Multi-frequency Global Navigation Satellite System Research Articles

State Estimation for a Multirotor using Tight-Coupling of GNSS and Inertial Navigation

Multicopters are becoming a major tool for diverse industrial outdoor usecases, requiring accurate absolute and relative localization and control. Robust and high-rate state estimation is therefore crucial, even in the event of poor reception of global navigation satellite systems (GNSS). To overcome this problem, this paper addresses the implementation and validation of a tightly-coupled fusion of GNSS and inertial sensors for micro aerial vehicles. The targeted experimental quadcopter provides an industrial-class inertial measurement unit and a multi-frequency GNSS receiver. The sensorfusion including initialization and parameterization is explained in detail, and practical implementations are given. The work focuses on outdoor validation tests using a highly accurate optical tracking system as reference. Results show an absolute horizontal position error of below 1 m and low standard deviations of 5 cm for horizontal position, 0.15 m/s for velocity, and 1° for orientation errors. Moreover, a comparison with a loosely-coupled filter using Real-Time-Kinematic (RTK) measurements is given, demonstrating the potential of further research when exploiting the advantages of both approaches.

Array-Aided Single-Frequency State-Space RTK with Combined GPS, Galileo, IRNSS, and QZSS L5/E5a Observations

The concept of real-time kinematic precise point positioning (PPP-RTK) is to achieve integer ambiguity resolution (IAR) at a single global navigation satellite system (GNSS) user by providing network-derived satellite phase biases (SPBs) in addition to the standard PPP corrections. The integerness of the user ambiguities gets recovered and resolved, obtaining high-precision position solutions with the aid of the precise carrier-phase observables. Most of current PPP-RTK methods focus on processing dual-frequency or multifrequency GNSS network observations. The new developing Indian regional navigation satellite system (IRNSS), however, provides only a single-frequency signal in L-band, and shares the L5 frequency with the American global positioning system (GPS), the European Galileo, and the Japanese quasi-zenith satellite system (QZSS). This contribution proposes a new array-aided state-space RTK (SS-RTK) method following the concept of PPP-RTK, which is applicable to the single-frequency network data processing. A small array of multi-GNSS stations, separated by a few meters, takes the role of reference station to provide a batch of single-frequency RTK corrections. Similar to PPP-RTK, the single-frequency stand-alone user ambiguities are a double-differenced (DD) form after applying the SS-RTK corrections. Based on the proposed array-aided SS-RTK concept, the authors analyze the capability of the single-receiver positioning with IAR using L5/E5a frequency observations from IRNSS, as well as GPS, Galileo, and QZSS. Results from real-data experiments demonstrate that even though stand-alone RTK using current IRNSS satellites is not yet possible, they effectively contribute to the tightly integrated multisystem RTK. By increasing the number of antennas in the array used for SS-RTK corrections, the user would achieve more precise and reliable positions. After increasing the dimension of the array to four antennas, a 4-10% improvement in the IAR success rate is experienced. Moreover, the convergence time of the float solutions, reaching a subdecimeter precision level, reduces from 30 to 40 min (single-antenna array) to about 20 min (four-antenna array).

A study on the evolution of plasma bubbles using the single station‐multisatellite and multistation‐single satellite techniques

AbstractThe characteristics of plasma bubble‐induced ionospheric irregularities were analyzed by estimating the drift velocity of plasma bubbles, their percentage of occurrence, seasonal/LT distributions, and east‐west spatial width using multifrequency Global Navigation Satellite Systems (GNSS) receiver systems at Trivandrum, Bangalore, Hyderabad, Delhi, and Hanle. Two techniques, namely, single station‐multisatellite and multistation‐single satellite observations, were used in the analysis by tracking two geostationary Indian satellites GSAT‐8 (PRN 127) and GSAT‐10 (PRN 128) for the year 2014. In addition, GNSS receiver data from a recently commissioned near‐equatorial station at Changanacherry, Kerala, were used to evaluate 15 plasma bubble events during the period of 29 October 2015 to 31 October 2016. Using, single station‐multisatellite technique, the distribution of drift velocity measurements from plasma bubble scintillations lies in the range of 120–140 m/s for Trivandrum, Changanacherry, and Hyderabad. For Bangalore, and Delhi, the most probable ranges of drift velocity were 120–160 m/s and 80–100 m/s, respectively. The highest probable value of east‐west width of plasma bubble evolution for Trivandrum and Changanacherry was within the range of 100–150 km. However, the same at Bangalore and Hyderabad was in the range of 150–200 km and 100–200 km for Delhi. The maximum probable LT of occurrence of plasma bubble is premidnight sector over the equator. The comparison of the characteristics of plasma bubble evolution over equatorial/low‐latitude Indian sector considering six stations by employing two unique techniques and an objective correlation method is the first time attempt.

Array-Aided Multifrequency GNSS Ionospheric Sensing: Estimability and Precision Analysis

The dual-frequency Global Positioning System has proven to be an effective means of measuring the Earth's ionosphere and its total electron content (TEC). With the advent of multifrequency signals from more Global Navigation Satellite Systems (GNSSs), the opportunity arises to construct many more ionosphere-sensing combinations of GNSS data. With such diversity, various estimable ionospheric delays with differing interpretations (and of different precision) can be formed. How such estimable ionospheric delays should be interpreted, and the extent to which they contribute to the precision with which the unbiased TEC can be estimated, are the topics of this paper. Based on multifrequency GNSS code-only, phase-only, and phase-and-code data, we derive the closed-form solutions of different types of ionospheric observables that each can serve as input of an externally provided ionospheric model for TEC determination. Within such a general least-squares framework, we generalize the widely used phase-to-code levelling technique to its multifrequency version. We also show that only certain specific linear combinations of the observables contribute to the TEC solutions. As a further improvement of the multifrequency GNSS-derived TEC solution, we propose and study the usage of an array of GNSS antennas. Analytical solutions, supported by numerical examples, of this array-based concept are presented, together with a discussion on its relevance for TEC determination. This concerns the roles of time averaging and time differencing, of integer ambiguity resolution, and of the number of frequencies and number of array antennas in determining TEC.

GNSS Jamming Resilience for Close to Shore Navigation in the Northern Sea

Navigational error accounts for half of the accidents and serious incidents in close to shore maritime transport in Norway predominantly due to the rapidly changing weather conditions and the dangerous nature of the narrow inshore waters found along the Norwegian coast. This creates a dependence on Differential Global Positioning System (DGPS) use and any disruption to this service can lead to an increased accident rate. The aim of this paper is to research the jamming vulnerability of existing maritime receivers and to understand if an upgrade to a multi-constellation or multi-frequency receiver would improve system resilience. The novelty of this work is a comparison of jamming resilience between different combinations of multiple constellations (GPS and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS)) and multi-frequency Global Navigation Satellite System (GNSS) signals. This paper presents results from GNSS jamming trials conducted in the northern part of Norway, confirming previous research and indicating that typical maritime GPS receivers are easy to jam and may produce erroneous positional information. Results demonstrate that the single frequency multi-constellation receivers offer better jamming resilience than multi-frequency (L1 + L2) GPS receivers. Further, the GLONASS constellation demonstrated a better resilience than GPS. Results demonstrate a known correlation between GPS L1 and L2 frequencies, as well as a probable over-dependence on GPS for signal acquisition, meaning that no signal can be received without GPS L1 present. With these limitations in mind, the authors suggest that the most economic update to the single frequency GPS receivers, currently used for maritime applications, should be multi-constellation GPS + GLONASS receivers. This solution is cheaper and it also offer better jamming resistance for close to shore navigation than dual frequency receivers.

On biases in precise point positioning with multi-constellation and multi-frequency GNSS data

Various types of biases in Global Navigation Satellite System (GNSS) data preclude integer ambiguity fixing and degrade solution accuracy when not being corrected during precise point positioning (PPP). In this contribution, these biases are first reviewed, including satellite and receiver hardware biases, differential code biases, differential phase biases, initial fractional phase biases, inter-system receiver time biases, and system time scale offset. PPP models that take account of these biases are presented for two cases using ionosphere-free observations. The first case is when using primary signals that are used to generate precise orbits and clock corrections. The second case applies when using additional signals to the primary ones. In both cases, measurements from single and multiple constellations are addressed. It is suggested that the satellite-related code biases be handled as calibrated quantities that are obtained from multi-GNSS experiment products and the fractional phase cycle biases obtained from a network to allow for integer ambiguity fixing. Some receiver-related biases are removed using between-satellite single differencing, whereas other receiver biases such as inter-system biases are lumped with differential code and phase biases and need to be estimated. The testing results show that the treatment of biases significantly improves solution convergence in the float ambiguity PPP mode, and leads to ambiguity-fixed PPP within a few minutes with a small improvement in solution precision.

On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of $$\mathcal {S}$$ S -system theory

The concept of integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) relies on appropriate network information for the parameters that are common between the single-receiver user that applies and the network that provides this information. Most of the current methods for PPP-RTK are based on forming the ionosphere-free combination using dual-frequency Global Navigation Satellite System (GNSS) observations. These methods are therefore restrictive in the light of the development of new multi-frequency GNSS constellations, as well as from the point of view that the PPP-RTK user requires ionospheric corrections to obtain integer ambiguity resolution results based on short observation time spans. The method for PPP-RTK that is presented in this article does not have above limitations as it is based on the undifferenced, uncombined GNSS observation equations, thereby keeping all parameters in the model. Working with the undifferenced observation equations implies that the models are rank-deficient; not all parameters are unbiasedly estimable, but only combinations of them. By application of $$\mathcal {S}$$ -system theory the model is made of full rank by constraining a minimum set of parameters, or S-basis. The choice of this S-basis determines the estimability and the interpretation of the parameters that are transmitted to the PPP-RTK users. As this choice is not unique, one has to be very careful when comparing network solutions in different $$\mathcal {S}$$ -systems; in that case the S-transformation, which is provided by the $$\mathcal {S}$$ -system method, should be used to make the comparison. Knowing the estimability and interpretation of the parameters estimated by the network is shown to be crucial for a correct interpretation of the estimable PPP-RTK user parameters, among others the essential ambiguity parameters, which have the integer property which is clearly following from the interpretation of satellite phase biases from the network. The flexibility of the $$\mathcal {S}$$ -system method is furthermore demonstrated by the fact that all models in this article are derived in multi-epoch mode, allowing to incorporate dynamic model constraints on all or subsets of parameters.

Relative Ionospheric Ranging Delay in LEO GNSS Oceanic Reflections

Global Navigation Satellite System (GNSS) reflectometry leverages signals of opportunity to remotely sense the Earth's surface for a variety of science investigations. However, ionospheric refraction affects GNSS reflections detected at low Earth orbit (LEO). While multifrequency GNSS enables the elimination of most of the ionospheric error, single-frequency missions are still susceptible to this ranging delay. Motivated by the planned launch of Cyclone GNSS (CYGNSS) in 2016, a single-frequency reflectometry mission, this letter presents a simulation of the relative ionospheric delay that will shift the Delay-Doppler Map (DDM) data product. A mathematical model is presented that defines and characterizes signal propagation delay in the DDM. The model differentiates direct and reflected signals as a sum of path lengths, atmospheric refraction effects, and noise. We simulate representative ionospheric delays from the model associated with the direct and reflected ray paths as a function of satellite elevation angle, latitude, and solar activity. Simulation using the International Reference Ionosphere 2007 shows that differential ionospheric content is inversely proportional to satellite elevation angle and that low latitudes present larger ionospheric impacts on the reflected signals. Finally, high solar activity conditions lift the ionospheric density profile to and possibly above the CYGNSS orbit altitude of 500 km. The ionospheric delay will not generally affect the estimation of wind speed but may affect the CYGNSS signal acquisition and open loop tracking process. Implications of the ionospheric delay in other GNSS reflectometry applications are also discussed.

Eliminating diffraction effects during multi-frequency correction in global navigation satellite systems

In the geometrical optics approximation, the ionospheric part of error in measuring phase and code delays of the satellite signal may be represented as a rapidly decreasing series in inverse power of frequency. Such a simple frequency dependence allows us to use multi-frequency measurements for eliminating the error in such multi-frequency Global Navigation Satellite Systems as GPS, GLONASS, BeiDou, and Galileo. However, the elimination of errors is handicapped by diffraction effects during signal propagation through turbulent ionospheric plasma. The numerical simulation has shown that when using the spatial processing in the form of Fresnel inversion the transition from dual-frequency to triple-frequency measurements reduces the average error of measurement. Yet fluctuations of the error diminish only if the inner scale exceeds the Fresnel radius. In the opposite case of excess of the Fresnel radius over the inner scale, the random component of the residual error is growing during the transition to triple-frequency measurements. The numerical simulation results also suggest that the Fresnel spatial processing in dual-frequency measurements at the optimal distance to the virtual screen can reduce the average error from centimeter to submillimeter level, which renders the transition to triple-frequency measurements unnecessary. The study of the residual error dependence on the distance from the virtual screen to the observer has revealed that the optimum value of this distance may be found from the minimum condition of amplitude scintillation index of the processed signal. The signal thus processed may be utilized both in geodetic precise measurements and in diagnostics of the lower atmosphere.

Influence of Ionospheric Irregularities on GNSS Remote Sensing

We have used numerical simulation to study the effects of ionospheric irregularities on accuracy of global navigation satellite system (GNSS) measurements, using ionosphere-free (in atmospheric research) and geometry-free (in ionospheric research) dual-frequency phase combinations. It is known that elimination of these effects from multifrequency GNSS measurements is handi-capped by diffraction effects during signal propagation through turbulent ionospheric plasma with the inner scale being smaller than the Fresnel radius. We demonstrated the possibility of reducing the residual ionospheric error in dual-frequency GNSS remote sensing in ionosphere-free combination by Fresnel inversion. The inversion parameter, the distance to the virtual screen, may be selected from the minimum of amplitude fluctuations. This suggests the possibility of improving the accuracy of GNSS remote sensing in meteorology. In the study of ionospheric disturbances with the aid of geometry-free combination, the Fresnel inversion eliminates only the third-order error. To eliminate the random TEC component which, like the measured average TEC, is the first-order correction, we should use temporal filtering (averaging).

Development of low-cost spaceborne multi-frequency GNSS receiver for navigation and GNSS remote sensing

This paper describes the development of a new generation of low-cost spaceborne multi-frequency global navigation satellite systems (GNSS) receivers for navigation and GNSS remote sensing applications. The spaceborne GNSS receiver-remote sensing instrument (SGR-ReSI) uses reflectometry to gather data, which may be used to derive information about the Earth: ocean, atmosphere, land, snow and ice. First, a review of the GNSS remote sensing including GNSS-reflectometry and radio occultation is presented. Then, the science and operational needs of GNSS receivers for the remote sensing of ocean, atmosphere, land, snow and ice are discussed. The design and development of a new generation of low-cost spaceborne multi-frequency GNSS receivers for navigation and GNSS remote sensing are described. Detailed results and designs of dual-band antennas and arrays for navigation, radio occultation and GNSS-reflectometry are presented. GNSS receiver designs, including both the software and hardware, are also explained. The processing algorithms and modelling techniques are described. Some initial results are also illustrated. This paper ends with discussions of future flight opportunities and a conclusion.

A-PPP: Array-Aided Precise Point Positioning With Global Navigation Satellite Systems

In this paper, the global navigation satellite system (GNSS) precise point positioning (PPP) concept is generalized to array-aided PPP (A-PPP). A-PPP is a measurement concept that uses GNSS data, from multiple antennas in an array of known geometry, to realize improved GNSS parameter estimation (position, attitude, time and atmospheric delays). The concept is formulated such that it applies to each current and future multifrequency GNSS, stand-alone or in combination. A-PPP is made possible through solving a novel orthonormality-constrained multivariate (mixed) integer least-squares problem. It is shown that the integer matrix constraint is necessary to obtain a precise instantaneous attitude- and position solution, whereas the inclusion of the orthonormality constraint in the integer ambiguity objective function is essential to achieve high instantaneous probabilities of correct integer estimation. Different A-PPP applications are discussed, with their performances illustrated by means of empirical GPS results.

Sensing the Earth using Global Navigation Satellite System signals

International Workshop on GNSS Remote Sensing for Future Missions and Sciences; Shanghai, China, 7–9 August 2011 The Global Navigation Satellite System (GNSS) has been widely used in navigation, positioning, and geoscience applications. Recently, the versatility of GNSS as a new remote sensing tool has been demonstrated with the use of refracted, reflected, and scattered GNSS signals to sound the atmosphere and ionosphere, ocean, land surfaces (including soil moisture), and cryosphere. Existing GPS radio occultation (RO) missions—e.g., the U.S.‐Argentina SAC‐C, German Challenging Minisatellite Payload (CHAMP), U.S.‐Germany Gravity Recovery and Climate Experiment (GRACE), Taiwan‐U.S. Formosa Satellite Mission‐3/Constellation Observing System for Meteorology, Ionosphere, and Climate (FORMOSAT‐3/COSMIC) satellites, German TerraSAR‐X satellite, and European MetOp—together with groundbased GNSS observations, have provided precise and high‐resolution information on tropospheric water vapor, pressure, temperature, tropopause parameters, ionospheric total electron content, and electron density profiles. GNSS signals reflected from the ocean and land surface can determine the ocean height, ocean surface wind speed and wind direction, soil moisture, and ice and snow thickness. With improvement expected due to the next generation of multifrequency GNSS systems and receivers, and new space‐based instruments tracking GNSS reflected and refracted signals, new scientific applications of GNSS are expected in the near future across a number of environmental remote sensing fields.

Real-time cycle slip detection in triple-frequency GNSS

The modernization of the global positioning system and the advent of the European project Galileo will lead to a multifrequency global navigation satellite system (GNSS). The presence of new frequencies introduces more degrees of freedom in the GNSS data combination. We define linear combinations of GNSS observations with the aim to detect and correct cycle slips in real time. In particular, the detection is based on five geometry-free linear combinations used in three cascading steps. Most of the jumps are detected in the first step using three minimum-noise combinations of phase and code observations. The remaining jumps with very small amplitude are detected in the other two steps by means of two-tailored linear combinations of phase observations. Once the epoch of the slip has been detected, its amplitude is estimated using other linear combinations of phase observations. These combinations are defined with the aim of discriminating between the possible combinations of jump amplitudes in the three carriers. The method has been tested on simulated data and 1-second triple-frequency undifferenced GPS data coming from a friendly multipath environment. Results show that the proposed method is able to detect and repair all combinations of cycle slips in the three carriers.

Potentialities of multifrequency ionospheric correction in Global Navigation Satellite Systems

The first-order ionospheric error is reduced in the dual-frequency Global Navigation Satellite Systems (GNSS). In this paper, the possibility of eliminating ionospheric higher-order errors in the multifrequency GNSS is explored. Since the second-order error associated with the geomagnetic field effect on the refractive index can be eliminated in dual-frequency measurements, we explore the possibility of eliminating third-order errors in triple-frequency GNSS in view of phase scintillations. A connection between the possibility of improving the multifrequency GNSS accuracy and diffraction effects in radio signal propagation through the randomly inhomogeneous ionosphere is shown. The numerical simulation has revealed that the systematic, residual ionospheric error is considerably reduced when we pass on from dual-frequency to triple-frequency measurements. The change in the residual error variance during such a transition depends however on the relationship between the inner scale of the turbulent spectrum of ionospheric irregularities and the Fresnel radius. Given the inner scale larger than the Fresnel radius, not only the systematic error, but also the standard deviation reduces when we pass on from dual-frequency to triple-frequency measurements. Otherwise, when the Fresnel radius exceeds the inner scale, the variance increases with increasing number of frequencies in use.

ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models

Successful carrier phase ambiguity resolution is the key to high-precision positioning with Global Navigation Satellite Systems (GNSS). The ambiguity dilution of precision (ADOP) is a well-known scalar measure which can be used to infer the strength of the GNSS model for carrier phase ambiguity resolution. In this contribution we present analytical closed-form expressions for the ADOP. This will be done for a whole class of different multi- frequency single baseline models. These models include the geometry-fixed, the geometry-free and the geometry-based models, respectively. And within the class of geometry-based models, we discriminate between short and long observation time spans, and between stationary and moving receivers. The easy-to-use ADOP expressions can be applied to infer the contribution of various GNSS model factors. They comprise, for instance, the type, the number and the precision of the GNSS observations, the number and selection of frequencies, the presence of atmospheric disturbances, the length of the observation time span and the length of the baseline.