Spaceborne Global Positioning System Receiver Research Articles

Application of adaptive EKF in real-time orbit determination

High-precision orbits are essential for low Earth orbit (LEO) satellite applications. Instead of determinating orbit by the ground monitoring stations, LEO missions are trending to incorporate spaceborne global positioning system receivers for autonomous navigation. Focusing on this issue, we propose a method of real-time orbit determination based on ionosphere combination observation of dual-frequency data using adaptive extended Kalman filter (AEKF). The traditional Kalman filter heavily relies on the initial values of measurement and process noise covariance matrix. However, the environment of the satellite is time-variant, and it is hard to keep the error covariance matrix in the optimal condition all the time. To overcome this disadvantage, the Sage–Husa Kalman filter is introduced. The performance of the proposed algorithm is compared with the conventional EKF, and the results show that the proposed method can guarantee the precision and stability of orbit determination. With the proposed algorithms, we developed a software to solve the orbit suitable for one-day Gravity Recovery and Climate Experiment (GRACE) observations. The obtained results show that the accuracy of orbit determination error is improved with unknown Kalman process noise compared with traditional method. Additionally, the performances of AEKF for different gravity field models are analyzed and compared.

Sensitivity of the Gravity Model and Orbital Frame for On-board Real-Time Orbit Determination: Operational Results of GPS-12 GPS Receiver

This paper describes the sensitivity of both the orbital frame domain selection and the gravity model on the performance of on-board real-time orbit determination. Practical error sources, which affect the navigation solution of spaceborne global positioning system (GPS) receivers, are analyzed first. Then, a reasonable orbital frame (radial, in-track, cross-track (RIC)) is proposed to clearly represent the characteristics of the error in order to improve the performance of the orbit determination (OD) logic. In addition, the sensitivity of the gravity model affecting the orbit determination logic is analyzed by comparison with the precise orbit ephemeris (POE) of the Challenging Minisatellite Payload (CHAMP) satellite, and it is confirmed that the Gravity Recovery And Climate Experiment (GRACE) Gravity Model 03 (GGM03) outperforms the Earth Gravity Model 1996 (EGM96). The effects of both proposed orbit frames and the gravity model on the orbit determination logic are verified using a GPS simulator and observation data from the CHAMP satellite. Moreover, the practical performance of on-board real-time orbit determination logic is verified by updating the software of the spaceborne GPS receiver, GPS-12, on DubaiSat-2 operating at low Earth orbit (LEO). The results show that the position accuracy of on-board real-time orbit determination logic in GPS-12 is improved by 59%, from 12.6 m (1 σ) to 5.1 m (1 σ), after applying the proposed methods. The velocity accuracy is also improved by 57%, from 13.7 mm/s (1 σ) to 5.9 mm/s (1 σ).

Plasma patches inside the polar cap and auroral oval: the impact on the spaceborne GPS receiver

In this study, we focus on plasma patches with very dense plasma in the southern hemisphere during the main phase of 2015 St. Patrick’s Day storm. With in situ electron densities exceeding 1.5 × 1012 m−3at 450–500 km altitude, the patches cause strong signal outages of the global positioning system (GPS) receivers on board Swarm satellites. By using the field-aligned currents derived from the Swarm magnetic measurements, we determined whether the satellites fly inside the auroral oval or not. Different influences on the spaceborne GPS receiver are seen when these patches are located at different latitude regions, e.g., inside the polar cap or auroral oval. The simultaneously measurements of 2 Hz electron density as well as 50 Hz magnetic signatures from Swarm show that when large-scale polar cap patches transported from dayside lower latitude entering the cusp region, irregularities with much finer scale-size are generated; associated with various instabilities inside the cusp region, the small-scale irregularities cause much more severe influence on the GPS signals. This is the first direct evidence to show that when plasma patches are located inside the cusp region, the spaceborne receiver experiences stronger outage of GPS signals.

Precise Orbit Determination of GRACE-A Satellite with Kinematic GPS PPP

Precise Point Positioning (PPP) has been widely used in navigation and orbit determination applications as we can obtain precise Global Positioning System (GPS) satellite orbit and clock products. Kinematic PPP, which is based on the GPS measurements only from the spaceborne GPS receiver, has some advantages for a simple precise orbit determination (POD). In this study, we developed kinematic PPP technique to estimate the orbits of GRACE-A satellite. The comparison of the mean position between the JPL's orbit product and our results showed the orbit differences 0.18 cm, 0.54 cm, and 0.98 cm in the Radial, in Along-track, and Cross-track direction respectively. In addition, we obtained the root mean square (rms) values of 4.06 cm, 3.90 cm, and 3.23 cm in the satellite coordinate components relative to the known coordinates.

Phase Residual Estimations for PCVs of Spaceborne GPS Receiver Antenna and Their Impacts on Precise Orbit Determination of GRACE Satellites

In-flight phase center systematic errors of global positioning system (GPS) receiver antenna are the main restriction for improving the precision of precise orbit determination using dual-frequency GPS. Residual approach is one of the valid methods for in-flight calibration of GPS receiver antenna phase center variations (PCVs) from ground calibration. In this paper, followed by the correction model of spaceborne GPS receiver antenna phase center, ionosphere-free PCVs can be directly estimated by ionosphere-free carrier phase post-fit residuals of reduced dynamic orbit determination. By the data processing of gravity recovery and climate experiment (GRACE) satellites, the following conclusions are drawn. Firstly, the distributions of ionosphere-free carrier phase post-fit residuals from different periods have the similar systematic characteristics. Secondly, simulations show that the influence of phase residual estimations for ionosphere-free PCVs on orbit determination can reach the centimeter level. Finally, it is shown by in-flight data processing that phase residual estimations of current period could not only be used for the calibration for GPS receiver antenna phase center of foretime and current period, but also be used for the forecast of ionosphere-free PCVs in future period, and the accuracy of orbit determination can be well improved.

Robustness assessment between sigma point and extended Kalman filter for orbit determination

A comparison between the extended Kalman filter (EKF) and the nonlinear sigma point Kalman filter (SPKF) for a real time satellite orbit determination problem, using GPS measurements is presented. Such comparison is based on testing the filters robustness for degraded initial conditions. The main subjects for the comparison between the estimators are convergence speed and computational implementation complexity. Based on the analysis of such criteria, the advantages and drawbacks of each estimator are presented. In this work, the orbit of an artificial satellite is determined using real data from a space borne Global Positioning System (GPS) receiver. This is a fully nonlinear problem, with respect to both the dynamics and measurements equations, in which the disturbing forces are not easily modeled. The problem of orbit determination consists essentially of estimating values that completely specify the body trajectory in the space, processing a set of measurements related to this body. In this orbit determination problem the focus is to analyze each filter convergence behavior in situations where the initial conditions are inaccurate, introducing since small up to larger errors in the initial accurate position conditions. Concomitantly another aim is to know how such inaccuracies affect the estimators performance. In this work, the extended Kalman filter (EKF) is compared with the nonlinear sigma point Kalman filter (SPKF) for a real time satellite orbit determination problem, using GPS measurements. The comparison is based on the assessing the robustness of the filters for purposely degraded initial conditions. The main subjects for the comparison between the estimators are convergence speed, divergence occurrence, flaws and statistical shortcomings. Based on the analysis of such criteria, the advantages and drawbacks of each estimator are presented. Here, the orbit of an artificial satellite is determined using real data from the Global Positioning System (GPS) receivers. In orbit determination of artificial satellites, both the dynamic system and the measurements equations are of nonlinear nature. Therefore one deals here with a fully nonlinear problem in which the acting forces as well as measurements are not easily modeled. The orbit determination problem consists of estimating variables that completely specify the body trajectory in the space, processing a set of information (pseudo-range measurements) related to this body. As far as this work is concerned, the more accurate GPS phase measurements are not used here, because the aim is not the search for accuracy, but a comparison of performance under different error levels of initial conditions. Besides using carrier phase measurements, the ambiguity resolution algorithm or any other artifacts to overcome such hindrance could eventually mask the results, misleading the conclusions. A spaceborne GPS receiver is a powerful means to determine orbits of artificial Earth satellites by providing many redundant measurements which ultimately yields high degree of the observability to the problem. The Topex/Poseidon (T/P) satellite is a nice example of using GPS for space positioning. Through an onboard GPS receiver, the pseudo- ranges (error corrupted distance from satellite to each of the tracked GPS satellites) can be measured and can be used to estimate the full orbital state.

Operation of the Radio Occultation Mission in KOMPSAT-5

Korea multi-purpose satellite-5 (KOMPSAT-5) is a low earth orbit (LEO) satellite scheduled to be launched in 2010. To satisfy the precision orbit determination (POD) requirement for a high resolution synthetic aperture radar image of KOMPSAT-5, KOMPSAT-5 has atmosphere occultation POD (AOPOD) system which consists of a space-borne dual frequency global positioning system (GPS) receiver and a laser retro reflector array. A space-borne dual frequency GPS receiver on a LEO satellite provides position data for the POD and radio occultation data for scientific applications. This paper describes an overview of AOPOD system and operation concepts of the radio occultation mission in KOMPSAT-5. We showed AOPOD system satisfies the requirements of KOMPSAT-5 in performance and stability.

Interferometric Baseline Performance Estimations for Multistatic Synthetic Aperture Radar Configurations Derived from GRACE GPS Observations

Recent studies have demonstrated the usefulness of global positioning system (GPS) receivers for relative positioning of formation-flying satellites using dual-frequency carrier-phase observations. The accurate determination of distances or baselines between satellites flying in formation can provide significant benefits to a wide area of geodetic studies. For spaceborne radar interferometry in particular, such measurements will improve the accuracy of interferometric products such as digital elevation models (DEM) or surface deformation maps. The aim of this study is to analyze the impact of relative position errors on the interferometric baseline performance of multistatic synthetic aperture radar (SAR) satellites flying in such a formation. Based on accuracy results obtained from differential GPS (DGPS) observations between the twin gravity recovery and climate experiment (GRACE) satellites, baseline uncertainties are derived for three interferometric scenarios of a dedicated SAR mission. For cross-track interferometry in a bistatic operational mode, a mean 2D baseline error (1σ) of 1.4 mm is derived, whereas baseline estimates necessary for a monostatic acquisition mode with a 50 km along-track separation reveal a 2D uncertainty of approximately 1.7 mm. Absolute orbit solutions based on reduced dynamic orbit determination techniques using GRACE GPS code and carrier-phase data allows a repeat-pass baseline estimation with an accuracy down to 4 cm (2D 1σ). To assess the accuracy with respect to quality requirements of high-resolution DEMs, topographic height errors are derived from the estimated baseline uncertainties. Taking the monostatic pursuit flight configuration as the worst case for baseline performance, the analysis reveals that the induced low-frequency modulation (height bias) fulfills the relative vertical accuracy requirement (σ<1 m linear point-to-point error) according to the digital terrain elevation data level 3 (DTED-3) specifications for most of the baseline constellations. The use of a GPS-based reduced dynamic orbit determination technique improves the baseline performance for repeat-pass interferometry. The problem of fulfilling the DTED-3 horizontal accuracy requirements is still an issue to be investigated. DGPS can be used as an operational navigation tool for high-precision baseline estimation if a geodetic-grade dual-frequency spaceborne GPS receiver is assumed to be the primary instrument onboard the SAR satellites. The possibility of using only single-frequency receivers, however, requires further research effort.

Use of global positioning system for Gravity Probe B relativity experiment and co-experiments

The primary objective of the Gravity Probe B (GP-B) Relativity Mission is to measure the relativistic drift of an Earth-orbiting gyroscope as predicted by the General Theory of Relativity. The Global Positioning System (GPS) will play one of the key roles providing time tags for the measurements and the velocity information to calibrate the cryogenic sensors. A spaceborne GPS receiver, implemented on the GP-B spacecraft, will provide real-time position, velocity, attitude solutions, timing pulses and raw measurements for post-processing that are necessary for the relativity experiment. In addition, it will be one of the primary navigation sensors for the clock, geodesy and aeronomy co-experiments.