussion ThisThis paper paper is is devoted devoted to to di discussingscussing the the contribution contribution of ofLEO LEO satellites satellites to toERP ERP estima- estimation. tion.The The SLR SLR observations observations to to seven seven LEO satellites satellites from from three three different different missions, missions, including including SentinelSentinel-3,-3, Swarm, Swarm, and and GRACE GRACE-FO,-FO, are areprocessed processed in this in study. this study. With Withthe proposed the proposed single- single- receiverreceiver phase phase ambig ambiguityuity resolution resolution method method in [39], in [39 the], ambiguity the ambiguity-fixed-fixed orbit orbitis used is for used for decreasingdecreasing the the impact impact of of possible possible orbit orbit error error in in the the ambiguity ambiguity-float-float orbit orbit for for ERP ERP estima- estimation. tion. We find that the single-LEO ERP solution cannot reach the comparable accuracy level We find that the single-LEO ERP solution cannot reach the comparable accuracy level of the of the LAGEOS solution, even if the ambiguity-fixed orbit is used. The same phenomenon LAGEOS solution, even if the ambiguity-fixed orbit is used. The same phenomenon also also occurs in [9]. This may be due to the limited observations for single-LEO satellites, or occurs in [9]. This may be due to the limited observations for single-LEO satellites, or the the LEO satellite orbit-related errors conveyed into the ERP solution. The station coordi- nate derived from the single-LEO solutions can reach the similar accuracy of a few centi- meters with that in [20]. For the estimated core station coordinates, the solution based on some LEO satellites, such as GRACE-C and GRACE-D, is comparable to that based on LAGEOS satellites. This phenomenon confirms the potential of LEO satellites in geodetic parameter estimation to some extent. Rather than just focus on the single-LEO satellite, the combination of multiple-LEO satellites for ERP estimation is highlighted in our study. By increasing the LEO number in the processing, a notable improvement can be observed in the ERP solution. With seven LEO satellites included, a better ERP result than that based on LAGEOS in [46] is obtained. Moreover, the combination of multiple LEO satellites is especially of benefit for weaken- ing the LEO orbit-related signal in single-LEO solutions. Furthermore, the combination of seven LEO satellites and LAGEOS satellites can reach the best result, with the smallest RMS for ERP. Such combination offers a large number of observations and maximizes the diversity of the orbit type, which is especially beneficial for estimating ERP and obtaining more reliable estimated station coordinates. Our result indicates that this method exhibits a great potential to be a strong supplement, even an alternative to the current SLR-based reference frame realization only based on LAGEOS and Etalon satellites.

6. Conclusions A large amount of SLR observations to LEO satellites offer an opportunity for inves- tigating the potential of LEO satellites in ERP estimation. In this study, we are devoted to recovering ERP using SLR and GPS observations from seven LEO satellites. We evaluate

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LEO satellite orbit-related errors conveyed into the ERP solution. The station coordinate derived from the single-LEO solutions can reach the similar accuracy of a few centimeters with that in [20]. For the estimated core station coordinates, the solution based on some LEO satellites, such as GRACE-C and GRACE-D, is comparable to that based on LAGEOS satellites. This phenomenon confirms the potential of LEO satellites in geodetic parameter estimation to some extent. Rather than just focus on the single-LEO satellite, the combination of multiple-LEO satellites for ERP estimation is highlighted in our study. By increasing the LEO number in the processing, a notable improvement can be observed in the ERP solution. With seven LEO satellites included, a better ERP result than that based on LAGEOS in [46] is obtained. Moreover, the combination of multiple LEO satellites is especially of benefit for weakening the LEO orbit-related signal in single-LEO solutions. Furthermore, the combination of seven LEO satellites and LAGEOS satellites can reach the best result, with the smallest RMS for ERP. Such combination offers a large number of observations and maximizes the diversity of the orbit type, which is especially beneficial for estimating ERP and obtaining more reliable estimated station coordinates. Our result indicates that this method exhibits a great potential to be a strong supplement, even an alternative to the current SLR-based reference frame realization only based on LAGEOS and Etalon satellites.

6. Conclusions A large amount of SLR observations to LEO satellites offer an opportunity for investi- gating the potential of LEO satellites in ERP estimation. In this study, we are devoted to recovering ERP using SLR and GPS observations from seven LEO satellites. We evaluate the impact of the LEO orbit improvement on ERP estimation, and compare the quality of the ERP solution based on different LEO satellites. The main focus is on the different performance of the single-LEO solution, and the benefit of the combination of LEO satellites. In addition, we also investigate the feasibility of the simultaneous estimation of LEO orbits and ERP, which is named the one-step method in this study. The contribution of the ambiguity-fixed orbit for ERP estimation is firstly confirmed. Compared to the ambiguity-float solution, an RMS decrease of 12 uas and 22 uas for X pole and Y pole is obtained in the ambiguity-fixed solution. Based on the ERP series of different single-LEO solutions, we find that the single-LEO ERP solution cannot reach the comparable accuracy level of the LAGEOS solution, due to the limited SLR observations or the orbit modeling deficiencies. Meanwhile, a 119-day period signal is observed in the spectrum of the Sentinel-3 solution, which is closely related to the perigee revolution of the Sentienl-3 satellite. For the SLR stations, it can be seen that the station coordinates at the accuracy level of 2–3 cm is achievable while only using one LEO satellite. For the core stations, some single-LEO solutions can achieve a comparable positioning accuracy to the LAGEOS solution. In particular, the GRACE-C and GRACE-D solutions present an improvement of 4 mm in the up component when compared to the LAGEOS solution. Then, multiple LEO solutions with different numbers of LEO satellites are explored, with three schemes of the 3-LEO, 5-LEO and 7-LEO. The best ERP estimation result is achieved by the 7-LEO solution, thanks to a large number of observations and the enhanced observation geometry. Compared to the 3-LEO solution, the accuracy of X pole, Y pole and LOD for the 7-LEO solution is improved by 57.5%, 57.6% and 43.8%, respectively. Moreover, with more satellites included, the correlation between orbit parameters and ERP is significantly reduced. It can be seen that the 119-day signal in the Sentinel-3A solution is weakened in the multiple-LEO satellite solutions. For the station coordinates, more obser- vations from multiple-LEO satellites contribute to a more accurate and stable positioning solution, especially for the non-core station, which usually owns few observations in the single-LEO solution or LAGEOS solution. It can be seen that when the number of LEO satellites increases from three to seven, the accuracy of the non-core station coordinates is improved by 13.7%, 27.3% and 16.2% in the east, north and up components, respectively. Remote Sens. 2021, 13, 3046 21 of 23

We also jointly processed the data of LAGEOS and seven LEO satellites for ERP estimation, and this combination scheme attains an RMS reduction of 0.644 ms, 0.629 ms and 0.028 ms for X pole, Y pole and LOD, compared to the LAGEOS solution. Besides, the results for the core station can reach the accuracy level below 10 mm in the east, north and up components. In addition, we discuss the possibility of simultaneously estimating LEO orbits and ERP using GPS and SLR data. A degraded ERP and the station coordinate result is observed when the integrated processing is performed, which may be attributed to the weakened solution strength caused by introducing a large number of orbit parameters. However, it is desirable to obtain a sub-millimeter improvement for LEO satellite orbit estimation from the one-step method, thanks to the combination of GPS and SLR observations in the precise orbit determination process. With more satellites of new GNSS [47,48] being equipped with laser retroreflectors dedicated to SLR today, the study can be extended by including SLR observations to GNSS satellites, to realize the combination of GNSS, LEO, and LAGEOS for the realization of a reference frame in the future.

Author Contributions: Conceptualization, X.L. and H.Z.; methodology, X.L. and H.Z.; software, X.L.; validation, H.Z. and K.Z.; formal analysis, H.Z.; investigation, H.Z. and K.Z.; resources, Y.Y. and Y.Q.; data curation, H.Z.; writing—original draft preparation, H.Z.; writing—review and editing, K.Z. and H.Z.; visualization, H.Z.; supervision, W.Z.; project administration, X.L.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Foundation of China (grant 41774030, grant 41974027 and grant 41974029), the Hubei Province Natural Science Foundation of China (grant 2020CFA002), the frontier project of basic application from Wuhan Science and Technology Bureau (grant 2019010701011395), and the Sino-German mobility programme (grant No. M-0054). Acknowledgments: We are grateful to the International GNSS Service (IGS) for providing the precise orbit, clock and correction products of GPS satellites at ftp://cddis.gsfc..gov (accessed on 1 June 2021) for free. The ILRS is acknowledged for providing SLR observations of LEO and LAGEOS satellites. The data onboard GRACE-FO, Swarm, and Sentinel-3 are publicly available from ftp://isdcftp.gfz-potsdam.de (accessed on 1 June 2021), ftp://swarm-diss.eo.esa.int (accessed on 1 June 2021) and https://scihub.copernicus.eu/gnss (accessed on 1 June 2021) respectively. The numerical calculations in this study have been done on the supercomputing system in the Supercomputing Center of Wuhan University. Conflicts of Interest: The authors declare no conflict of interest.

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