One-Centimeter Orbit Determination for Jason-1: New GPS-Based Strategies

The U.S./French Jason-1 satellite is carrying a state-of-the-art GPS receiver to support precise orbit determination (POD) requirements. The performance of the Jason-1 “BlackJack” GPS receiver was strongly reflected in early POD results from the mission, enabling radial accuracies of 1-2 cm soon after the satellite's 2001 launch. We have made further advances in the GPS-based POD for Jason-1, most notably in describing the phase center variations of the on-board GPS antenna. We have also adopted new geopotential models from the Gravity Recovery and Climate Experiment (GRACE). The new strategies have enabled us to better exploit the unique contributions of the BlackJack GPS tracking data in the POD process. Results of both internal and external (e.g., laser ranging) comparisons indicate that orbit accuracies of 1 cm (radial RMS) are being achieved for Jason-1 using GPS data alone.     

Jason-1 Precision Orbit Determination by Combining SLR and DORIS with GPS Tracking Data

With the implementation of the Jason-1 satellite altimeter mission, the goal of reaching the 1-cm level in orbit accuracy was set. To support the Precision Orbit Determination (POD) requirements, the Jason-1 spacecraft carries receivers for DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) and GPS (Global Positioning System), as well as a retroreflector for SLR (Satellite Laser Ranging). The overall orbit accuracy for Jason will depend on the quality and the relative weighting of the available tracking data. In this study, the relative importance of the SLR, DORIS, and GPS tracking data is assessed along with the most effective parameterization for accounting for the unmodeled accelerations through the application of empirical accelerations. The optimal relative weighting for each type of tracking data was examined. It is demonstrated that GPS tracking alone is capable of supporting a radial orbit accuracy for Jason-1 at the 1-cm level, and that including SLR tracking provides additional benefits. It is also shown that the GRACE (Gravity Recovery and Climate Experiment) gravity model GGM01S provides a significant improvement in the orbit accuracy and reduction in the level of geographically correlated orbit errors.     

Jason-1 Precision Orbit Determination by Combining SLR and DORIS with GPS Tracking Data

With the implementation of the Jason-1 satellite altimeter mission, the goal of reaching the 1-cm level in orbit accuracy was set. To support the Precision Orbit Determination (POD) requirements, the Jason-1 spacecraft carries receivers for DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) and GPS (Global Positioning System), as well as a retroreflector for SLR (Satellite Laser Ranging). The overall orbit accuracy for Jason will depend on the quality and the relative weighting of the available tracking data. In this study, the relative importance of the SLR, DORIS, and GPS tracking data is assessed along with the most effective parameterization for accounting for the unmodeled accelerations through the application of empirical accelerations. The optimal relative weighting for each type of tracking data was examined. It is demonstrated that GPS tracking alone is capable of supporting a radial orbit accuracy for Jason-1 at the 1-cm level, and that including SLR tracking provides additional benefits. It is also shown that the GRACE (Gravity Recovery and Climate Experiment) gravity model GGM01S provides a significant improvement in the orbit accuracy and reduction in the level of geographically correlated orbit errors.     

One-Centimeter Orbit Determination for Jason-1: New GPS-Based Strategies

The U.S./French Jason-1 satellite is carrying a state-of-the-art GPS receiver to support precise orbit determination (POD) requirements. The performance of the Jason-1 “BlackJack” GPS receiver was strongly reflected in early POD results from the mission, enabling radial accuracies of 1–2 cm soon after the satellite's 2001 launch. We have made further advances in the GPS-based POD for Jason-1, most notably in describing the phase center variations of the on-board GPS antenna. We have also adopted new geopotential models from the Gravity Recovery and Climate Experiment (GRACE). The new strategies have enabled us to better exploit the unique contributions of the BlackJack GPS tracking data in the POD process. Results of both internal and external (e.g., laser ranging) comparisons indicate that orbit accuracies of 1 cm (radial RMS) are being achieved for Jason-1 using GPS data alone.     

实时GPS姿态测量中整周模糊度的快速解算方法

姿态测量核心问题是整周模糊度解算.提出了一种适合实时姿态测量的模糊度解算方法,利用单差平滑伪距进行解算,与传统的模糊度解算方法相比具有许多优点.通过仿真实验验证了该方法的有效性和实用性.     

一种优化模糊度搜索方法的研究

对于高精度测量和导航,GPS载波相位整周模糊度的快速求解仍然是一个难点,尤其对于单频接收机。提出一种快速求解整周模糊度的方法,其基本思想采用分步求解,首先应用最小二乘模糊去耦调节法(LAMBDA)搜索出来的模糊度作为初始值,然后应用卫星分组方法降低搜索维数,并应用极大似然准则,构造搜索函数,最后应用最优化原理,搜索出最优的模糊度参数,并从三个方面对其进行检验,即RATIO检验,OVT检验,多项式拟合残差检验。为验证该算法,我们用单频GPS接收机进行了实验,利用本文方法在11 S以内正确确定了模糊度,其基线长误差小于3MM,表明该方法不但可以改进模糊度的搜索速度,而且可以进一步提高其可靠性和成功率。该方法可广泛应用于定向及姿态测量。     

Absolute Calibration of TOPEX/Poseidon and Jason-1 Using GPS Buoys in Bass Strait, Australia

An absolute calibration of the TOPEX/Poseidon (T/P) and Jason-1 altimeters has been undertaken during the dedicated calibration phase of the Jason-1 mission, in Bass Strait, Australia. The present study incorporates several improvements to the earlier calibration methodology used for Bass Strait, namely the use of GPS buoys and the determination of absolute bias in a purely geometrical sense, without the necessity of estimating a marine geoid. This article focuses on technical issues surrounding the GPS buoy methodology for use in altimeter calibration studies. We present absolute bias estimates computed solely from the GPS buoy deployments and derive formal uncertainty estimates for bias calculation from a single overflight at the 40-45 mm level. Estimates of the absolute bias derived from the GPS buoys is -10 ± 19 mm for T/P and +147 ± 21 mm for Jason-1 (MOE orbit) and +131 ± 21 mm for Jason-1 (GPS orbit). Considering the estimated error budget, our bias values are equivalent to other determinations from the dedicated NASA and CNES calibration sites.     

Validation of Jason-1 Nadir Ionosphere TEC Using GEONET

The Jason-1 dual-frequency nadir ionosphere Total Electron Content (TEC) for 10-day cycles 1–67 is validated using absolute TEC measured by Japan's GPS Earth Observation Network (GEONET), or the GEONET Regional Ionosphere Map (RIM). The bias estimates (Jason–RIM) are small and statistically insignificant: 1.62 ± 9 TECu (TEC unit or 10¹⁶ electrons/m², 1 TECu = 2.2 mm delay at Ku-band) and 0.73 ± 0.05 TECu, using the along-track difference and Gaussian distribution method, respectively. The bias estimates are –3.05 ± 10.44 TECu during daytime passes, and 0.02 ± 8.05 TECu during nighttime passes, respectively. When global Jason-1 TEC is compared with the Global Ionosphere Map (GIM) from the Center for Orbit Determination in Europe (or CODE) TEC, the bias (Jason–GIM) estimate is 0.68 ± 1.00 TECu, indicating Jason-1 ionosphere delay at Ku-band is longer than GIM by 3.1 mm, which is at present statistically insignificant. Significant zonal distributions of biases are found when the differences are projected into a sun-fixed geomagnetic reference frame. The observed biases range from –7 TECu (GIM larger by 15.4 mm) in the equatorial region, to +2 TECu in the Arctic region, and to +7 TECu in the Antarctica region, indicating significant geographical variations. This phenomena is primarily attributed to the uneven and poorly distributed global GPS stations particularly over ocean and near polar regions. Finally, when the Jason-1 and TOPEX/Poseidon (T/P) TECs were compared during Jason-1 cycles 1–67 (where cycles 1–21 represent the formation flight with T/P, cycles 22–67 represent the interleave orbits), the estimated bias is 1.42 ± 0.04 TECu. It is concluded that the offset between Jason/TOPEX and GPS (RIM or GIM) TECs is < 4 mm at Ku-band, which at present is negligible.     

The 1-Centimeter Orbit: Jason-1 Precision Orbit Determination Using GPS,SLR, DORIS,and Altimeter Data Special Issue: Jason-1 Calibration/Validation

The Jason-1 radar altimeter satellite, launched on December 7, 2001 is the follow on to the highly successful TOPEX/Poseidon (T/P) mission and will continue the time series of centimeter level ocean topography measurements. Orbit error is a major component in the overall error budget of all altimeter satellite missions. Jason-1 is no exception and has set a 1-cm radial orbit accuracy goal, which represents a factor of two improvement over what is currently being achieved for T/P. The challenge to precision orbit determination (POD) is both achieving the 1-cm radial orbit accuracy and evaluating the performance of the 1-cm orbit. There is reason to hope such an improvement is possible. The early years of T/P showed that GPS tracking data collected by an on-board receiver holds great promise for precise orbit determination. In the years following the T/P launch there have been several enhancements to GPS, improving its POD capability. In addition, Jason-1 carries aboard an enhanced GPS receiver and significantly improved SLR and DORIS tracking systems along with the altimeter itself. In this article we demonstrate the 1-cm radial orbit accuracy goal has been achieved using GPS data alone in a reduced dynamic solution. It is also shown that adding SLR data to the GPS-based solutions improves the orbits even further. In order to assess the performance of these orbits it is necessary to process all of the available tracking data (GPS, SLR, DORIS, and altimeter crossover differences) as either dependent or independent of the orbit solutions. It was also necessary to compute orbit solutions using various combinations of the four available tracking data in order to independently assess the orbit performance. Towards this end, we have greatly improved orbits determined solely from SLR+DORIS data by applying the reduced dynamic solution strategy. In addition, we have computed reduced dynamic orbits based on SLR, DORIS, and crossover data that are a significant improvement over the SLR- and DORIS-based dynamic solutions. These solutions provide the best performing orbits for independent validation of the GPS-based reduced dynamic orbits. The application of the 1-cm orbit will significantly improve the resolution of the altimeter measurement, making possible further strides in radar altimeter remote sensing.     

The Harvest Experiment: Monitoring Jason-1 and TOPEX/POSEIDON from a California Offshore Platform Special Issue: Jason-1 Calibration/Validation

We present calibration results from Jason-1 (2001–) and TOPEX/POSEIDON (1992–) overflights of a California offshore oil platform (Harvest). Data from Harvest indicate that current Jason-1 sea-surface height (SSH) measurements are high by 138 ± 18 mm. Excepting the bias, the high accuracy of the Jason-1 measurements is in evidence from the overflights. In orbit for over 10 years, the T/P measurement system is well calibrated, and the SSH bias is statistically indistinguishable from zero. Also reviewed are over 10 years of geodetic results from the Harvest experiment.     

Monitoring the TOPEX and Jason-1 Microwave Radiometers with GPS and VLBI Wet Zenith Path Delays

Monitoring of altimeter microwave radiometer measurements is necessary in order to identify radiometer drifts or offsets that if uncorrected will introduce systematic errors into ocean height measurements. To examine TOPEX Microwave Radiometer (TMR) and Jason-1 Microwave Radiometer (JMR) behavior, we have used coincident wet zenith delay estimates from Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) geodetic sites near altimeter ground tracks. We derived a TMR path delay drift rate of ?1.1 ± 0.1 mm/yr using GPS data for the period from 1993.0–1999.0 and ?1.2 ± 0.5 mm/yr using VLBI data. Thereafter, the drift appears to have leveled off. Already after 2.3 years (82 cycles) of the Jason-1 mission, it is clear that there have been significant systematic errors in the JMR path delay measurements. From comparison with GPS wet delays, there is an offset of ?5.2 ± 0.6 mm at about cycle 30 and a more abrupt offset of ?11.5 ± 0.8 mm at cycle 69. If we look at the behavior of the JMR coldest brightness temperatures, we see that the offsets near cycle 30 and cycle 69 are mainly caused by corresponding offsets in the 23.8 GHz channel of ?0.49 ± 0.12 K and ?1.18 ± 0.13 K, although there is a small 34.0 GHz offset at cycle 69 of 0.75 ± 0.22 K. Drifts in the 18.0 and 34.0 GHz channels produce a small path delay drift of 0.3 ± 0.5 mm/yr.     

TOPEX/Poseidon and Jason-1: Absolute Calibration in Bass Strait, Australia

Updated absolute calibration results from Bass Strait, Australia, are presented for the TOPEX/Poseidon (T/P) and Jason-1 altimeter missions. Data from an oceanographic mooring array and coastal tide gauge have been used in addition to the previously described episodic GPS buoy deployments. The results represent a significant improvement in absolute bias estimates for the Bass Strait site. The extended methodology has allowed comparison between the altimeter and in situ data on a cycle-by-cycle basis over the duration of the dedicated calibration phase (formation flight period) of the Jason-1 mission. In addition, it has allowed absolute bias results to be extended to include all cycles since the T/P launch, and all Jason-1 data up to cycle 60. Updated estimates and formal 1-sigma uncertainties of the absolute bias computed throughout the formation flight period are 0 ± 14 mm for T/P and +152 + 13 mm for Jason-1 (for the GDR POE orbits). When JPL GPS orbits are used for cycles 1 to 60, the Jason-1 bias estimate is 131 mm, virtually identical to the NASA estimate from the Harvest Platform off California calculated with the GPS orbits and not significantly different to the CNES estimate from Corsica. The inference of geographically correlated errors in the GDR POE orbits (estimated to be approximately 17 mm at Bass Strait) highlights the importance of maintaining globally distributed verification sites and makes it clear that further work is required to improve our understanding of the Jason-1 instrument and algorithm behavior.     

Monitoring the TOPEX and Jason-1 Microwave Radiometers with GPS and VLBI Wet Zenith Path Delays

Monitoring of altimeter microwave radiometer measurements is necessary in order to identify radiometer drifts or offsets that if uncorrected will introduce systematic errors into ocean height measurements. To examine TOPEX Microwave Radiometer (TMR) and Jason-1 Microwave Radiometer (JMR) behavior, we have used coincident wet zenith delay estimates from Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) geodetic sites near altimeter ground tracks. We derived a TMR path delay drift rate of -1.1 ± 0.1 mm/yr using GPS data for the period from 1993.0-1999.0 and -1.2 ± 0.5 mm/yr using VLBI data. Thereafter, the drift appears to have leveled off. Already after 2.3 years (82 cycles) of the Jason-1 mission, it is clear that there have been significant systematic errors in the JMR path delay measurements. From comparison with GPS wet delays, there is an offset of -5.2 ± 0.6 mm at about cycle 30 and a more abrupt offset of -11.5 ± 0.8 mm at cycle 69. If we look at the behavior of the JMR coldest brightness temperatures, we see that the offsets near cycle 30 and cycle 69 are mainly caused by corresponding offsets in the 23.8 GHz channel of -0.49 ± 0.12 K and -1.18 ± 0.13 K, although there is a small 34.0 GHz offset at cycle 69 of 0.75 ± 0.22 K. Drifts in the 18.0 and 34.0 GHz channels produce a small path delay drift of 0.3 ± 0.5 mm/yr.     

The 1-Centimeter Orbit: Jason-1 Precision Orbit Determination Using GPS, SLR, DORIS, and Altimeter Data

The Jason-1 radar altimeter satellite, launched on December 7, 2001 is the follow on to the highly successful TOPEX/Poseidon (T/P) mission and will continue the time series of centimeter level ocean topography measurements. Orbit error is a major component in the overall error budget of all altimeter satellite missions. Jason-1 is no exception and has set a 1-cm radial orbit accuracy goal, which represents a factor of two improvement over what is currently being achieved for T/P. The challenge to precision orbit determination (POD) is both achieving the 1-cm radial orbit accuracy and evaluating the performance of the 1-cm orbit. There is reason to hope such an improvement is possible. The early years of T/P showed that GPS tracking data collected by an on-board receiver holds great promise for precise orbit determination. In the years following the T/P launch there have been several enhancements to GPS, improving its POD capability. In addition, Jason-1 carries aboard an enhanced GPS receiver and significantly improved SLR and DORIS tracking systems along with the altimeter itself. In this article we demonstrate the 1-cm radial orbit accuracy goal has been achieved using GPS data alone in a reduced dynamic solution. It is also shown that adding SLR data to the GPS-based solutions improves the orbits even further. In order to assess the performance of these orbits it is necessary to process all of the available tracking data (GPS, SLR, DORIS, and altimeter crossover differences) as either dependent or independent of the orbit solutions. It was also necessary to compute orbit solutions using various combinations of the four available tracking data in order to independently assess the orbit performance. Towards this end, we have greatly improved orbits determined solely from SLR+DORIS data by applying the reduced dynamic solution strategy. In addition, we have computed reduced dynamic orbits based on SLR, DORIS, and crossover data that are a significant improvement over the SLR- and DORIS-based dynamic solutions. These solutions provide the best performing orbits for independent validation of the GPS-based reduced dynamic orbits. The application of the 1-cm orbit will significantly improve the resolution of the altimeter measurement, making possible further strides in radar altimeter remote sensing.     

Ambiguity Recovery Using the Triple-Differenced Carrier Phase Type Approach for Long-Range GPS Kinematic Positioning

Precise, long-range GPS kinematic positioning to centimeter accuracy requires that carrier phase ambiguities be resolved correctly during an initialization period, and subsequently to recover the “lost" ambiguities in the event of a cycle slip. Furthermore, to maximize navigational efficiency, ambiguity resolution and carrier phase-based positioning need to be carried out in real-time. Due to the presence of the ionospheric signal delay, satellite orbit errors, and the tropospheric delay, so-called absolute ambiguity resolution “on-the-fly” for long-range applications becomes very difficult, and largely impossible. However, all of these errors exhibit a high degree of spatial and temporal correlation. In the case of short-range ambiguity resolution, because of the high spatial correlation, their effect can be neglected, but their influence will dramatically increase as the baseline length increases. On the other hand, between discrete trajectory epochs, they will still exhibit a large degree of similarity for short time spans. In this article, a method is described in which similar triple-differenced observables formed between one epoch with unknown ambiguities and another epoch with fixed ambiguities can be used to derive relative ambiguity values, which are ordinarily equal to zero (or to the number of cycles that have slipped when loss-of-lock occurred). Because of the temporal correlation characteristics of the error sources, the cycle slips can be recovered using the proposed methodology. In order to test the performance of this algorithm an experiment involving the precise positioning of an aircraft, over distances ranging from a few hundred meters up to 700 kilometres, was carried out. The results indicate that the proposed technique can successfully resolve relative ambiguities (or cycle slips) over long distances in an efficient manner that can be implemented in real-time.     

Ambiguity Recovery Using the Triple-Differenced Carrier Phase Type Approach for Long-Range GPS Kinematic Positioning

Precise, long-range GPS kinematic positioning to centimeter accuracy requires that carrier phase ambiguities be resolved correctly during an initialization period, and subsequently to recover the “lost" ambiguities in the event of a cycle slip. Furthermore, to maximize navigational efficiency, ambiguity resolution and carrier phase-based positioning need to be carried out in real-time. Due to the presence of the ionospheric signal delay, satellite orbit errors, and the tropospheric delay, so-called absolute ambiguity resolution “on-the-fly” for long-range applications becomes very difficult, and largely impossible. However, all of these errors exhibit a high degree of spatial and temporal correlation. In the case of short-range ambiguity resolution, because of the high spatial correlation, their effect can be neglected, but their influence will dramatically increase as the baseline length increases. On the other hand, between discrete trajectory epochs, they will still exhibit a large degree of similarity for short time spans. In this article, a method is described in which similar triple-differenced observables formed between one epoch with unknown ambiguities and another epoch with fixed ambiguities can be used to derive relative ambiguity values, which are ordinarily equal to zero (or to the number of cycles that have slipped when loss-of-lock occurred). Because of the temporal correlation characteristics of the error sources, the cycle slips can be recovered using the proposed methodology. In order to test the performance of this algorithm an experiment involving the precise positioning of an aircraft, over distances ranging from a few hundred meters up to 700 kilometres, was carried out. The results indicate that the proposed technique can successfully resolve relative ambiguities (or cycle slips) over long distances in an efficient manner that can be implemented in real-time.     

基于GPS数据的CHAMP卫星简化动力法轨道确定

利用CHAMP卫星星载GPS实测数据,通过非差简化动力学定轨的方法,计算了CHAMP卫星2008年3月3日～10日的轨道,并以GFZ的快速轨道作为参考标准,评价了本文简化动力法轨道精度.结果表明,CHAMP卫星非差简化动力学轨道1D位置精度可达到7cm,1D的速度精度可达到0.1mm/s.     

The GAVDOS Mean Sea Level and Altimeter Calibration Facility: Results for Jason-1

The location of the GAVDOS facility is under a crossing point of the original ground-tracks of TOPEX/Poseidon and the present ones for Jason-1, and adjacent to an ENVISAT pass, about 50 km south of Crete, Greece. Ground observations and altimetry comparisons over cycles 70 to 90, indicate that a preliminary estimate of the absolute measurement bias for the Jason-1 altimeter is 144.7 ± 15 mm. Comparison of Jason microwave radiometer data from cycles 37 and 62, with locally collected water vapor radiometer and solar spectrometer observations indicate a 1–2 mm agreement.     

Improving the Jason-1 Ground Retracking to Better Account for Attitude Effects

After two years of verification and validation activities of the Jason-1 altimeter data, it appears that all the mission specifications are completely fulfilled. Performances of all instruments embarked onboard the platform meet all the requirements of the mission. However, the star tracker system has shown some occasional abnormal behavior leading to mispointing angles out of the range of Jason-1 system specification which states that the altimeter antenna shall be pointed to the nadir direction with an accuracy below 0.2 degree (3 sigma). This article discusses the platform attitude angle and its consequences on the altimetric estimates. We propose improvements of the Jason-1 retracking process to better account for attitude effects.

The first star tracker anomalies for the Jason-1 mission were detected in April 2002. The Poseidon-2 algorithms were specified assuming an antenna off-nadir angle smaller than 0.3 degree. For higher values, the current method to estimate the ocean parameters is known to be inaccurate. Thus, the algorithm has to be reviewed, and more specifically, the present altimeter echo model has to be modified to meet the desired instrument performance.

Therefore, we derive a second order analytical model of the altimeter echo to take into account attitude angles up to 0.8 degree, and consequently, we adapt the retracking algorithm. This new model is tested on theoretical simulated data using a maximum likelihood estimation. Biases and noise performance characteristics are computed for the different estimated parameters. They are compared to the ones obtained with the current algorithm. This new method provides highly improved estimations for high attitude angles. It is statistically validated on real data by applying it on several cycles of Poseidon-2 raw measurements. The results are found to be consistent with those obtained from simulations. They also fully agree with the TOPEX estimates when flying along the same ground track. Finally, the estimates are also in agreement with the ones available in the current I/GDR (Intermediate Geophysical Data Record) products when mispointing lies in the mission specifications.     

Improving the Jason-1 Ground Retracking to Better Account for Attitude Effects

After two years of verification and validation activities of the Jason-1 altimeter data, it appears that all the mission specifications are completely fulfilled. Performances of all instruments embarked onboard the platform meet all the requirements of the mission. However, the star tracker system has shown some occasional abnormal behavior leading to mispointing angles out of the range of Jason-1 system specification which states that the altimeter antenna shall be pointed to the nadir direction with an accuracy below 0.2 degree (3 sigma). This article discusses the platform attitude angle and its consequences on the altimetric estimates. We propose improvements of the Jason-1 retracking process to better account for attitude effects.

The first star tracker anomalies for the Jason-1 mission were detected in April 2002. The Poseidon-2 algorithms were specified assuming an antenna off-nadir angle smaller than 0.3 degree. For higher values, the current method to estimate the ocean parameters is known to be inaccurate. Thus, the algorithm has to be reviewed, and more specifically, the present altimeter echo model has to be modified to meet the desired instrument performance.

Therefore, we derive a second order analytical model of the altimeter echo to take into account attitude angles up to 0.8 degree, and consequently, we adapt the retracking algorithm. This new model is tested on theoretical simulated data using a maximum likelihood estimation. Biases and noise performance characteristics are computed for the different estimated parameters. They are compared to the ones obtained with the current algorithm. This new method provides highly improved estimations for high attitude angles. It is statistically validated on real data by applying it on several cycles of Poseidon-2 raw measurements. The results are found to be consistent with those obtained from simulations. They also fully agree with the TOPEX estimates when flying along the same ground track. Finally, the estimates are also in agreement with the ones available in the current I/GDR (Intermediate Geophysical Data Record) products when mispointing lies in the mission specifications.