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Sea surface height (SSH), a measurement widely used in marine science, can be used to compute the marine gravity field while providing underlying information on the ocean current, tide, and...

A gravity sensor onboard an aircraft always measures the sum of all accelerations acting on it. To separate the accelerations caused by the movement of the aircraft from the total measured acceleration, the movement, including position, velocity and acceleration of the aircraft, must be measured independently. Nowadays, this is possible using GNSS. Obviously, this means that the kinematic acceleration must be measured or derived from GNSS measurements as accurately as the intended gravity survey. Compared to the traditional airborne gravimetry, the determination of positions and velocities from GNSS is a big challenge for the special HALO and similar jet aircrafts, which are characterized by high-altitude and long-range flying capabilities. A strategy of integrated GNSS Doppler velocity determination based on a combination of robust estimation and Helmert’s Variance Components Estimation (VCE) is proposed in this study to fulfill the requirements for such an aircraft. This strategy is tested by processing GNSS Doppler data recorded onboard the HALO aircraft. The velocity obtained has been applied in the data processing of the GEOHALO airborne gravimetry campaign of 2012. The results show that the proposed strategy improves GNSS Doppler velocity determination accuracy and allows the subtraction of the kinematic vertical accelerations from the GEOHALO airborne gravimetry records., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

The high-precision navigation and positioning with GNSS has become widely used in various applications with the development of new GNSS systems, such as BeiDou and Galileo. For marine applications, high-precision navigation and positioning with GNSS is still a challenge since the requirement of the communication link is a problem on sea. Both DGNSS and RTK require data communication between base station on land and the rover station on sea. The data communication can be performed by providers of the marine satellite communication service, such as Intelsat, Eutelsat, Telesat and the SpaceX. However, the cost is too high to be afforded by ordinary GNSS users. The BeiDou short-message service provides an efficient way for the data communication between reference station on land and rover station on sea. Each BeiDou message length is limited to 78 bytes, and the communication frequency is limited to 60 s. Based on the BeiDou short-message service, the high-precision positioning has been achieved in previous studies. However, multiple set of short-message devices are used and the cost is still high. In this research, based on dual-frequency GNSS data, we propose the high-precision navigation on sea with single set of short-message device. The space-relative and time-relative positioning methods are integrated to reduce the data requirements. That is, first, every minute precise position is acquired with traditional space-relative positioning method and then the position of the other epochs is derived with time-relative positioning method. The experimental results based on buoy observations on sea show that the navigation accuracy can reach up to cm level in both horizontal and vertical directions. The proposed method can meet the requirements of different marine applications such as tide monitoring and wave monitoring.

There are two important aspects in optimally processing the acoustic measurements: the establishment of the functional model and the refinement of the associated stochastic model. In most cases the functional model may be sufficiently well-established, but the stochastic model error has not received considerable attention and it still remains a challenging research topic in real-time positioning. The equal weight stochastic model (EWSM) commonly used at present is under the assumption of equal-precision observation, which is imprecise and not coincident with reality. The purpose of this paper is to develop an approach to obtaining more accurate weights of observables by real-time estimating the variance of observations. The inaccurate stochastic model effect is analyzed and the real time stochastic model (RTSM) estimated by using the least squares residual of observations is presented to improve the positioning accuracy. Simulation results have shown that the underwater positioning accuracy goes from 0.173 m to 0.157 m based on GPS Intelligent Buoy (GIB) by employing the real time stochastic model, while that can be improved from 0.426 m to 0.306 m based on surveying vessel (SV) when adopting RTSM. Both simulations based on GIB and SV indicate that real-time stochastic model can perform better than conventional equal weight stochastic model in positioning accuracy.

Shipborne gravimetry is an essential method to measure the Earth’s gravity field in the coastal and offshore areas. It has the special advantages of high-accuracy and high-resolution measurements in coastal areas compared to other techniques (e.g., satellite gravimetry, airborne gravimetry, and altimetry) used to obtain information about the gravity field. In this paper, we present the data processing strategies of shipborne gravimetry in GFZ. One key point is that the most suitable filter parameters to eliminate disturbing accelerations are determined by studying the GNSS-derived kinematic vertical accelerations and the measurement differences at crossover points. Apart from that, two crucial issues impacting on shipborne gravimetry are the seiches in some harbors and the squat effect in the shallow water. We identified that inclusion of GNSS-derived kinematic vertical accelerations can help to improve the shipborne gravimetry results at these special cases in the Baltic Sea. In the absence of the GNSS-derived vertical accelerations, the cutoff wavelength of the low-pass filter should be large enough to filter out these disturbing acceleration signals which causes a coarser spatial resolution of the gravity measurements. Therefore, the GNSS-derived kinematic vertical accelerations are very useful for optimum shipborne gravimetry. Finally, our shipborne gravimetry measurements are successfully used to verify the previous gravimetry data and improve the current geoid models in the Baltic Sea.

Real-time precise point positioning (RTPPP) is a popular positioning method that uses a real-time service (RTS) product to mitigate various Global Navigation Satellite Systems (GNSS) errors. However, communication links are not available in the ocean. The use of a communication satellite for data transmission is so expensive that normal users could not afford it. The BeiDou short-message service provides an efficient option for data transmission at sea, with an annual fee of approximately 160 USD. To perform RTPPP using BeiDou short messages, the following two challenges should be appropriately addressed: the maximum size of each BeiDou message is 78 bytes, and the communication frequency is limited to once a minute. We simplify the content of RTS data to minimize the required bandwidth. Moreover, the orbit and clock corrections are predicted based on minute-interval RTS orbital and clock corrections. An experiment was conducted to test the performance of the proposed method. The numerical results show that the three-dimensional positioning precision can reach approximately 0.4 m with combined GPS + GLONASS and approximately 0.2 m with combined GPS + GLONASS + Galileo + BeiDou.

An accurate observation model and statistical model are critical in underwater integrated navigation. However, it is often the case that the statistical characteristics of noise are unknown through the ultra-short baseline (USBL) system/Doppler velocity log (DVL) integrated navigation in the deep-sea. Additionally, the velocity of underwater vehicles relative to the bottom of the sea or the currents is commonly provided by the DVL, and an adaptive filtering solution is needed to correctly estimate the velocity with unknown currents. This paper focuses on the estimation of unknown currents and measurement noise covariance for an underwater vehicle based on the USBL, DVL, and a pressure gauge (PG), and proposes a novel unbiased adaptive two-stage information filter (ATSIF) for the underwater vehicle (UV) with an unknown time-varying currents velocity. In the proposed algorithm, the adaptive filter is decomposed into a standard information filter and an unknown currents velocity information filter with interconnections, and the time-varying unknown ocean currents and measurement noise covariance are estimated. The simulation and experimental results illustrate that the proposed algorithm can make full use of high-precision observation information and has better robustness and navigation accuracy to deal with time-varying currents and measurement outliers than existing state-of-the-art algorithms.

Global navigation satellite systems (GNSS) can attain centimeter level positioning accuracy, which is conventionally provided by real-time precise point positioning (PPP) and real-time kinematic (RTK) techniques. Corrections from the data center or the reference stations are required in these techniques to reduce various GNSS errors. The time-relative positioning approach differs from the traditional PPP and RTK in the sense that it does not require external real-time corrections. It computes the differences in positions of a single receiver at different epochs using phase observations. As the code observations are not used in this approach, its performance is not affected by the noise and multipath of code observations. High reliability is another advantage of time-relative precise positioning because the ambiguity resolution is not needed in this approach. Since the data link is not required in the method, this approach has been widely used in remote areas where wireless data link is not available. The main limitation of time-relative positioning is that its accuracy degrades over time between epochs because of the temporal variation of various errors. The application of the approach is usually limited to be within a time interval of less than 20 min. The purpose of this study was to increase the time interval of time-relative positioning and to extend the use of this method to applications with a longer time requirement, especially in remote areas without wireless communication. In this paper, the main error sources of the time-relative method are first analyzed in detail, and then the approach to improve the accumulated time relative positioning method is proposed. The performance of the proposed method is assessed using both static and dynamic observations with a duration as long as several hours. The experiments presented in this paper show that, among the four scenarios tested (i.e., GPS, GPS/Galileo, GPS/Galileo/BeiDou, and GPS/Galileo/BeiDou/GLONASS), GPS/Galileo/BeiDou performed best and GPS/Galileo/BeiDou/GLONASS performed worst. The maximum positioning errors were mostly within 0.5 m in the horizontal direction, even after three hours with GPS/Galileo/BeiDou. It is expected that the method could be used for positioning and navigation for as long as several hours with decimeter level horizontal accuracy in remote areas without wireless communication.

Real-time precise point positioning (PPP) based on open-access real-time service (RTS) of the international GNSS service (IGS) has attracted increasing attention in recent years. For offshore applications, the receiving of RTS corrections becomes a major obstacle due to lack of internet-based infrastructures. Short-message communication (SMC) is a particular technique of BeiDou navigation satellite system (BDS), which can provide bidirectional communication between users in a cost-effective way. However, the limited bandwidth and frequency of BDS SMC make it impossible to directly broadcast IGS RTS corrections with BDS SMC. An offshore real-time PPP technique is proposed based on IGS RTS corrections with a single set of BDS SMC devices for communication. RTS orbit corrections in the along-track, cross-track and radial directions, the clock correction and the code bias correction of each satellite are together converted into an equivalent range correction on the basis of user approximate position and will-be-used code observation types. The range corrections within 1 min are fitted into a first-order polynomial. Only the range and range-rate corrections at the reference time are broadcast with BDS SMC. In addition, different from broadcasting corrections of all satellites in the IGS RTS, corrections of only visible satellites are encoded into a BDS SMC correction message to further reduce the data size. The encoding strategy of BDS SMC correction message and a detailed procedure of the offshore real-time PPP technique are presented. The land-simulated and offshore experiment results show that the proposed technique can meet the demands of high-precision offshore applications.

In the application of GNSS in the velocity determination, it is often the case that some GNSS receivers give an opposite sign for the raw Doppler observations which do not correspond to the real Doppler shift. This is caused by different methods of the GNSS signal processing in different GNSS receivers. If the velocities of kinematic platforms are calculated by using raw Doppler observations from the GNSS receiver directly, the directions of the estimated velocities may be reversed, and the value of the velocity is wrong with respect to the actual movement. This would lead to incorrect results, and unacceptable for research and applications. To overcome this problem, a new method of sign correction for raw Doppler observations is proposed in this study. This algorithm constructs a correction function based on the GNSS carrier-phase-derived Doppler observations. To test this approach, GNSS data of GEOHALO airborne gravimetric missions have been used. The results show that the proposed method, which is straightforward and practical, can produce the correct velocity for a kinematic platform in any case, independent of the internal hardware structure and the specific way of the signal processing of the GNSS receivers in question.

Objective: To study the effect of knee arthroscopy combined with Liuwei Gubi Pill on degenerative meniscus injury in middle-aged and elderly patients. Methods: A total of 92 middle-aged and elderly patients with degenerative meniscus injury who were treated in our hospital from August 2018 to February 2020 were collected. They were divided into two groups by envelope lottery. Knee arthroscopy was used for the reference group of 46 patients, and they were guided to perform joint function exercises after surgery; 46 patients in the experimental group took Liuwei Gubi Pill on the basis of the reference group, and compared the efficacy of the two groups. Results: The total effective rate of treatment in the experimental group was 97.83%, which was higher than the reference group’s 84.78%. The experimental group’s VAS score at 1st month, 2nd month, and 3rd month after surgery was lower than that in the reference group. The Lysholm score of the experimental group at 1st month, 2nd month, and 3rd month after operation was significantly higher than that of the reference group, and the data of the two groups was compared by PConclusion: The treatment of middle-aged and elderly patients with degenerative meniscus injury by knee arthroscopy combined with Liuwei Gubi Pill has an ideal effect, which can alleviate postoperative pain and benefit the recovery of knee function.

Traditionally, if full ambiguity resolution is not successful, partial ambiguity resolution (PAR) will be tried. However, identifying which subset of ambiguities to fix is not easy and is still an ...

Conventional relative kinematic positioning is difficult to be applied in the polar region of Earth since there is a very sparse distribution of reference stations, while precise point positioning (PPP), using data of a stand-alone receiver, is recognized as a promising tool for obtaining reliable and accurate trajectories of moving platforms. However, PPP and its integer ambiguity fixing performance could be much degraded by satellite orbits and clocks of poor quality, such as those of the geostationary Earth orbit (GEO) satellites of the BeiDou navigation satellite system (BDS), because temporal variation of orbit errors cannot be fully absorbed by ambiguities. To overcome such problems, a network-based processing, referred to as precise orbit positioning (POP), in which the satellite clock offsets are estimated with fixed precise orbits, is implemented in this study. The POP approach is validated in comparison with PPP in terms of integer ambiguity fixing and trajectory accuracy. In a simulation test, multi-GNSS (global navigation satellite system) observations over 14 days from 136 globally distributed MGEX (the multi-GNSS Experiment) receivers are used and four of them on the coast of Antarctica are processed in kinematic mode as moving stations. The results show that POP can improve the ambiguity fixing of all system combinations and significant improvement is found in the solution with BDS, since its large orbit errors are reduced in an integrated adjustment with satellite clock offsets. The four-system GPS+GLONASS+Galileo+BDS (GREC) fixed solution enables the highest 3D position accuracy of about 3.0 cm compared to 4.3 cm of the GPS-only solution. Through a real flight experiment over Antarctica, it is also confirmed that POP ambiguity fixing performs better and thus can considerably speed up (re-)convergence and reduce most of the fluctuations in PPP solutions, since the continuous tracking time is short compared to that in other regions.

Accurate position, velocity, and acceleration information are critical for airborne gravimetry. In Antarctica, there is a sparse distribution of IGS stations, and the rough terrain makes it impractical to set up nearby reference stations. Therefore, traditional differential GPS techniques may be difficult to implement. Precise point positioning (PPP) is independent of reference stations and provides an unlimited operating distance. However, it is highly dependent on precise satellite orbit and clock information, and may be vulnerable to discontinuities of orbit or clock offsets. An extended PPP method, called precise orbit positioning (POP), is implemented towards multi-GNSS. This approach introduces a widely spaced network of stations and is independent of precise clock information, as it estimates satellite clock offsets and drifts "on-the-fly" and only relies on precise orbit information. The advantage of being independent of clock information is that the IGS ultra-rapid (predicted) products can be applied to real-time POP since the orbits can achieve an accuracy of about 5 cm. This becomes significant when applied to airborne gravimetry, as gravity results calculated from gravity measurements and GNSS solutions can be investigated in real time. By means of processing of 5 IGS stations over Antarctica, it turns out that the PPP solution is greatly affected by discontinuities of the IGS orbit and clock offsets at the day boundaries, accompanied with some biases as large as several decimeters in the vertical component. However, the POP solution remains robust and almost no large positioning errors appear, and the accuracy improves by about 50% in the north, east, and up coordinate components. The aircraft positions derived from relative positioning, PPP, and POP during the kinematic flight period generally agree at the decimeter level because of the lack of observed satellites with elevation angles higher than 60°. Nevertheless, the potential for POP to generate centimeter-level kinematic vertical positions over long baselines is illustrated. Moreover, the POP and double-difference derived velocities and accelerations agree with each other well in both static and kinematic flight periods. After a low-pass filter, the GNSS-based accelerations are of the order of 1 mgal and are considered useful for separating the disturbing kinematic accelerations from the gravity measurements.

A conventional Differential GPS (DGPS) techniques-based velocity and acceleration method (named here as ‘DVA’) may be difficult to implement in the Antarctic as there is a sparse distribution of reference stations over Antarctica. Thus, in order to overcome the baseline limitations and to obtain highly accurate and reliable velocity and acceleration estimates for airborne gravimetry, a network-based velocity and acceleration determination approach (named here as ‘NVA’), which introduces a wide network of stations and is independent of precise clock information, is applied. Here its performance for velocity and acceleration determination is fully exploited by using Global Positioning System (GPS), GLONASS, Galileo and BeiDou observations. Additionally, a standalone receiver-based method named ‘SVA’, which requires precise clock information, is also implemented for comparison. During static tests and a flight experiment over Antarctica, it was found that the NVA method yields more robust results than the SVA and DVA methods when applied to a wide area network. Moreover, the addition of GLONASS, Galileo and BeiDou systems can increase the accuracy of velocity and acceleration estimates by 39% and 43% with NVA compared to a GPS-only solution.

Objective: To study and analyze the effect of traditional Chinese medicine orthopedic rehabilitation therapy on senile osteoarthritis from the analysis of big data. METHODS: Seventy elderly patients with osteoarthritis admitted to our hospital from March 2015 to March 2017 were enrolled. The grouping method is a random number table method, which is divided into an experimental group and a reference group, each of which is 35 cases. The patients in the reference group were treated with nimesulide orally, and the patients in the experimental group were treated with traditional Chinese medicine orthopedics. The clinical effects of the two groups were compared. RESULTS: The effective rate of treatment in the experimental group (97.14%) was significantly higher than that in the reference group (82.86%). The difference between the two groups was statistically significant (P

Global navigation satellite system/acoustic (GNSS/A) underwater positioning technique has drawn increasing attention in the fields of marine scientific research and engineering application. The conventional positioning strategy of GNSS/A is to fix the positions of sea-surface transducer, in other words, the positions of the transducer determined by GNSS positioning at different epochs are regarded as accurate and unbiased, and then estimate the underwater transponder's coordinate with acoustic ranging data. However, there inevitably exists bias in the estimation of transducer's positions, and the precision varies at different epochs. Ignoring precision differences of the transducer's positions will lead to a worse estimation of the transponder's coordinate. In this contribution, we propose a total adjustment (TA) method, where the positions of both sea-surface transducer and seafloor transponder are treated as unknown parameters, and the transducer's positions determined by GNSS positioning at different epochs are introduced as virtual observations. In order to reduce the computation load caused by large increase of estimation parameters, an equivalent transformation is applied to observation equations to remove estimation parameters for the transducer's positions at different epochs. To evaluate the performance of the proposed total adjustment method, a series of simulation tests and a sea-trail experiment were carried out. Testing results show that, as compared with the traditional method, the positioning accuracy with the proposed method can be improved by about 10%–33% in the simulation tests and 15% in the field test.

Underwater Towed Vehicle navigation and localization in deep sea environments are particularly challenging without high-precision inertial sensors. In this paper, the multi-sensors navigation fusion method of a towed underwater vehicle based on the ultrashort baseline (USBL) system, Doppler velocity log (DVL) and a pressure gauge in the deep sea is investigated. Combined with GPS real-time tide detection technology, the positioning principle of the USBL based on the depth constraint is given, and a straight-line model be proposed to estimate the position of the vehicle used the average heading when underwater towed vehicle is working normally in deep sea without DVL. The interacting multiple model (IMM) algorithm based on smoothing algorithm is proposed to improve the positioning accuracy in the deep sea, and the nonlinearity of the model, precision and stability of filtering are considered simultaneously using the adaptive robust square root cubature Kalman filter. The results of the simulated and practical experiments at 4800 m verify that the new algorithm can take full use of high-precision observation information and greatly improve the positioning accuracy and robustness of a deep sea underwater towed system.

Objective: To explore the clinical intervention effect of applying Huoxue Jiangu Decoction in the treatment of patients with osteoarthritis. Methods: Research work was carried out in our hospital from December 2018 to December 2019. A total of 100 patients with osteoarthritis received treatment during this period were selected and divided into two groups using random number method. One group was given sodium hyaluronate injection for treatment, which was the control group, and the other group was given Huoxuejiangu Decoction combined with sodium hyaluronate injection, which was the experimental group. The clinical treatment of the two groups of patients was compared and analyzed. Results: The patients' pain levels were compared. There was no significant difference between the groups before the intervention treatment. After treatment, the experimental group score was (3.05±0.55), which was lower than the control group, the improvement effect was more significant, and the difference between the groups was significant (P< 0.05), the experimental group had a better effect. The clinical treatment of the two groups of patients was compared and analyzed. There was no significant difference in the WOMAS index between the two groups before treatment. After treatment, the score of the experimental group was (34.33±6.98), and the improvement rate was (37.45±13.22). After treatment, the score was lower and the improvement rate was higher, which was significantly higher than the control group (P Conclusion: For the patients with osteoarthritis, the application of Huoxue Jiangu Decoction has a significant clinical effect, which can reduce the patient's pain level, improve the patient's clinical symptoms, have high clinical value, and it can be promoted.

Information on trajectory and attitude is essential for analyzing gravimetric data collected on kinematic platforms. Usually, a Kalman filter is used to obtain high-accuracy positional and velocity information. However, this can be affected by measurement outliers and by state disturbances that occur frequently under a fast-changing environment. To overcome these problems, a robust adaptive Kalman filtering algorithm is applied for state estimates, which introduces an equivalent weight to resist measurement outliers and an optimal adaptive factor to balance the contributions of the kinematic model information and the measurements. In addition to the conventional robust estimator, an improved Current Statistical (CS) model is proposed. The improved CS model adopts a variance adaptive learning algorithm, and it can perform self-adaptation of acceleration variance with the innovation information; thus, it can overcome the shortcoming of lower tracking accuracy and avoid setting the maximum acceleration. Following a gravimetry campaign on the Baltic Sea, it is shown in theory and in practice that the robust adaptive Kalman filter is not only simple in its calculation but also more reliable in controlling the colored observation noise and kinematic state disturbance compared with the classical Kalman filter. The improved CS model performs best, especially when analyzing the positioning errors at the turns due to the target maneuvering. Compared to the CS model, the RMS values of the positional estimates derived from the improved CS model decrease by almost 30% in the horizontal direction, and no significant improvement in the vertical direction is found.

GEOHALO is a joint experiment of several German institutes for atmospheric research and earth observation where exploring airborne gravimetry over Italy using the High Altitude and LOng Range (HALO) aircraft data is one of the major goals. The kinematic positioning of the aircraft, on which all remote sensing instruments are located, by Global Navigation Satellite System (GNSS) is affected by the characteristics of long-distance, long-time duration, and high-platform dynamics which are a key factor for the success of the GEOHALO project. We outline the strategy and method of GNSS data processing which takes into account multiple GNSS systems (GPS and GLONASS), multiple static reference stations including stations from the International GNSS Service (IGS) and the EUropean REFerence network (EUREF), multiple GNSS-receiving equipments mounted on the kinematic platform, geometric relations between multiple antennas, and assumptions of similar characteristic of atmospheric effects within a small area above the aircraft. From this precondition, various data processing methods for kinematic positioning have been developed, applied and compared. It is shown that the proposed method based on multiple reference stations and multiple kinematic stations with a common atmospheric delay parameter can effectively improve the reliability and accuracy of GNSS kinematic positioning.

Airborne gravimetry is a crucial method to improve our knowledge about the Earth gravity field, especially in hard-to-access regions. Generally, the accuracy of airborne gravimetry is several milligals, which is suitable for filling the so-called polar gaps in satellite-derived global gravity field models. Here some investigations based on airborne gravity measurements from the GEOHALO mission over Italy are presented. To subtract the vertical accelerations from the values measured by the gravimeter, four different versions of kinematic accelerations were derived from Global Navigation Satellite Systems (GNSS) recordings. To remove the high-frequency noise, a low-pass filter with a cutoff wavelength of 200 s was applied to both Chekan-AM measurements and kinematic accelerations from GNSS. To investigate how future airborne gravity campaigns could be designed, a dedicated flight track was repeated two times showing that the equipment worked well also at higher altitude and speed. From the final best results follows an RMS of gravity differences at crossover points of 1.4 mGal, which, according to the law of error propagation, implies the accuracy of a single measurement to be 1.4/2≈1 mGal. To demonstrate how a satellite-only gravity field model can be improved by airborne measurements, a gravity field model for the GEOHALO region has been computed. To compute also an improved regional geoid model, the point mass modeling (PMM) and the remove-compute-restore (RCR) technique, using a recent satellite-only model and residual terrain modeling (RTM), were applied. Finally, GNSS/leveling points have been used to check the quality of the regional point mass model.

Satellite deficiency degrades the performance of GPS single point positioning (SPP) in city urban areas. If the number of observed satellites is smaller than that of the unknown independent parameters in the data processing, extended Kalman filter (EKF) methods will usually be employed to transit the variable values epoch by epoch. In this case, the prediction model in EKF is very important for the positioning results. This paper focuses on the receiver clock offset models in the prediction equation. The investigation shows that, the clock offset model with clock shift is able to improve the accuracy of the clock offset prediction for internal crystal clocks within a short time span, compared with the clock offset model without clock shift. Besides, in order to further improve the performance of positioning in the case of satellite deficiency, an adaptive EKF is developed to enhance the clock prediction. The experiments show that this approach can improve the positioning accuracy in the scenarios that only fewer satellites are available.

An efficient method for gravity field determination from CHAMP orbits and accelerometer data is referred to as the energy balance approach. A new CHAMP gravity field recovery strategy based on the improved energy balance approach is developed in this paper. The method simultaneously solves the spherical harmonic coefficients, daily integration constant, scale and bias parameters. Two 60 degree and order gravitational potential models, XISM-CHAMP01S from the classical energy balance approach, and XISM-CHAMP02S from the improved energy balance, are determined using about one year’s worth of CHAMP kinematic orbits from TUM and accelerometer data from GFZ. Comparisons among XISM-CHAMP01S, XISM-CHAMP02S, EIGEN-CG03C, EIGEN-CHAMP03S, EIGEN2, ENIGN1S and EGM96 are made. The results show that the XISM-CHAMP02S model is more accurate than EGM96, EIGEN1S, EIGEN2 and XISM-CHAMP01S at the same degree and order, and has almost the same accuracy as EIGEN-CHAMP03S.

Sea surface topography observations are deduced from an airborne reflectometry experiment. A GNSS (Global Navigation Satellite System) receiver dedicated for reflectometry was set up aboard the German HALO (High Altitude Long Range) research aircraft. Flights were conducted over the Mediterranean Sea about 3500 m above sea level. A signal path model divided into large- and small-scale contributions is used for phase altimetry. The results depict geoid undulations and resolve anomalies of the sea surface topography. For the whole experiment 65 tracks over the Mediterranean Sea are retrieved and compared with a topography model. Tracks differ between right-handed and left-handed circular polarization. The difference, however, is not significant for this study. Precision and spatial resolution decrease disproportionately at low elevations. Eight tracks with centimeter precision are obtained between 11° and 33° of elevation. At higher elevation angles the number of tracks is significantly reduced due to surface roughness. In future such retrievals could contribute to ocean eddy detection.

A two-way adaptive Kalman filter is proposed by combining a two-way filter with an adaptive filter for orbit determination of a maneuvered GEO satellite. A method of using Newton’s high-resolution differential formula and polynomial fitting for modeling the thrust force of a maneuvered GEO satellite is developed. The adaptive factor, which balances the contributions of the measurements and the dynamic model information, is determined by using a two-segment function and predicted residual statistics. Simulations with a maneuvered GEO satellite tracked by the Chinese ground tracking network were conducted to verify the performance of the proposed orbit determination technique and the method of thrust force modeling. The results show that refining the thrust force model is beneficial for the orbit determination of a maneuvered GEO satellite; the two-way adaptive Kalman filter can efficiently control the influence of the dynamic model errors on the orbit state estimate.