Abstract In high-accuracy positioning using GNSS, the most common solution is still relative positioning using double-difference observations of dual-frequency measurements. An increasingly popular alternative to relative positioning are undifferenced approaches, which are designed to make full use of modern satellite systems and signals. Positions referenced to global International Terrestrial Reference Frame (ITRF2008) obtained from Precise Point Positioning (PPP) or Undifferenced (UD) network solutions have to be transformed to national (regional) reference frame, which introduces additional bases related to the transformation process. In this paper, satellite observations from two test networks using different observation time series were processed. The first test concerns the positioning accuracy from processing one year of dual-frequency GPS observations from 14 EUREF Permanent Network (EPN) stations using NAPEOS 3.3.1 software. The results were transformed into a national reference frame (PL-ETRF2000) and compared to positions from an EPN cumulative solution, which was adopted as the true coordinates. Daily observations were processed using PPP and UD multi-station solutions to determine the final accuracy resulting from satellite positioning, the transformation to national coordinate systems and Eurasian intraplate plate velocities. The second numerical test involved similar processing strategies of post-processing carried out using different observation time series (30 min., 1 hour, 2 hours, daily) and different classes of GNSS receivers. The centimeter accuracy of results presented in the national coordinate system satisfies the requirements of many surveying and engineering applications.
{"title":"Application of the Undifferenced GNSS Precise Positioning in Determining Coordinates in National Reference Frames","authors":"G. Krzan, K. Stępniak","doi":"10.1515/arsa-2017-0006","DOIUrl":"https://doi.org/10.1515/arsa-2017-0006","url":null,"abstract":"Abstract In high-accuracy positioning using GNSS, the most common solution is still relative positioning using double-difference observations of dual-frequency measurements. An increasingly popular alternative to relative positioning are undifferenced approaches, which are designed to make full use of modern satellite systems and signals. Positions referenced to global International Terrestrial Reference Frame (ITRF2008) obtained from Precise Point Positioning (PPP) or Undifferenced (UD) network solutions have to be transformed to national (regional) reference frame, which introduces additional bases related to the transformation process. In this paper, satellite observations from two test networks using different observation time series were processed. The first test concerns the positioning accuracy from processing one year of dual-frequency GPS observations from 14 EUREF Permanent Network (EPN) stations using NAPEOS 3.3.1 software. The results were transformed into a national reference frame (PL-ETRF2000) and compared to positions from an EPN cumulative solution, which was adopted as the true coordinates. Daily observations were processed using PPP and UD multi-station solutions to determine the final accuracy resulting from satellite positioning, the transformation to national coordinate systems and Eurasian intraplate plate velocities. The second numerical test involved similar processing strategies of post-processing carried out using different observation time series (30 min., 1 hour, 2 hours, daily) and different classes of GNSS receivers. The centimeter accuracy of results presented in the national coordinate system satisfies the requirements of many surveying and engineering applications.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"52 1","pages":"49 - 69"},"PeriodicalIF":0.9,"publicationDate":"2017-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/arsa-2017-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46082196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Precise Point Positioning (PPP) is a technique used for position computation with a high accuracy using only one GNSS receiver. It depends on highly accurate satellite position and clock data rather than broadcast ephemeries. PPP precision varies based on positioning technique (static or kinematic), observations type (single or dual frequency) and the duration of collected observations. PPP-(dual frequency receivers) offers comparable accuracy to differential GPS. PPP-single frequency receivers has many applications such as infrastructure, hydrography and precision agriculture. PPP using low cost GPS single-frequency receivers is an area of great interest for millions of users in developing countries such as Egypt. This research presents a study for the variability of single frequency static GPS-PPP precision based on different observation durations.
{"title":"Variation of Static-PPP Positioning Accuracy Using GPS-Single Frequency Observations (Aswan, Egypt)","authors":"A. Farah","doi":"10.1515/arsa-2017-0003","DOIUrl":"https://doi.org/10.1515/arsa-2017-0003","url":null,"abstract":"Abstract Precise Point Positioning (PPP) is a technique used for position computation with a high accuracy using only one GNSS receiver. It depends on highly accurate satellite position and clock data rather than broadcast ephemeries. PPP precision varies based on positioning technique (static or kinematic), observations type (single or dual frequency) and the duration of collected observations. PPP-(dual frequency receivers) offers comparable accuracy to differential GPS. PPP-single frequency receivers has many applications such as infrastructure, hydrography and precision agriculture. PPP using low cost GPS single-frequency receivers is an area of great interest for millions of users in developing countries such as Egypt. This research presents a study for the variability of single frequency static GPS-PPP precision based on different observation durations.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"52 1","pages":"19 - 26"},"PeriodicalIF":0.9,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/arsa-2017-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44514281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Emad El Manaily, M. Abd Rabbou, A. El-Shazly, M. Baraka
Abstract Commonly, relative GPS positioning technique is used in Egypt for precise positioning applications. However, the requirement of a reference station is usually problematic for some applications as it limits the operational range of the system and increases the system cost and complexity On the other hand; the single point positioning is traditionally used for low accuracy applications such as land vehicle navigation with positioning accuracy up to 10 meters in some scenarios which caused navigation problems especially in downtown areas. Recently, high positioning accuracy can be obtained through Precise Point Positioning (PPP) technique in which only once GNSS receiver is used. However, the major drawback of PPP is the long convergence time to reach to the surveying grade accuracy compared to the existing relative techniques. Moreover, the PPP accuracy is significantly degraded due to shortage in satellite availability in urban areas. To overcome these limitations, the quad constellation GNSS systems namely; GPS.GLONASS, Galileo and BeiDou can be combined to increase the satellite availability and enhance the satellite geometry which in turn reduces the convergence time. In Egypt, at the moment, the signals of both Galileo and BeiDou could be logged with limited number of satellites up to four and six satellites for both Systems respectively. In this paper, we investigated the performance of the Quad-GNSS positioning in both dual- and single-frequency ionosphere free PPP modes for both high accurate and low cost navigation application, respectively. The performance of the developed PPP models will be investigated through GNSS data sets collected at three Egyptian cities namely, Cairo, Alexandria and Aswan.
{"title":"Evaluation of Quad-Constellation GNSS Precise Point Positioning in Egypt","authors":"Emad El Manaily, M. Abd Rabbou, A. El-Shazly, M. Baraka","doi":"10.1515/arsa-2017-0002","DOIUrl":"https://doi.org/10.1515/arsa-2017-0002","url":null,"abstract":"Abstract Commonly, relative GPS positioning technique is used in Egypt for precise positioning applications. However, the requirement of a reference station is usually problematic for some applications as it limits the operational range of the system and increases the system cost and complexity On the other hand; the single point positioning is traditionally used for low accuracy applications such as land vehicle navigation with positioning accuracy up to 10 meters in some scenarios which caused navigation problems especially in downtown areas. Recently, high positioning accuracy can be obtained through Precise Point Positioning (PPP) technique in which only once GNSS receiver is used. However, the major drawback of PPP is the long convergence time to reach to the surveying grade accuracy compared to the existing relative techniques. Moreover, the PPP accuracy is significantly degraded due to shortage in satellite availability in urban areas. To overcome these limitations, the quad constellation GNSS systems namely; GPS.GLONASS, Galileo and BeiDou can be combined to increase the satellite availability and enhance the satellite geometry which in turn reduces the convergence time. In Egypt, at the moment, the signals of both Galileo and BeiDou could be logged with limited number of satellites up to four and six satellites for both Systems respectively. In this paper, we investigated the performance of the Quad-GNSS positioning in both dual- and single-frequency ionosphere free PPP modes for both high accurate and low cost navigation application, respectively. The performance of the developed PPP models will be investigated through GNSS data sets collected at three Egyptian cities namely, Cairo, Alexandria and Aswan.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"52 1","pages":"18 - 9"},"PeriodicalIF":0.9,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/arsa-2017-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47615681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Results of long-term static GNSS observation processing adjustment prove that the often assumed “averaging multipath effect due to extended observation periods” does not actually apply. It is instead visible a bias that falsifies the coordinate estimation. The comparisons between the height difference measured with a geometrical precise leveling and the height difference provided by GNSS clearly verify the impact of the near-field multipath effect. The aim of this paper is analysis the near-field interference effect with respect to the coordinate domain. We demonstrate that the way of antennas mounting during observation campaign (distance from nearest antennas) can cause visible changes in pseudo-kinematic precise point positioning results. GNSS measured height differences comparison revealed that bias of up to 3 mm can be noticed in Up component when some object (additional GNSS antenna) was placed in radiating near-field region of measuring antenna. Additionally, for both processing scenario (GPS and GPS/GLONASS) the scattering of results clearly increased when additional antenna crosses radiating near-field region of measuring antenna. It is especially true for big choke ring antennas. In short session (15, 30 min.) the standard deviation was about twice bigger in comparison to scenario without additional antenna. When we used typical surveying antennas (short near-field region radius) the effect is almost invisible. In this case it can be observed the standard deviation increase of about 20%. On the other hand we found that surveying antennas are generally characterized by lower accuracy than choke ring antennas. The standard deviation obtained on point with this type of antenna was bigger in all processing scenarios (in comparison to standard deviation obtained on point with choke ring antenna).
{"title":"GNSS Antenna Caused Near-Field Interference Effect in Precise Point Positioning Results","authors":"K. Dawidowicz, R. Baryla","doi":"10.1515/arsa-2017-0004","DOIUrl":"https://doi.org/10.1515/arsa-2017-0004","url":null,"abstract":"Abstract Results of long-term static GNSS observation processing adjustment prove that the often assumed “averaging multipath effect due to extended observation periods” does not actually apply. It is instead visible a bias that falsifies the coordinate estimation. The comparisons between the height difference measured with a geometrical precise leveling and the height difference provided by GNSS clearly verify the impact of the near-field multipath effect. The aim of this paper is analysis the near-field interference effect with respect to the coordinate domain. We demonstrate that the way of antennas mounting during observation campaign (distance from nearest antennas) can cause visible changes in pseudo-kinematic precise point positioning results. GNSS measured height differences comparison revealed that bias of up to 3 mm can be noticed in Up component when some object (additional GNSS antenna) was placed in radiating near-field region of measuring antenna. Additionally, for both processing scenario (GPS and GPS/GLONASS) the scattering of results clearly increased when additional antenna crosses radiating near-field region of measuring antenna. It is especially true for big choke ring antennas. In short session (15, 30 min.) the standard deviation was about twice bigger in comparison to scenario without additional antenna. When we used typical surveying antennas (short near-field region radius) the effect is almost invisible. In this case it can be observed the standard deviation increase of about 20%. On the other hand we found that surveying antennas are generally characterized by lower accuracy than choke ring antennas. The standard deviation obtained on point with this type of antenna was bigger in all processing scenarios (in comparison to standard deviation obtained on point with choke ring antenna).","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"52 1","pages":"27 - 40"},"PeriodicalIF":0.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67379815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.
{"title":"MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation","authors":"V. Pashkevich","doi":"10.1515/arsa-2017-0001","DOIUrl":"https://doi.org/10.1515/arsa-2017-0001","url":null,"abstract":"Abstract The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"52 1","pages":"1 - 8"},"PeriodicalIF":0.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/arsa-2017-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67380159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.
{"title":"Optimal Estimation of a Subset of Integers with Application to GNSS","authors":"A. Brack","doi":"10.1515/arsa-2016-0011","DOIUrl":"https://doi.org/10.1515/arsa-2016-0011","url":null,"abstract":"Abstract The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"51 1","pages":"123 - 134"},"PeriodicalIF":0.9,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67379866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The hydrological contribution to decadal, inter-annual and multi-annual suppress polar motion derived from climate model as well as from GRACE (Gravity Recovery and Climate Experiment) data is discussed here for the period 2002.3-2016.0. The data set used here are Earth Orientation Parameters Combined 04 (EOP C04), Flexible Global Ocean-Atmosphere-Land System Model: Grid-point Version 2 (FGOAL-g2) and Global Land Data Assimilation System (GLDAS) climate models and GRACE CSR RL05 data for polar motion, hydrological and gravimetric excitation, respectively. Several Hydrological Angular Momentum (HAM) functions are calculated here from the selected variables: precipitation, evaporation, runoff, soil moisture, accumulated snow of the FGOALS and GLDAS climate models as well as from the global mass change fields from GRACE data provided by the International Earth Rotation and Reference System Service (IERS) Global Geophysical Fluids Center (GGFC). The contribution of different HAM excitation functions to achieve the full agreement between geodetic observations and geophysical excitation functions of polar motion is studied here.
{"title":"Hydrological Excitations of Polar Motion Derived from Different Variables of Fgoals − g2 Climate Model","authors":"M. Wińska","doi":"10.1515/arsa-2016-0010","DOIUrl":"https://doi.org/10.1515/arsa-2016-0010","url":null,"abstract":"Abstract The hydrological contribution to decadal, inter-annual and multi-annual suppress polar motion derived from climate model as well as from GRACE (Gravity Recovery and Climate Experiment) data is discussed here for the period 2002.3-2016.0. The data set used here are Earth Orientation Parameters Combined 04 (EOP C04), Flexible Global Ocean-Atmosphere-Land System Model: Grid-point Version 2 (FGOAL-g2) and Global Land Data Assimilation System (GLDAS) climate models and GRACE CSR RL05 data for polar motion, hydrological and gravimetric excitation, respectively. Several Hydrological Angular Momentum (HAM) functions are calculated here from the selected variables: precipitation, evaporation, runoff, soil moisture, accumulated snow of the FGOALS and GLDAS climate models as well as from the global mass change fields from GRACE data provided by the International Earth Rotation and Reference System Service (IERS) Global Geophysical Fluids Center (GGFC). The contribution of different HAM excitation functions to achieve the full agreement between geodetic observations and geophysical excitation functions of polar motion is studied here.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"711 1","pages":"107 - 122"},"PeriodicalIF":0.9,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/arsa-2016-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67379666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The complex demodulation (CD) algorithm is an efficient tool for extracting the diurnal and subdiurnal components of Earth rotation from the routine VLBI observations (Brzeziński, 2012). This algorithm was implemented by Böhm et al (2012b) into a dedicated version of the VLBI analysis software VieVs. The authors processed around 3700 geodetic 24-hour observing sessions in 1984.0-2010.5 and estimated simultaneously the time series of the long period components as well as diurnal, semidiurnal, terdiurnal and quarterdiurnal components of polar motion (PM) and universal time UT1. This paper describes the tests of the CD algorithm by checking consistency of the low frequency components of PM and UT1 estimated by VieVS CD and those from the IERS and IVS combined solutions. Moreover, the retrograde diurnal component of PM demodulated from VLBI observations has been compared to the celestial pole offsets series included in the IERS and IVS solutions. We found for all three components a good agreement of the results based on the CD approach and those based on the standard parameterization recommended by the IERS Conventions (IERS, 2010) and applied by the IERS and IVS. We conclude that an application of the CD parameterization in VLBI data analysis does not change those components of EOP which are included in the standard adjustment, while enabling simultaneous estimation of the high frequency components from the routine VLBI observations. Moreover, we deem that the CD algorithm can also be implemented in analysis of other space geodetic observations, like GNSS or SLR, enabling retrieval of subdiurnal signals in EOP from the past data.
{"title":"Complex Demodulation in Monitoring Earth Rotation by VLBI: Testing the Algorithm by Analysis of Long Periodic EOP Components","authors":"A. Wielgosz, A. Brzeziński, S. Böhm","doi":"10.1515/arsa-2016-0012","DOIUrl":"https://doi.org/10.1515/arsa-2016-0012","url":null,"abstract":"Abstract The complex demodulation (CD) algorithm is an efficient tool for extracting the diurnal and subdiurnal components of Earth rotation from the routine VLBI observations (Brzeziński, 2012). This algorithm was implemented by Böhm et al (2012b) into a dedicated version of the VLBI analysis software VieVs. The authors processed around 3700 geodetic 24-hour observing sessions in 1984.0-2010.5 and estimated simultaneously the time series of the long period components as well as diurnal, semidiurnal, terdiurnal and quarterdiurnal components of polar motion (PM) and universal time UT1. This paper describes the tests of the CD algorithm by checking consistency of the low frequency components of PM and UT1 estimated by VieVS CD and those from the IERS and IVS combined solutions. Moreover, the retrograde diurnal component of PM demodulated from VLBI observations has been compared to the celestial pole offsets series included in the IERS and IVS solutions. We found for all three components a good agreement of the results based on the CD approach and those based on the standard parameterization recommended by the IERS Conventions (IERS, 2010) and applied by the IERS and IVS. We conclude that an application of the CD parameterization in VLBI data analysis does not change those components of EOP which are included in the standard adjustment, while enabling simultaneous estimation of the high frequency components from the routine VLBI observations. Moreover, we deem that the CD algorithm can also be implemented in analysis of other space geodetic observations, like GNSS or SLR, enabling retrieval of subdiurnal signals in EOP from the past data.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"10 1","pages":"135 - 147"},"PeriodicalIF":0.9,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67380021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Occasionally, there is a necessity in high-accurate prediction of celestial body trajectory. The most common way to do that is to solve Kepler’s equation analytically or to use Runge-Kutta or Adams integrators to solve equation of motion numerically. For low-orbit satellites, there is a critical need in accounting geopotential and another forces which influence motion. As the result, the right side of equation of motion becomes much bigger, and classical integrators will not be quite effective. On the other hand, there is a multistep-out-of-grid (MOG) method which combines Runge-Kutta and Adams methods. The MOG method is based on using m on-grid values of the solution and n × m off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, O (hm+mn+n−1). The main subject of this research was to implement and analyze the MOG method for solving satellite equation of motion with taking into account Earth geopotential model (ex. EGM2008 (Pavlis at al., 2008)) and with possibility to add other perturbations such as atmospheric drag or solar radiation pressure. Simulations were made for satellites on low orbit and with various eccentricities (from 0.1 to 0.9). Results of the MOG integrator were compared with results of Runge-Kutta and Adams integrators. It was shown that the MOG method has better accuracy than classical ones of the same order and less right-hand value estimations when is working on high orders. That gives it some advantage over ”classical” methods.
摘要有时候，需要对天体轨迹进行高精度的预测。最常见的方法是解析解开普勒方程或者用龙格-库塔或亚当斯积分器数值解运动方程。对于低轨道卫星，迫切需要计算重力势和其他影响运动的力。结果，运动方程的右侧变得更大，经典积分器将不太有效。另一方面，有一种结合了龙格-库塔法和亚当斯法的多步出网格法。MOG方法是基于使用m个解的在网值和n × m个离网导数估计。该方法可以提供最大可能阶的稳定积分器O (hm+mn+n−1)。本研究的主要课题是在考虑地球位势模型(例如EGM2008 (Pavlis at al.， 2008))并考虑大气阻力或太阳辐射压力等其他扰动的情况下，实现和分析求解卫星运动方程的MOG方法。对低轨道和不同偏心率(从0.1到0.9)的卫星进行了模拟。将MOG积分器的结果与Runge-Kutta积分器和Adams积分器的结果进行比较。结果表明，在处理高阶时，MOG方法比同阶的经典方法具有更好的精度和较少的右值估计。这使得它比“经典”方法有一些优势。
{"title":"On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks","authors":"L. Olifer, V. Choliy","doi":"10.1515/arsa-2016-0009","DOIUrl":"https://doi.org/10.1515/arsa-2016-0009","url":null,"abstract":"Abstract Occasionally, there is a necessity in high-accurate prediction of celestial body trajectory. The most common way to do that is to solve Kepler’s equation analytically or to use Runge-Kutta or Adams integrators to solve equation of motion numerically. For low-orbit satellites, there is a critical need in accounting geopotential and another forces which influence motion. As the result, the right side of equation of motion becomes much bigger, and classical integrators will not be quite effective. On the other hand, there is a multistep-out-of-grid (MOG) method which combines Runge-Kutta and Adams methods. The MOG method is based on using m on-grid values of the solution and n × m off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, O (hm+mn+n−1). The main subject of this research was to implement and analyze the MOG method for solving satellite equation of motion with taking into account Earth geopotential model (ex. EGM2008 (Pavlis at al., 2008)) and with possibility to add other perturbations such as atmospheric drag or solar radiation pressure. Simulations were made for satellites on low orbit and with various eccentricities (from 0.1 to 0.9). Results of the MOG integrator were compared with results of Runge-Kutta and Adams integrators. It was shown that the MOG method has better accuracy than classical ones of the same order and less right-hand value estimations when is working on high orders. That gives it some advantage over ”classical” methods.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"51 1","pages":"105 - 99"},"PeriodicalIF":0.9,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67379554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Digital Elevation Models (DEMs) comprise valuable source of elevation data required for many engineering applications. Contour lines, slope - aspect maps are part of their many uses. Moreover, DEMs are used often in geographic information systems (GIS), and are the most common basis for digitally-produced relief maps. This paper proposes a method of generating DEM by using Google Earth elevation data which is easier and free. The case study consisted of three different small regions in the northern beach in Egypt. The accuracy of the Google earth derived elevation data are reported using root mean square error (RMSE), mean error (ME) and maximum absolute error (MAE). All these accuracy statistics were computed using the ground coordinates of 200 reference points for each region of the case study. The reference data was collected with total station survey. The results showed that the accuracies for the prepared DEMs are suitable for some certain engineering applications but inadequate to meet the standard required for fine/small scale DEM for very precise engineering study. The obtained accuracies for terrain with small height difference can be used for preparing large area cadastral, city planning, or land classification maps. In general, Google Earth elevation data can be used only for investigation and preliminary studies with low cost. It is strongly concluded that the users of Google Earth have to test the accuracy of elevation data by comparing with reference data before using it.
{"title":"Investigation of the Accuracy of Google Earth Elevation Data","authors":"K. El-Ashmawy","doi":"10.1515/arsa-2016-0008","DOIUrl":"https://doi.org/10.1515/arsa-2016-0008","url":null,"abstract":"Abstract Digital Elevation Models (DEMs) comprise valuable source of elevation data required for many engineering applications. Contour lines, slope - aspect maps are part of their many uses. Moreover, DEMs are used often in geographic information systems (GIS), and are the most common basis for digitally-produced relief maps. This paper proposes a method of generating DEM by using Google Earth elevation data which is easier and free. The case study consisted of three different small regions in the northern beach in Egypt. The accuracy of the Google earth derived elevation data are reported using root mean square error (RMSE), mean error (ME) and maximum absolute error (MAE). All these accuracy statistics were computed using the ground coordinates of 200 reference points for each region of the case study. The reference data was collected with total station survey. The results showed that the accuracies for the prepared DEMs are suitable for some certain engineering applications but inadequate to meet the standard required for fine/small scale DEM for very precise engineering study. The obtained accuracies for terrain with small height difference can be used for preparing large area cadastral, city planning, or land classification maps. In general, Google Earth elevation data can be used only for investigation and preliminary studies with low cost. It is strongly concluded that the users of Google Earth have to test the accuracy of elevation data by comparing with reference data before using it.","PeriodicalId":43216,"journal":{"name":"Artificial Satellites-Journal of Planetary Geodesy","volume":"51 1","pages":"89 - 97"},"PeriodicalIF":0.9,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/arsa-2016-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67379643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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