Showing papers in "Annual of Navigation in 2019"

Introduction to BeiDou-3 navigation satellite system

Abstract: China's BeiDou navigation system (BDS) has evolved from the demonstration navigation satellite system (BDS-1) to the regional navigation satellite system (BDS-2). Now, the global BeiDou navigation system (BDS-3) is in construction and is proceeding well. The design and functions of BDS-3 are quite different from those of both BDS-1 and BDS-2. In this paper, the general design, the coordinate reference system, and the system time basis of BDS-3 are introduced. Several new payloads designed to accomplish different objectives are described as well as the platforms on which they are hosted. Since BDS-3 consists of several different constellations, the general service capabilities and special service functions provided by these different constellations are described. The performances of the initial BDS-3 platforms are evaluated based on the available eight-medium Earth orbit (MEO) satellite configuration. The results of satellite orbit determination and prediction with and without the BDS-3 inter-satellite links (ISL) are compared and analyzed.

The BeiDou global broadcast ionospheric delay correction model (BDGIM) and its preliminary performance evaluation results

Abstract: A global ionospheric delay correction model (BeiDou global broadcast ionospheric delay correction model [BDGIM]) is proposed for the single-frequency ionospheric delay correction of the third phase of the BeiDou navigation satellite system (BDS-3). An initial performance assessment of BDGIM was conducted with data collected in China and worldwide. For regional analysis, the broadcast coefficients of BDGIM were provided by the operational control system of BDS, while for global analysis, the coefficients of BDGIM were estimated using global positioning system (GPS)-derived total electron contents (TECs) obtained from 19 globally distributed monitoring sites. In China, the performance of BDGIM was evaluated by GPS-TEC derived from 40 test sites during day of year (DOY) 060 to 181, 2015. The ionospheric errors can be mitigated by 80.9% for BDGIM. On the global scale, the ionospheric TECs derived from 50 sites of the International Global Navigation Satellite System (GNSS) Services (IGS) were used as references during DOY 220 to 365, 2014, and BDGIM can correct for 77.6% of the ionospheric delay.

Overview of BDS III new signals

Abstract: With the completion of the experimental and regional phases, China's BeiDou Navigation Satellite System (BDS) is being speedily expanded to a global and multifunctional satellite navigation system, BDS III. Confronted with challenges such as limited frequency resources and diversified user requirements, new signals with novel modulation techniques are adopted in BDS III. In addition to the legacy B1I and B3I signals, new open service signals, B1C and B2a/B2b, as well as some new authorized service signals, will be broadcast by BDS III satellites. Among them, B1C and B2a are compatible and interoperable with GPS and Galileo. The modulation techniques and the detailed signal structures of B1C and B2a are introduced in this paper, along with analysis of the initial in-orbit test results of the new signals.

The contribution of intersatellite links to BDS-3 orbit determination: Model refinement and comparisons

Abstract: By end-2018, the Chinese BeiDou satellite system (BDS) has entered its third phase of global scale coverage (BDS-3). This study presents and validates a modified modeling aspect concerning an intersatellite link (ISL) hardware delay estimation. The precise orbit determination (POD) results of BDS-3 demonstrate this aspect along with calibrated phase center offsets (PCOs) of the ISL terminal to help improve the orbit accuracy. After onboarding the ISL data, two additional sets of POD solutions using regional and global ground stations are conducted. About a 40% improvement can be achieved for regional cases and 20% for global cases after ISL data were used for POD. The best POD performance solution is obtained with observations from both the global ground stations and ISL when the averaged 3D root mean squares of the orbit overlapping differences can reach around 20 cm and the signal-in-space range errors (SISREs) obtained by 6-hour predicted clock and orbit solutions show an average value of 25 cm.

Probabilistic graphical fusion of LiDAR, GPS, and 3D building maps for urban UAV navigation

Abstract: Because of the recent interest in unmanned air vehicle (UAV) commercialization, there is a great need for navigation algorithms that provide accurate and robust positioning in urban environments that are often Global Positioning Systems (GPS) challenged or denied. In this paper, we present a probabilistic graph-based navigation algorithm resilient to GPS errors. Fusing GPS pseudorange and Light Detection and Ranging (LiDAR) odometry measurements with 3D building maps, we apply a batch estimation approach to generate a robust trajectory estimate and maps of the surrounding environment.We then leverage the maps to locate potential sources of GPS multipath and mitigate the effects of degraded pseudorange measurements on the trajectory estimate. We experimentally validate our results with flight tests conducted in GPS-challenged and GPS-denied environments.

Robust transform domain signal processing for GNSS

Abstract: Robust signal processing techniques are effective mitigation approaches that can enable Global Navigation Satellite System (GNSS) receiver operations even in the presence of strong interference. We extend robust GNSS signal processing to the case where interference admits a sparse representation in a transform domain (TD). More specifically, an orthonormal transformation is used to project the received GNSS samples into an appropriate TD. Robust signal processing strategies are then applied. The robust transform domain (RTD) cross-ambiguity function (CAF) is obtained by applying a zero-memory nonlinearity (ZMNL) to the TD samples, which, in turn, are used for the evaluation of the CAF. Different nonlinearities are analyzed and different implementations for the evaluation of the RTD CAF are proposed. The RTD approach is characterized from a theoretical point of view, with the usage of Monte Carlo simulations and through the processing of GNSS signals generated with a hardware simulator.

Performance assessment of 3D‐mapping‐aided GNSS part 2: Environment and mapping

Abstract: A full performance assessment of 3D-mapping-aided (3DMA) GNSS in dense urban areas is presented. This second part of a two-part paper focusses on the effects of the surrounding environment and 3D mapping, based on data collected in London using a u-blox EVK M8T GNSS receiver. A theoretical assessment is followed by experimental results comparing conventional GNSS, shadow matching, 3DMA ranging and integrated 3DMA GNSS under a wide range of conditions. All positioning methods perform best when the proportion of sky that is directly visible is high, the building height to street width ratio is low and the average building height is below 20m as there are more direct LOS signals under these conditions. In terms of relative accuracy, all 3DMA GNSS methods demonstrate maximum benefit at sky visibilities between about 15% and 35%. All methods exhibit poorer accuracy in environments dominated by glass and steel buildings. Temporary features of the environment, such as large buses and lorries, also degrade 3DMA accuracy. Using full 3D city models gives significantly higher accuracy than simple block models. Missing buildings due to mapping errors or construction activity also lead to larger positioning errors. Based on the results of both parts of the study, further enhancements to the 3DMA GNSS algorithms are recommended, including multi-epoch filtered positioning, outlier detection, improved statistical models, selfcalibration and context adaptation.

Improved design of control segment in BDS-3

Abstract: The Chinese BeiDou Navigation Satellite System (BDS) is accelerating its development and has been applied in various fields. Compared with other satellite navigation systems in the world, BDS has many unique features such as multiservices integrated with Radio Determination Satellite Service (RDSS), Radio Navigation Satellite Service (RNSS), and Satellite-Based Augmentation Service (SBAS), a mixed-orbit satellite constellation, and flexible navigation messages, etc. This paper presents the distinctive innovative designs as well as processing strategies in BDS. First, this paper introduces the characteristics of BeiDou navigation messages broadcast by the hybrid constellation of satellites in Geostationary Earth Orbit (GEO), Inclined Geo-Synchronization Orbit (IGSO), and Medium Earth Orbit (MEO). Next, the innovative design and operation of the control segment are discussed. Finally, highlights of the unique usage algorithm of the BDS navigation message information are presented, such as the BDS satellite clock correction and TGD parameters, satellite ephemeris and almanac, and ionospheric delay parameters.

A Regression-Based Methodology to Improve Estimation of Inertial Sensor Errors Using Allan Variance Data

Abstract: This research proposes a novel, autonomous, regression-based methodology for Allan variance analysis of inertial measurement unit (IMU) sensors. Current methods for Allan variance analysis have been rooted in the human-based interpretation of linear trends, referred to as the slope method. The slope method is so prolific; it is referenced among electrical and electronics engineering standards for IMU error analysis. However, the graphical nature and visual-inspection–based use of the method limit its ability to be programmed as a generalized algorithm,which hinders the autonomy desired in modern-day navigation computations. Using nonlinear regression with a ridge-regression initial guess, the proposed method is shown to produce comparable results to the gold standard slope method when using standard-length data collections and outperforms the slope method when the amount of available data is limited. This development directly enables accurate navigation solutions for all vehicles in land, air, sea, and space operations.

Relativistic effects to the onboard BeiDou satellite clocks

Abstract: The relationship between the proper time of a satellite clock and the geocentric coordinate time (TCG) is discussed in the framework of general relativity. The influences of Earth's shape and the tidal potentials of the Sun and Moon are analyzed for onboard satellite clocks in different orbits. The results show that the influence of the shape of the Earth on Middle Earth Orbit (MEO) satellite reaches the level of 4.0 × 10-15, and it may be the direct cause of the half orbital-period variation in the clock frequency. The influences of the tidal potentials of the Sun and the Moon are relatively smaller. These influences on the frequencies of the clocks in the BeiDou MEO and GEO/IGSO (Geosynchronous Earth Orbit/Inclined Geosynchronous Satellite Orbit) satellites are 5.9 × 10-16 and 1.2 × 10-15, respectively, and appear to be half-day periodic variations. Therefore, these effects need to be considered in the precise assessment and application of BeiDou satellite clocks.

Performance assessment of 3D‐mapping–aided GNSS part 1: Algorithms, user equipment, and review

Abstract: A full performance assessment of 3D mapping–aided (3DMA) GNSS in dense urban areas is presented. This first part of a two‐part paper focuses on the effects of algorithm design and user equipment, based on data collected in London using Leica Viva GS15 and u‐blox EVK‐M8T GNSS receivers and a Nexus 9 Android tablet. Best performance is obtained by combining shadow matching with likelihood‐based 3DMA GNSS ranging using hypothesis‐domain integration. Improved versions of the algorithms, together with a comprehensive tuning process, are described. Root mean square horizontal position errors obtained using data from Leica, u‐blox, and Nexus receivers are 3.5, 4.7, and 4.9 m, respectively, compared with 23.6, 26.4, and 31.0 m using conventional GNSS positioning, about a factor of six improvement. Optimal algorithm tuning depends on the environment and the impact of varying grid spacing of the candidate positions is assessed. Algorithms have also been shown to operate in real time on both a Raspberry Pi 3 and a Samsung Galaxy S8+ Android smartphone.

Distributed multi-GNSS timing and localization for nanosatellites

Abstract: Recent advances in distribution and miniaturization among spacecraft and expansion of global navigation satellite systems (GNSS) motivate the Distributed Multi-GNSS Timing and Localization system. The DiGiTaL system is intended to provide nanosatellite swarms with unprecedented centimeter-level relative navigation accuracy in real time and nanosecond-level time synchronization through the integration of a multiconstellation GNSS receiver, a chipscale atomic clock, and an intersatellite link. This paper describes DiGiTaL's hardware and software design, architecture, and navigation software in detail. The swarming spacecraft are grouped into subsets, where differential GNSS is performed by a precise orbit determination module with integer ambiguity resolution in real time. The resulting precise orbits are then exchanged and fused by a swarm determination module, creating full-swarm knowledge. Finally, the DiGiTaL architecture is integrated into CubeSat avionics and tested with key hardware in the loop using Stanford's GNSS navigation testbed. For the first time, this paper shows the capability to perform centimeter-level precise relative navigation using commercial-off-the-shelf CubeSat hardware for spacecraft swarms.

Quantum-resistant authentication algorithms for satellite-based augmentation systems

Abstract: Cryptography in the form of digital signatures can be part of the solution to the threat of spoofing and is going to be implemented on Galileo and other Global Navigation Satellite Systems. Digital signatures incorporated into the data stream authenticate the integrity of the data as well as the origin of the message. Implementing a digital signature on a satellite-based augmentation system for use in aviation will require the signature to be short and the signing procedure to be cryptographically relevant for the next 30 or more years. With the advent of quantum computing, many state-of-the-art authentication schemes are no longer viable, so an authentication scheme implemented in satellite-based augmentation system will need to be quantum secure. This paper introduces the cryptographic primitives (foundational problems) necessary to understand the vulnerabilities in modern-day cryptography due to quantum computing and investigates the use of TESLA (Timed Efficient Stream Loss-tolerant Algorithm) and EC-Schnorr (Elliptic Curve-Schnorr) algorithms in broadcast systems.

Assessment and mitigation of equatorial plasma bubble impacts on category I GBAS operations in the Brazilian region

Abstract: Prior to initiating GBAS service in equatorial regions, it is vital to evaluate potential integrity threats posed by equatorial plasma bubble (EPB)-induced ionospheric gradients and assess availability when implementing ionospheric threat mitigation methods. Earlier work developed a preliminary EPB model with a gradient bound larger than twice that for mid-latitude ionospheric storms. Position-domain geometry screening (PDGS) with this higher gradient bound decreases availability to 58.3% at the Galeao International Airport, Brazil, during nighttime. A new mitigation method using Monte Carlo simulation randomizes ionospheric scenarios using randomly generated parameter combinations within the threat model and assesses the ensemble impacts. By taking credit for a prior probability of an extreme EPB, this algorithm determines the inflated integrity parameters to meet the safety requirement in the probabilistic definition. This paper shows that with this method, the system availability for category I precision approaches dramatically improved to 89.6% when a data-driven prior probability of 10-5 was applied.

Adaptive covariance estimation of LiDAR-based positioning errors for UAVs

Abstract: Outdoor positioning for unmanned aerial vehicles (UAVs) commonly relies on global navigation satellite system (GNSS) signals, which might be reflected or blocked in urban areas. Thus, additional on-board sensors such as light detection and ranging (LiDAR) are desirable to aid positioning. To fuse measurements from different sensors, it is important to accurately characterize the error covariance matrices of individual sensor measurements. We propose a novel method for adaptively estimating the LiDAR-based positioning error covariance matrix based on the point cloud features surrounding the UAV. We model the position error as a multivariate Gaussian distribution and estimate its covariance matrix from individual surface and edge feature points. Simulations show that our model is more accurate than a distance-based covariance matrix model. Furthermore, we conduct an outdoor experiment that fuses global positioning system (GPS) signals and LiDAR position measurements. We demonstrate a clear improvement in the UAV's global position estimation using our adaptive covariance matrix for LiDAR-based measurements.

Design and implementation of a real-time software receiver for BDS-3 signals

Abstract: The BeiDou Navigation Satellite System (BDS) is currently building its third phase (BDS-3), which will provide services to users around the world. In addition to backward compatibility with BDS-2, BDS-3 satellites are equipped with the B1C and B2 interoperable signals for compatibility with GPS and Galileo systems. To evaluate performance and optimize processing methods, we designed and implemented a real-time software receiver with the ability to process all BDS-3 signals in parallel. A complete description of all signal processing aspects is given. To reduce the reliance on high-performance hardware while maintaining the independent analysis capabilities of acquisition performance in real-time software receivers, a B1I-aided acquisition method for reducing the search space of other signals from the same satellite is applied. An unambiguous tracking method is proposed to solve the ambiguity problem of the Quadrature Multiplexed Binary Offset Carrier (QMBOC) signal that can be used for matching reception of the pilot component of the B1C signal.

Bias and variance of asymmetric double‐sided two‐way ranging

Abstract: Asymmetric double-sided two-way ranging (ADS-TWR) is a method of range estimation through precisely time-stamped messages sent between two transceivers. In contrast to symmetric double-sided two-way ranging (SDS-TWR), ADS-TWR suppresses the errors induced by transceiver clock drifts even when the message reply delays are unequal. However, due to the nonlinearity of the ADS-TWR estimator, its mean and variance cannot be evaluated in a straightforward or exact way. This article presents an analytical approach of evaluating an approximation of bias and variance of the range estimators and applies it on an exemplary set of parameters, typical for ultra-wide band (UWB) localization systems. Moreover, the obtained results are verified by a Monte Carlo simulation. It will be proven that ADS-TWR is safe to be used in most of the present applications, and its precision is rather similar to SDS-TWR.

Introduction to the special issue on the BeiDou navigation system

Abstract: China's BeiDou Navigation Satellite System (BDS) has evolved from a demonstration system (BDS-1) to a regional navigation satellite system (BDS-2) and has finally entered the phase of a global navigation system (BDS-3). In 2018, the BDS-3 implementation achieved historic milestones. A baseline constellation with 18 MEO satellites and one GEO satellite has been established. The BDS has the ability to provide fundamental positioning, navigation, and timing (PNT) services to global users. The current BDS features some distinctive design and unique service capabilities. First, the BDS provides a regional message communication service and a global short message communication service with 1000 and 40 Chinese characters at a time, respectively. Second, the BDS also provides a global search and rescue (SAR) service, a satellite-based augmentation service (SBAS), as well as a regional precise point positioning (PPP) service. This special issue of the Institute of Navigation's journal, NAVIGATION, provides a collection of papers presenting research achievements in the BDS over the last 2 years. It covers essential fields necessary to ensure the successful operation of BDS, such as constellation design, operational and control system design and construction, frequency and signal design, updated coordinate reference system and time system, satellite orbit determination, ionospheric model, and software receiver. Papers in this special issue present the development status of the BDS from several perspectives and introduce the main performance and progress to readers, which is helpful for researchers in the field of satellite navigation and beneficial to GNSS terminal manufacturers as well. The publication of the issue also provides an opportunity to promote users' understanding and applications of the BDS. We hope that readers find useful information in this issue, and we look forward to sharing our continued success in future BDS development.

Urban environment recognition based on the GNSS signal characteristics

Abstract: Statistical characteristics of signal reception conditions vary greatly in different types of environments. Hence, Global National Satellite System (GNSS) receivers must recognize surroundings for choosing the most suitable positioning methods in real time. Targeting vehicular positioning applications in a city, a novel environment recognition algorithm based only on the GNSS signal characteristics is proposed to distinguish between six distinct settings. To characterize different environmental interferences, a signal feature vector is built to represent the signal attenuation, blockage, and multipath. By training the classification model with labeled feature vectors, the support vector machine (SVM) algorithm is used to predict the scene type. A temporal filtering method is proposed to improve the accuracy. With advanced training of the model, this recognition method can work for the receiver in real time. To prove the extensive applicability of the proposed algorithm, the prediction data set and the training data set are collected in different cities. The testing results show overall recognition accuracy of 89.3% across different environments.

Design and analysis of a public key infrastructure for SBAS data authentication

Abstract: Integral to any authentication system is the design of its public key infrastructure (PKI), allowing the system to distribute, maintain, and revoke cryptographic keys while dividing and allocating the responsibility of security between different entities. This paper develops a PKI for two SBAS candidate authentication schemes: one each for an L5 I-channel and Q-channel implementation. A simulator, introduced as MCOS, is developed to enable large scale Monte Carlo tests of these PKI designs. This work concludes that once a receiver has been deployed with a set of preinstalled encrypted public keys, a strictly over-the-air method of delivering PKI information is feasible for SBAS data authentication in nominal conditions. This work also provides a strong candidate PKI that is designed to be standardized internationally for current and future SBAS service providers.

Antenna influence on Global Navigation Satellite System pseudorange performance for future aeronautics multifrequency standardization

Abstract: Current standardization activities in the aeronautical community are paving the way to using multifrequency multiconstellation GNSS as a primary means of aircraft navigation. The increase in the number of satellites from different constellations as well as the increasing use of multiple frequency GNSS receivers promise improvements in the achievable accuracy in GNSS positioning. The effects of receiver antennas shall be investigated because of the stronger impact of possible imperfections on the overall error budget for multifrequency combinations. The scope of this paper is to show the possibility of properly modeling and indeed characterizing the antenna-induced GNSS pseudorange errors, through simulations and electromagnetic measurement. An insight into antenna characteristics giving rise to such errors will be given, by analyzing the impact of the feeding technique on the achievable pattern uniformity and hence on antenna-related pseudorange errors. The technique is then validated through GNSS field measurement.

Interference mitigation using a dual-polarized antenna array in a real environment

Abstract: This paper presents a new approach to interference mitigation. We propose to equip a Global Navigation Satellite System (GNSS) receiver with a diversely polarized antenna array in order to combine signal processing in the spatial and polarization domains in a novel way. The new algorithm is evaluated using measurement data, and results show significant improvement in receiver robustness against interferences when the dual-polarization approach is used. Two specific benefits come to light. First, the carrier-to-noise-density ratios of the line-of-sight components are improved since the receiver can make use of the power present on the left-hand circularly polarized (LHCP) channels because of non-ideal polarization purity of the antenna, resulting in better receiver computed position, velocity, and time (PVT) solutions. Second, interference mitigation becomes more effective because of the possibility of filtering in the polarization domain and the additional number of available degrees of freedom, increasing receiver robustness and enabling tracking and PVT in severe interference scenarios.

Angular accelerometer-based inertial navigation system

Abstract: Angular acceleration sensors technologies are evolving and emerging in various applications. In this paper, we propose an angular accelerometer-based inertial navigation system. One application of such systems can be highly maneuvering platforms where direct measurement of angular acceleration is desired. To that end, a review of modern angular acceleration sensor technologies and their possible applications is provided. Two angular acceleration-based inertial navigation system architectures are suggested, and their equations of motion are derived. Additionally, an analytical assessment for short time periods of pure inertial navigation is provided with a comparison to traditional and gyro-free inertial navigation architectures.

Flight results of GPS‐based attitude determination for the microsatellite Flying Laptop

Abstract: The paper presents attitude determination results obtained with the "GPS-Enhanced Navigation system for the University of Stuttgart microsatellite" (GENIUS) onboard “Flying Laptop.” Real flight data have been collected in different measurement campaigns. The performance of the algorithm is evaluated in the presence of typical satellite attitude maneuvers. It is shown that the major sources of errors are offsets and variations of the differential antenna phase patterns. The variations depend on azimuth and elevation angle of the line-of-sight vector to the tracked satellite. They lead to systematic errors in the carrier-phase single differences on the order of a few tens of millimeters. These errors translate into attitude errors up to 1?. It will be demonstrated how much these errors can be mitigated by in-flight calibration based on carrier-phase measurement residuals. The flight results will be compared with the prelaunch ground tests and simulations performed, which will provide valuable insight into how realistically the flight performance can be predicted before launch.

Impact of terrain factors on the matching performance of terrain‐aided navigation

Abstract: Aiming at describing terrain variation in an easily understandable way, a new method is proposed to describe the terrain elevations quantitatively by factor analysis for terrain-aided navigation. After as many terrain factors as possible are collected describing the terrain elevations from various aspects, they are simplified by correlation to remove the redundant factors. The simplified terrain factors are processed to derive the extracted factors by principal component analysis. With such factor analysis, three extracted factors dubbed "variation," "similarity," and "information" are derived in the conceptual level. A classifier is derived by logistic regression using the extracted factors. The percentages of the correct classification are very high both for the suitable and the unsuitable regions of matching in two maps, which proves the effectiveness of the extracted factors for the terrain elevations.

Frequency tracking and mitigation method based on CPHD filter and adaptive multiple linear Kalman notch filter for multiple GNSS interference

Abstract: In this paper, a frequency tracking method based on a cardinalized probability hypothesis density (CPHD) filter with cardinality compensation and fuzzy-c means (FCM) clustering is proposed to precisely estimate multiple interference frequencies in the received Global Navigation Satellite System (GNSS) signal. In addition, an adaptive multiple linear Kalman notch filter is applied in order to mitigate multiple GNSS interference signals by using tracking results from the proposed CPHD filter. The cardinality refers to the number of interference frequencies, and estimation accuracy on the cardinality has an effect on the tracking and mitigation performance of the filter. For that reason, the cardinality compensation process and FCM clustering are added in the CPHD filter. The proposed tracking and mitigation method is evaluated by theoretical analysis including simulations. It is confirmed that the proposed algorithm has better tracking and mitigation performance compared with the conventional algorithms.

GNSS yaw attitude estimation: Results for the Japanese Quasi-Zenith Satellite System Block-II satellites using single- or triple-frequency signals from two antennas

Abstract: The Japanese Quasi-Zenith Satellite System (QZSS) constellation has added three new Block-II satellites. Two of these satellites have been launched into inclined geosynchronous orbits and one into a geostationary orbit. All three spacecraft broadcast ranging signals on GPS L1, L2 and L5 frequencies from their main L-band antenna together with the centimeter-level augmentation service (CLAS) signal L6 (formerly LEX) on the Galileo E6 frequency band. Like on the Block-I satellite, a sub-meter level augmentation service (SLAS) signal is transmitted from a separate antenna on the GPS L1 frequency. A new feature is the addition of the position technology verification service (PTV) Signal on the L5 frequency from yet another antenna. After determination of the antenna baseline vector, differential processing of measurements from different observations allows for an estimation of the satellite’s yaw attitude. The L1 SLAS and the L1 C/A-code signals have been used to estimate the yaw attitude with an accuracy of less than 1°. Differential carrier-phase center variation maps have been derived for this signal combination. Yaw estimation results are presented for periods of special interest, for example 360° yaw rotations, orbit correction maneuvers and the satellite’s eclipse period, where a special pseudo yaw steering attitude mode is applied. The second part of the paper introduces a new concept using triple-frequency signals from two different antennas for attitude determination. This method is demonstrated with QZSS measurements, but is also applicable to other satellite navigation system, like the enhanced GLONASS-M satellites with L3 signal capabilities.

Satellite stellar refraction navigation using star pixel coordinates

Abstract: When stellar refraction occurs, the refraction apparent rays contain two kinds of refraction information, stellar refraction angle and stellar refraction direction. The refraction apparent height and the stellar refraction angle are two typical measurements used in stellar refraction navigation, which essentially only uses stellar refraction angle, and does not use stellar refraction direction. In fact, the stellar refraction direction is a function of the satellite position vector, which is useful in determining the satellite position. In this paper, a new stellar refraction navigation method using the star pixel coordinates as a measurement is proposed to improve navigation accuracy by using two kinds of refraction information at the same time. The corresponding measurement model for the star pixel coordinates is established. Simulations show that the proposed method's navigation performance is better than that of refraction apparent height and stellar refraction angle.

Computing GPS satellite velocity and acceleration from the broadcast navigation message

Abstract: We present an extension to the Global Positioning System (GPS) broadcast navigation message user equations for computing GPS space vehicle (SV) velocity and acceleration. Although similar extensions have been published, the extension presented herein includes a distinct kinematic method for computing SV acceleration, which significantly reduces the complexity of the equations and improves the mean magnitude results by approximately one order of magnitude by including oblate Earth perturbation effects. Additionally, detailed analyses and validation results using multiple days of precise ephemeris data and multiple broadcast navigation messages are presented. Improvements in the equations for computing SV position are also included, removing ambiguity and redundancy in the existing user equations. The recommended changes make the user equations more complete and more suitable for implementation in a wide variety of programming languages employed by GPS users. Furthermore, relativistic SV clock error rate computation is enabled by the recommended equations. A complete, stand-alone table of the equations in the format and notation of the GPS interface specification is provided, along with benchmark test cases to simplify implementation and verification.