Orbit Determination Research Articles

Measuring the Orbit Drift of Near-Earth Asteroids by the Yarkovsky Effect

The Yarkovsky effect causes the semimajor axis drift of near-Earth asteroids. The drift can be detected by a precise orbit determination process. Using the proposed algorithm, 2233 out of 27,078 near-Earth asteroids are chosen as the initial candidates. Out of these initial candidates, 769 have a measurable Yarkovsky effect with a signal-to-noise ratio (S/N) larger than 1, and 166 have a measurable Yarkovsky effect with an S/N larger than 3. The ratio between retrograde and prograde near-Earth asteroids is plotted with respect to their size. An average ratio of 2 is found for asteroids with an absolute magnitude between 14 and 21. The measurement work is carried out based on orbit determination software developed by the authors that considers a high-precision dynamical model.

Study on Differential Phase Delay of Same‐Beam VLBI in Rendezvous and Docking of Chang'E‐5

AbstractThe Chang'E‐5 (CE5) ascender achieved lunar orbit autonomous rendezvous and docking with orbiter‐returner successfully on 5 December 2020. Same‐beam Very Long Baseline Interferometry (VLBI) (SBI) observations were performed for the first time for autonomous rendezvous and docking in lunar orbit. In this paper, by studying the CE5 rendezvous and docking data observed by the Chinese VLBI network and analyzing the residual differential phase delay of the autonomous control phase, we successfully captured the maneuver of the 5 km holding of the orbiter‐returner. The differential phase delay (DPD) data of the far‐range guidance phase were used to perform orbit determination of the ascender and orbiter‐returner successfully. The results of orbit determination show that the DPD data can improve the relative position accuracy between the ascender and the orbiter‐returner, and the residual root mean square of the DPD data is 5 ps. Furthermore, when one of the probes has only DPD data, its orbit can also be determined.

Continuous Streak Image Acquisition Optical Observation System Design for Initial Orbit Determination of Uncharted Space Objects

Continuous Streak Image Acquisition Optical Observation System Design for Initial Orbit Determination of Uncharted Space Objects

Comprehensive Analysis of the Global Zenith Tropospheric Delay Real-Time Correction Model Based GPT3

To obtain a higher accuracy for the real-time Zenith Tropospheric Delay (ZTD), a refined tropospheric delay correction model was constructed by combining the tropospheric delay correction model based on meteorological parameters and the GPT3 model. The meteorological parameters provided by the Global Geodetic Observing System (GGOS) Atmosphere and the zenith tropospheric delay data provided by Centre for Orbit Determination in Europe (CODE) were used as references, and the accuracy and spatial–temporal characteristics of the proposed model were compared and studied. The results show the following: (1) Compared with the UNB3m, GPT and GPT2w models, the accuracy and stability of the GPT3 model were significantly improved, especially the estimation accuracy of temperature, the deviation (Bias) of the estimated temperature was reduced by 90.60%, 32.44% and 0.30%, and the root mean square error (RMS) was reduced by 42.40%, 11.02% and 0.11%, respectively. (2) At different latitudes, the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models had great differences in accuracy and applicability. In the middle and high latitudes, the Biases of the GPT3 + Saastamoinen model and the GPT3 + Hopfield model were within 0.60 cm, and the RMS values were within 4 cm; the Bias of the UNB3m model was within 2 cm, and the RMS was within 5 cm; in low latitudes, the accuracy and stability of the GPT3 + Saastamoinen model were better than those of the GPT3 + Hopfield and UNB3m models; compared with the GPT3 + Hopfield model, the Bias was reduced by 22.56%, and the RMS was reduced by 5.67%. At different heights, the RMS values of the GPT3 + Saastamoinen model and GPT3 + Hopfield model were better than that of the UNB3m model. When the height was less than 500 m, the Biases of the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models were 3.46 cm, 3.59 cm and 4.54 cm, respectively. At more than 500 m, the Biases of the three models were within 4 cm. In different seasons, the Bias of the ZTD estimated by the UNB3m model had obvious global seasonal variation. The GPT3 + Saastamoinen model and the GPT3 + Hopfield model were more stable, and the values were within 5 cm. The research results can provide a useful reference for the ZTD correction accuracy and applicability of GNSS navigation and positioning at different latitudes, at different heights and in different seasons.

Onboard observer-enhanced filter in handling orbital elements estimation of non-cooperative target

The purpose of this paper is to develop an effective method for onboard absolute orbital elements estimation of the non-cooperative target, which may beneficial to collision avoidance. The proposed estimator consists of two parts: the target acceleration observer and the orbital elements filter, where the observer generates partial input for the filter. For the estimator, the data source comes from the orbit determination information of the obstacle-avoidance-satellite and the relative measurement information of the non-cooperative target. These data are fed into an observer to estimate the maneuvering acceleration of the target. Then, the square root cubature adaptive H∞ information filter (SCAHIF) for target-orbital-elements estimation under the complicated noise condition is designed, which is driven by the observer outputs and the target data source. The performance of the overall “observer-enhanced SCAHIF” (OSCAHIF) is evaluated through three scenarios where the target is under zero maneuvering thrust, constant maneuvering thrust, and time-varying maneuvering thrust. Test results indicate that the proposed OSCAHIF provides a feasible solution to real-time absolute orbital elements estimation of the non-cooperative target with the presence of time-variant mixed Gaussian white noise.

Assessment of Swarm Kinematic Orbit Determination Using Two Different Double-Difference Methods

The Swarm mission aims to study the principle and change regularities of the Earth’s magnetic field. Precise orbit determination is essential to the successful implementation of the mission and relevant scientific research. This article focuses on using two different double-difference methods to improve the accuracy of Swarm kinematic orbit determination. The accuracy of the kinematic orbit determination relies entirely on the space-borne observation data, independent of any dynamic parameters. The article analyzes the data quality of the Swarm space-borne global positioning system (GPS) receiver and presents a detailed introduction to the data pre-processing algorithms. The double-difference observation gathering and the applied orbit determination strategy using two different double-difference methods are discussed. The results of the kinematic orbits under different solar cycle conditions are presented, along with an evaluation based on analysis of GPS carrier phase residuals, subtracting from the post-processed orbits, and assessment with satellite laser ranging (SLR) measurements. The results show that the accuracy of the kinematic orbit determination is at the centimeter level for the three Swarm satellites’ orbit solutions. The daily root mean square (RMS) values of the three satellites’ phase residuals remain at around the 6 mm level. The RMS values of the position residuals between the kinematic orbits and the reduced dynamic orbits released by the European Space Agency (ESA) are at about the 2–3 cm level. The external evaluation with SLR measurements shows a good agreement with the ESA level, with the RMS values of the SLR residuals for kinematic orbits around 2 cm.

Absolute and relative POD of LEO satellites in formation flying: Undifferenced and uncombined approach

Absolute or relative precise orbit determination (POD) is an essential prerequisite for many low earth orbit (LEO) missions. The POD of LEO satellites typically relays on processing the onboard global navigation satellite system (GNSS) measurements. The absolute POD is usually based on an ionosphere-free (IF) combination, and currently, integer ambiguity resolution (IAR) can be achieved only when external GNSS satellite phase bias (SPB) products are used. The use of these products is not flexible in multi-frequency/multi-constellation scenarios and is difficult to achieve in real-time missions. For relative POD, the double-differenced (DD) with IAR is the most general method. However, the differencing process amplifies observation noise and loses the opportunity to impose dynamic constraints on some eliminated parameters. In this contribution, based on the use of undifferenced and uncombined (UDUC) observations, a new model for both absolute and relative POD is proposed. In this model, the ambiguities of common-view satellites are constructed into DD form, thus IAR can be achieved without any external SPB products. Working with the UDUC observations, multi-frequency scenarios can be easily applied, and residuals can be separated for each frequency. In addition, with precise GNSS satellite clock/orbit products, both the absolute and relative orbits can be derived, which supports absolute and relative LEO POD. Based on onboard GPS observations of T-A and T-B satellites in formation flying, the performance of the UDUC POD model with DD ambiguity was evaluated. With the UDUC algorithm and IAR, the proposed model presented a consistency of 2.8–3.8 cm in 3D with the reference orbits, and the orbit difference was reduced by 16.3% and 10.6% for T-A and T-B compared with the IF-based POD, respectively. In addition, the relative orbit of the two satellites derived from the proposed model showed a consistency of 1.1–1.5 mm, which proved the feasibility of the UDUC POD model with DD ambiguity for formation flying missions.

An Improved Parameter Estimation Method for High-Efficiency Multi-GNSS-Integrated Orbit Determination

The increased number of satellites and stations leads to the serious time consumption of the integrated precise orbit determination (POD), especially in the current global navigation satellite system (GNSS) with more than 120 satellites. To improve the computational efficiency of multi-GNSS-integrated POD, this paper proposed an improved parameter estimation method based on intel oneAPI high-performance computing, where the inactive parameters are eliminated in a batch mode. Compared with the classical estimation method based on the “one-by-one” elimination, the efficiencies were significantly improved with ratios of 2.53, 4.21, and 5.38 for 79, 126, and 171 stations’ GPS/BDS/Galileo/GLONASS-integrated POD, respectively. The elapsed time of the improved method by using 126 stations was the same as that of 79 stations’ POD by the classical estimation method. In terms of precision, the one-dimensional root mean square error (RMS) reductions were 0.1 cm (7%), 34.3 cm (11%), 1.9 cm (18%), 0.4 cm (8%), 0.2 cm (13%), and 0.4 cm (13%) for GPS, BDS GEO, BDS IGSO, BDS MEO, Galileo, and GLONASS satellites, respectively.

Observability analysis of cooperative orbit determination using inertial inter-spacecraft angle measurements

The cooperative orbit determination (OD) using inertial inter-spacecraft measurements is of great value for the constellation. Previous studies concluded that the cooperative OD system in the two-body dynamics is observable using the inertial angle measurement. This paper performs an observability analysis for the inertial angle-only cooperative OD system based on the observability matrix (OM), and finds that the previous conclusions do not hold for some special configurations. Eight special configurations are proposed, and for each configuration, the unobservable orbit elements are analytically revealed by analyzing the linear relationship among different columns of the OM. Moreover, a method of improving the observability of the two-spacecraft system is proposed by adding another spacecraft. An extended Kalman filter is employed to numerically illustrate the observability of the proposed special configurations and to show the relationship between the observability and the convergence ratio of estimations. Monte Carlo simulations show that the convergence ratios of the observable orbit elements and state combinations are higher than 97%, while convergence ratios of the unobservable states are lower than 70%. With one non-planar elliptic orbit added, all the elements of the three-spacecraft system are observable, and the estimated errors converge within 6 h. The results found in this paper can provide a reference for the design and management of the constellation.

BDS Orbit Maneuver Detection Based on Epoch-Updated Orbits Estimated by SRIF

The orbit maneuver detection is crucial in Global Navigation Satellite System (GNSS) precise orbit determination, which is necessary for adjusting data processing strategies. The frequency of orbit maneuvers for the BeiDou Navigation System is significantly higher than that of other navigation systems, especially for geosynchronous orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. We propose a novel real-time and postprocessing method for detecting orbit maneuvers for BeiDou satellites based on the orbit differences between the epoch-updated orbit estimated using square root information (SRIF) and the predicted orbit according to the precise orbit estimated during non-maneuver period, as well as the orbital state difference during maneuver and non-maneuver periods. This method has significant advantages over using observation residuals and it is not affected by observation outliers, thus improving the accuracy and timeliness of orbit maneuver detection. We demonstrated that 32 orbit maneuver events of BeiDou satellites were successfully detected in 2022, of which 1 was for medium Earth orbit (MEO), 7 were for IGSO with an average detected maneuvering time of 7–8 min, and 24 were for GEO satellites with an average detected time of 4–5 min. Moreover, our method can be easily integrated into current real-time filter-based precise orbit determination (POD) processing without any extra task line, which simplifies the overall data processing. The data used in this method can be accessed easily, including GNSS observation data, broadcast ephemeris, and other open-source information files.

An architecture for a visual-based PNT alternative

This paper treats the problem of positioning and navigation in the absence of GNSS. Given recently raised vulnerabilities for GNSS both on Earth and in space, the work revisits the old problem of the sextant in new light. The combination of stars and planetary horizons was the popular tool for autonomous navigation on-board spacecraft, but given the rise of GNSS receivers, this solution has been largely disregarded. New spacecraft missions beyond Earth have made new progress in visual-based navigation. The work utilises these new methodologies in the scenario that RF-derived positioning is unavailable, achieving a performance below 100 m.An additional important consideration is the development of new navigation infrastructure in LEO and the Moon. Current methods seek to use GNSS and RF-derived sources for orbit determination, however, to be seen as ‘redundancy infrastructure’ for critical Earth and beyond applications, these signals cannot be the primary and only source of navigation reference. This paper utilises derived performances for visual-based methods and applies them to the ranging service problem. Most user scenarios in maritime, aviation and lunar domains are satisfied.This work illustrates implementation using the simple architecture of a star tracker camera. Known as CROSS, the technology is a new navigation tool in development by the University of Sydney. As a star tracker is common device to many spacecraft platform, it simplifies implementation, given that redundant systems are always not a priority to the manufacturer.

Reference clock impact on GNSS clock outliers

Abstract With the advent of the Global Navigation Satellite System (GNSS), the need for precise and highly accurate orbit and clock products becomes crucial in processing GNSS data. Clocks in GNSS observations form the basis of positioning. Their high quality and stability enable high accuracy and the reliability of the obtained results. The clock modelling algorithms are continuously improved; thus, the accuracy of the clock products is evolving. At present, 8 Analysis Centers (ACs) contribute to the International GNSS Service final clock products. These products are based on GNSS observations on a network of reference stations, where for a given day one of the reference station clocks is the reference clock. In this paper, the authors determined the impact of the reference clock on the quality of clock product, especially outliers, for the first time. For this purpose, the multi-GNSS final clock products provided by the Center for Orbit Determination in Europe (CODE) for the period 2014–2021 (1773–2190 GPS week, 2921 days) were analysed. Analysis shows that by applying the Median Absolute Deviation (MAD) algorithm for outlier detection, the Passive Hydrogen Maser (PHM) clock installed on board the GALILEO satellites have the lowest level of noise, whereas the Block IIR GPS satellite launched in 1999 appears to have the highest levels of noise. Furthermore, the GNSS station OHIE3, when used as a reference clock, generates an increase in the level of noise, especially noticeable on the G09 and E03 satellites.

A-contrario detection and tracking from optical telescope data

The precipitous growth of the Anthropogenic Space Object population demands new approaches to high-volume detection and measurement for orbital analyses and conjunction assessment. Optical sensors, which can be smaller and more cost-effective than other mechanisms such as radar sensors, have potential for rapid network expansion, community-driven data acquisition, and space-based sensing. However, traditional detection methods of source extraction and track filtering require high-fidelity a-priori assumptions of data content and are limited by extensive calibration requirements costing time, resources, and expert knowledge of particular detection pipelines. Machine learning methods mitigate a-priori assumptions but require extensive training data which is costly to manually label and restricts applicable use cases. We instead consider a new approach to optical Space Surveillance and Tracking based on a-contrario analysis, detecting features which cannot be attributed to noise from the hardware, atmosphere, or background celestial environment. In such an approach, we reduce epistemic uncertainty by recursive conditioning and inference of data structures. This approach is implemented and assessed on data from the ASTRIANet telescope network of The University of Texas at Austin, and we demonstrate the capacity for orbit determination by quantifying detection rates for actively tracked objects, discussing applicability to sidereal tracking and object discovery, and evaluating the resulting orbit estimates.

Real‐time precise orbit determination for FY‐3C and FY‐3D based on BDS and GPS onboard observation

AbstractThe code multipath error associated with elevation in BDS‐2 is one of the main factors whose impact on the precision of real‐time reduced‐dynamic precise orbit determination (POD) using spaceborne multi‐global navigation satellite systems (GNSS) observation data for FengYun‐3C (FY‐3C) and FengYun‐3D (FY‐3D) satellites. The aim is to construct a code multipath piece‐wise linear error model and analyse the contribution of BDS‐2 to the performance of low earth orbit POD. Conclusions are drawn out from the experimental results: (1) the real‐time POD average precision of FY‐3C and FY‐3D is improved by about 11% and 12% after the correction of BDS‐2 code multipath error; (2) Due to the small number of available BDS‐2 satellites and the limited accuracy of geostationary earth orbit (GEO) satellite real‐time orbit products, the precision of the real‐time overlapping comparison for FY‐3C/FY‐3D by using the BDS‐2 onboard observation data can only reach the decimetre level. However, with the BDS‐2 signal capture capability of the FY‐3D onboard GNSS Occultation Sounder upgraded, the average precision of the BDS‐2‐based POD for FY‐3D is better than that of FY‐3C in each direction and with 10% improvement in the average 3 dimensional‐root mean square (3D‐RMS); (3) Cases of onboard global positioning system (GPS), GPS + BDS‐2 (with GEO), and GPS + BDS‐2 (without GEO) for real‐time POD can meet 5–8 cm precision requirement. The average 3D‐RMS of the real‐time POD for FY‐3C/FY‐3D, which utilises onboard GPS + BDS‐2 data is inferior only to GPS data, owing to the influence of the orbit accuracy of GEO satellites. However, after excluding the influence of GEO satellites, the average result (3D‐RMS) of the real‐time POD for FY‐3C (6.11 cm) and FY‐3D (5.95 cm) is better than those of other cases.

Phasing analysis on DRO with impulsive maneuver

The cis-lunar periodic orbit exhibits some unique dynamic characteristics. Among them is the distant retrograde orbit, which has long-term stability and is one of the ideal candidate deployment orbits for cis-lunar space stations and deep-space exploration transfer stations. Orbiting, rendezvous, and docking are among the flight operations involved in space station on-orbit construction, material supply, spacecraft monitoring, and other tasks. Suitable initial conditions can be created for these operations by shortening the relative distance between spacecraft through phasing. In this study, the characteristics of a two-impulse phasing orbit on a distant retrograde orbit (DRO) are summarized, and its phasing ability is globally analyzed. Based on these analyses, a phasing optimization problem was presented and solved. Using DRO’s dynamic characteristics, a DRO multi-impulse phasing rolling solution method is presented. For accuracy purposes, the orbit determination error is also considered in this method. The simulation analysis was performed using the circular restricted three-body problem (CR3BP) dynamic model and the ephemeris model. Compared with the results of two-impulse phasing, this method reduces the offset of the end position of the DRO phasing orbit from hundreds to tens of kilometers. This result satisfies the relative distance requirements for subsequent spacecraft operations. The total pulse requirement of this phasing method for the two models was within a reasonable and feasible range.

LEO Satellite Navigation Based on Optical Measurements of a Cooperative Constellation

Autonomous, anti-jamming, and high-precision satellite navigation are of great importance to current and future space technologies. This paper proposes a cooperative constellation navigation system for low Earth orbit (LEO) satellites that use only the optical measurements of cooperative satellites. Based on photometry, an optical transmission link model of the system is built. With the pixel coordinates of the cooperative satellites on the optical images, the line of sight (LoS) vectors of the cooperative satellites with respect to the LEO spacecraft are first calculated, and a single-point positioning method based on the LoS vectors’ inner products is proposed. The single-point positioning results are then fed into a least square batch filter to estimate a high-precision spacecraft orbit. Simulations are conducted to evaluate the potential navigation accuracy. With a cooperative satellite ephemeris error of 100 m and an optical measurement noise level of 5 arcsecs, position accuracies of single-point positioning and dynamic orbit determination in the order of hundreds of meters and eight meters, respectively, are realized. In addition, the influences of the orbital altitude of the cooperative constellation, the ephemeris error of the cooperative satellite, the noise level of the optical measurements, and the Earth’s gravitational model on navigation accuracy are investigated via comparative simulations.

GEORB: Release for precise orbit determination of low Earth orbiters and satellite gravity missions

GEORB: Release for precise orbit determination of low Earth orbiters and satellite gravity missions

A Double-Adaptive Adjustment Algorithm for Ionospheric Tomography

A double-adaptive adjustment algorithm (DAAA) is proposed to reconstruct three-dimensional ionospheric electron density (IED) distribution. In the DAAA method, the relaxation factor of the multiplicative algebraic reconstruction technique (MART) is first adaptively adjusted by introducing adaptive MART (AMART). To avoid the voxels without any rays traversing them becoming dependent on the initial IED values, smoothing constraints are generally imposed on the adaptive multiplicative algebraic reconstruction technique (AMART). In general, the elements of the smoothing matrices are invariant in the iterative process. They affect the accuracy and efficiency of the IED inversion. To overcome the above limitation, the adaptive adjustments of the constrained matrix elements are subsequently carried out. Both numerical simulation and actual global navigation satellite system (GNSS) experimental results validate that the accuracy and efficiency of ionospheric tomography have been improved by the DAAA method. Finally, the new algorithm is applied to reconstruct the three-dimensional structure of the ionosphere during different geomagnetic activities. The comparisons show that the vertical profiles of the DAAA method are in agreement with those recorded from the ionosonde, and the inverted vertical total electron content (VTEC) of the DAAA method also agrees with the ionospheric products of center for orbit determination in Europe (CODE) during geomagnetic quiet and geomagnetic storms. The comparisons confirm the reliability and superiority of the DAAA method.

Improved undifferenced ambiguity resolution for LEO precise orbit determination

Ambiguity resolution (AR) is critical for enhancing the orbit accuracy in precise orbit determination (POD) for low earth orbit (LEO) satellites. While orbit estimation using single-difference (SD) AR has been widely researched, the investigation of orbit estimation using undifferenced (UD) AR for LEO satellites is limited due to time-varying hardware biases at the LEO receiver end. To address this deficiency, we propose an improved UD AR method for LEO satellite orbit determination. The method employs the optimal integer datum ambiguity for a 1-day observation arc, and the random-walk clock model is utilized to transfer the integer ambiguity datum to the other epochs, which enables the arc-wise ambiguities to regain the integer property within the time frame. To validate the effectiveness of our improved method, numerical experiments are conducted. Moreover, we assess the performance of the random-walk clock model for a spaceborne ultra-stable oscillator (USO). The high frequency stability of the USO establishes the satisfactory requirements for this study. Both in the kinematic and dynamic modes, the AR success rates of our improved method are ∼ 2% higher than that of the current SD AR method, and the orbit results indicate a slight improvement. The 3-Dimensional (3D) root-mean-squares (RMS) of the orbit differences between JPL precise science orbits (PSO) and our orbits are reduced by up to 4% and 5% for kinematic and dynamic orbits, respectively. The subtle benefit is also proven by K-band ranging (KBR) system validations. In the case of the Gravity Recovery and Climate Experiment Follow-on (GFO) satellites, the results indicate that the effect of our improved UD AR can be equivalent to that of SD AR. Our improved UD AR method can be a good alternative for its superior ability to generate hardware delay at the LEO receiver end.

Improvement of international reference ionospheric model total electron content maps: a case study using artificial neural network in Egypt

Abstract An essential ionosphere parameter that can be applied for ionosphere corrections in radio systems is the ionosphere’s total electron content (TEC). TEC is a crucial parameter for ionospheric correction in the Global Navigation Satellite Systems (GNSS) of positioning, navigation, and radio science. This study uses the artificial neural network (ANN) application to improve the International Reference Ionospheric Model (IRI-2016) TEC maps across Egypt. The study period is based on the data that were accessible between 2013 and 2020. The ANN model input parameters are (year, day, hour, latitude, and longitude). The ANN1 and ANN2 estimate TEC values of the enhanced IRI-2020 and IRI-2016 according to the Center for Orbit Determination in Europe (CODE), respectively. ANN3 and ANN4 estimate TEC values of the enhanced IRI-2020 and IRI-2016 regarding IGS stations data analyzed by GNSS Analysis software for the multi-constellation and multi-frequency Precise Positioning (GAMP) model, respectively. The ANN model’s validations were based on the root mean square error (RMSE), correlation coefficient (CC), and T-test. According to the results, the suggested ANN can accurately predict the TEC over Egypt. In comparison to the IRI model, the TEC maps that the ANN models produced are significantly more in accordance with the related CODE and GAMP TEC maps. These results demonstrate that the developed approach can enhance IRI 2016 and IRI-2020s ability to estimate global TEC maps. For the ANN1 model, the mean CC and RMSE are 0.92, and 5.15 TECU for all the global data sets compared by CODE. On the other hand, the CC and RMSE between IRI-2020 and CODE are 0.847 and 7.67 TECU. For the ANN2, the mean CC and RMSE are 0.87, 5.59 TECU compared by CODE, respectively. Although the CC and RMSE between IRI-2016 and CODE are 0.820 and 9.052 TECU respectively. For the ANN3, the CC and RMSE are 0.830 and 4.87 TECU compared with GAMP for all global data, respectively. On the other hand, the CC and RMSE between IRI-2020 and GAMP are 0.644 and 10.41, respectively. For the ANN4 the CC and RMSE are 0.82, and 5.95 TECU compared with GAMP, respectively. Although the CC and RMSE between IRI-2016 and GAMP are 0.665 and 12.347 TECU respectively.