Double-differenced Ambiguities Research Articles

Improving integrated precise orbit determination of GPS, GLONASS, BDS and Galileo through integer ambiguity resolution

The China Satellite Navigation Office announced on December 27, 2018 that the BDS-3 preliminary system had been completed to provide global services. Before this, GPS and GLONASS were the only two global navigation satellite systems (GNSS) supporting global positioning service, and have totally more than 50 satellites in normal operation. Furthermore, Galileo is intending to reach its full constellation around 2020. By that time, the number of available GNSS satellites will increase to more than 100, which brings both opportunities and challenges for high-precision positioning and orbit determination. The precision of orbits could be significantly improved through integer ambiguity resolution (AR), while AR is particularly difficult to achieve especially for GLONASS and BDS due to inter-frequency biases and satellite-induced code biases. Therefore, to address this limitation and further enhance the precision of multi-GNSS orbit determination, we try to fix the double-differenced intra-system ambiguities to integers and propose an integer AR method for multi-GNSS POD. To verify the contribution of AR, an experiment of 141 sites with global coverage is conducted. The results imply that the approach realizes an average fixing rate of 98.1%, 96.4%, 84.6% and 92.6% for GPS, GLONASS, BDS and Galileo over a whole year. The GNSS orbits are further improved with AR in terms of the precision compared with the International GNSS Service (IGS) final orbits, the discontinuity at overlapping day boundaries, and satellite laser ranging residuals. Thus, the integer AR improves the precision of multi-GNSS precise orbit determination, which can enhance integrated data processing of multi-GNSS and their applications in the future.

Multi-GNSS Relative Positioning with Fixed Inter-System Ambiguity

In multi-GNSS cases, two types of Double Difference (DD) ambiguity could be formed including an intra-system ambiguity and an inter-system ambiguity, which are identified as the DD ambiguity between satellites from the same and from different GNSS systems, respectively. We studied the relative positioning methods using intra-system DD observations and using Un-Difference (UD) observations, and developed a frequency-free approach for fixing inter-system ambiguity based on UD observations for multi-GNSS positioning, where the inter-system phase bias is calculated with the help of a fixed Single-Difference (SD) ambiguity. The consistency between the receiver-end uncalibrated phase delays (RUPD) and the SD ambiguity were investigated and the positioning performance of this new approach was assessed. The results show that RUPD could be modeled as a constant if the receiver were tracking satellites continuously. Furthermore, compared to the method using DD observations with only an intra-system DD ambiguity fixed, the new ambiguity fixing approach has a better performance, especially in hard environments with a large cut-off angle or serve signal obstructions.

Multi-dimensional particle filter-based estimation of inter-system phase biases for multi-GNSS real-time integer ambiguity resolution

In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm.

An improved RTK model adding double-differenced observations between different frequencies

This study has developed an improved real-time kinematic (RTK) algorithm by adding the double-differenced (DD) observations between L1 and L2 frequencies. It also introduces new biases between the frequencies to recover the integer of the DD ambiguities. The validations show that the new bias between the frequencies is stable and can be estimated as a constant in the same reference period. Compared with the standard RTK method, the new RTK model increased the observation number. The availability and reliability is thus greatly improved, especially in environmental conditions unsuitable for observation, and in which the observed satellite number is small.

Introduction of the Double-Differenced Ambiguity Resolution into Precise Point Positioning

According to the advantages of the precise point positioning (PPP) and the double-differenced (DD) model based algorithm, a new method for the integration of DD integer ambiguity resolution into PPP is presented. This method uses the undifferenced ambiguity estimated with PPP computation and the DD ambiguity generated from the DD model based algorithm to realize the PPP ambiguity fixing. In the presented method, the selection of the undifferenced ambiguity bases on the ratio test of the DD ambiguity and the ratio values based weight is used in PPP processing. This ensures the quality of the used undifferenced ambiguity. To validate the presented method, two experiments are implemented using the ten days (11 to 20 August 2014) data from local and regional reference stations and the moved two receivers. The results of the presented strategy show that improvements are achieved in all three coordinate components. The 1-h, 2-h, and 4-h PPP results indicate that the mean relative improvements were about 19%, 18%, and 15% for north, east, and up components. These results also show that prominent improvements of 29%, 31%, and 25% for north, east, and up components were obtained when the ratio values based weight was used. The application of the presented method in the displacement monitoring was implemented with the experiment and it showed that the PPP estimation computed with the presented strategy benefits local or regional displacement monitoring and improves the detecting ability for displacement.

RTK model and positioning performance analysis using Galileo four-frequency observations

This paper proposes a real-time kinematic (RTK) model that uses one common reference satellite for the Galileo system with four frequency observations. In the proposed model, the double-differenced (DD) pseudorange and carrier phase biases among the different frequencies are estimated as unknown parameters to recover the integer features of the DD ambiguities among the different frequencies for ambiguity resolution and precise positioning. Analysis results show that the E5a, E5b, and E5 frequencies have virtually the same performance in terms of the positioning accuracy, observation residuals, and ratio values of ambiguity resolution. However, the E1 frequency performs worse than the E5a, E5b, and E5 frequencies. The RTK results for the combination of multiple frequencies are much better than those for a single-frequency observation, the coordinates’ standard deviation is improved about 20–30%, and the ambiguity fix time is improved about 10%.

An Improved PSO Algorithm and Its Application in GNSS Ambiguity Resolution

In this study, we proposed a novel method for global navigation satellite system (GNSS) ambiguity resolution (AR). The proposed method utilizes an improved particle swarm optimization (IPSO) algorithm to obtain the GNSS integer ambiguity with the double differenced (DD) float resolution and its corresponding covariance matrix. First, we introduced population maturity to the standard PSO (SPSO) algorithm for the adaptive adjustment of inertia weight. Next, to improve the global convergence and robustness of the SPSO algorithm, we adopted population classification and constructed a Gauss mutation for the particle evolution process of the optimal population. Then, we applied the IPSO algorithm in the field of GNSS AR, called IPSO–AR. Finally, we evaluated the performance of the IPSO–AR algorithm under different DD ambiguity float resolutions with various dimensions and precisions. Numerical results showed that compared with the SPSO–AR algorithm, the IPSO–AR algorithm has a superior correct rate, but low efficiency. Under the appropriate parameter settings, the efficiency of the IPSO–AR algorithm is mainly dependent on the dimensions of DD ambiguity, whereas the correct rate of the IPSO–AR algorithm is mainly dependent on the precision of DD ambiguity. The proposed IPSO–AR algorithm has potential applications under the conditions of few visible satellites or constrained baseline length.

Improvements on the particle-filter-based GLONASS phase inter-frequency bias estimation approach

The carrier phase inter-frequency bias (IFB) of GLONASS between receivers of different types is usually not zero. This bias must be estimated and removed in data processing so that the integer double difference (DD) ambiguities can be fixed successfully. Recently, the particle filter approach has been proposed to estimate the IFB rate in real time. In this approach, the IFB rate samples are first generated and used to correct the phase IFB in the GLONASS observations. Then, the weights of the rate samples are updated with a function related to RATIO which is for ambiguity acceptance testing in integer ambiguity resolution. Afterwards, the IFB rate is estimated according to the weighted particles. This approach can estimate IFB accurately with short convergence time and without prior information. However, when the system noise is set too low, the estimated results are unstable due to the serious problem of particle diversity-loss, even though the system model is accurate. Additionally, the computational burden is dependent on the number of particles, which has to be optimized for the computation at hand. Therefore, this study proposes two improvements for the IFB estimation in regard to the above two aspects. The first improvement is to solve the noise setting problem by employing a regularized particle filter (RPF). The second improvement optimizes the number of particles in the resampling step according to the standard deviation (STD) of the weighted particles via a controlling function. The two improvements result in significantly better performances. The regularization method allows for the system noise to be set as zero without disturbing the estimates, and consequently, more precise estimates can be achieved. In addition, the approach using the controlling function for adapting the number of particles has comparable performance in precision but the computation load is largely reduced.

Estimation of satellite position, clock and phase bias corrections

Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.

A Model for Combined GPS and BDS Real-Time Kinematic Positioning using one Common Reference Ambiguity

This paper proposes a model for combined Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) Real-Time Kinematic (RTK) positioning. The approach uses only one common reference ambiguity, for example, that of GPS L1, and estimates the pseudo-range and carrier phase system and frequency biases. The validations show that these biases are stable during a continuous reference ambiguity period and can be easily estimated, and the other estimated double-differenced ambiguities, such as those of GPS L2, BDS L1, and BDS L2, are not affected. Therefore, our approach solves the problems of a frequently changing reference satellite. In addition, because all the carrier phase observations use the same reference ambiguity, a relationship is established between the different systems and frequencies, and the strength of the combined model is thus increased.

Triple-Frequency Code-Phase Combination Determination: A Comparison with the Hatch-Melbourne-Wübbena Combination Using BDS Signals

Considering the influence of the ionosphere, troposphere, and other systematic errors on double-differenced ambiguity resolution (AR), we present an optimal triple-frequency code-phase combination determination method driven by both the model and the real data. The new method makes full use of triple-frequency code measurements (especially the low-noise of the code on the B3 signal) to minimize the total noise level and achieve the largest AR success rate (model-driven) under different ionosphere residual situations (data-driven), thus speeding up the AR by directly rounding. With the triple-frequency Beidou Navigation Satellite System (BDS) data collected at five stations from a continuously-operating reference station network in Guangdong Province of China, different testing scenarios are defined (a medium baseline, whose distance is between 20 km and 50 km; a medium-long baseline, whose distance is between 50 km and 100 km; and a long baseline, whose distance is larger than 100 km). The efficiency of the optimal code-phase combination on the AR success rate was compared with that of the geometry-free and ionosphere-free (GIF) combination and the Hatch-Melbourne-Wübbena (HMW) combination. Results show that the optimal combinations can always achieve better results than the HMW combination with B2 and B3 signals, especially when the satellite elevation angle is larger than 45°. For the wide-lane AR which aims to obtain decimeter-level kinematic positioning service, the standard deviation (STD) of ambiguity residuals for the suboptimal combination are only about 0.2 cycles, and the AR success rate by directly rounding can be up to 99%. Compared with the HMW combinations using B1 and B2 signals and using B1 and B3 signals, the suboptimal combination achieves the best results in all baselines, with an overall improvement of about 40% and 20%, respectively. Additionally, the STD difference between the optimal and the GIF code-phase combinations decreases as the baseline length increases. This indicates that the GIF combination is more suitable for long baselines. The proposed optimal code-phase combination determination method can be applied to other multi-frequency global navigation satellite systems, such as new-generation BDS, Galileo, and modernized GPS.

Determining inter-system bias of GNSS signals with narrowly spaced frequencies for GNSS positioning

Relative positioning using multi-GNSS (global navigation satellite systems) can improve accuracy, reliability, and availability compared to the use of a single constellation system. Intra-system double-difference (DD) ambiguities (ISDDAs) refer to the DD ambiguities between satellites of a single constellation system and can be fixed to an integer to derive the precise fixed solution. Inter-system ambiguities, which denote the DD ambiguities between different constellation systems, can also be fixed to integers on overlapping frequencies, once the inter-system bias (ISB) is removed. Compared with fixing ISDDAs, fixing both integer intra- and inter-system DD ambiguities (IIDDAs) means an increase of positioning precision through an integration of multiple GNSS constellations. Previously, researchers have studied IIDDA fixing with systems of the same frequencies, but not with systems of different frequencies. Integer IIDDAs can be determined from single-difference (SD) ambiguities, even if the frequencies of multi-GNSS signals used in the positioning are different. In this study, we investigated IIDDA fixing for multi-GNSS signals of narrowly spaced frequencies. First, the inter-system DD models of multi-GNSS signals of different frequencies are introduced, and the strategy for compensating for ISB is presented. The ISB is decomposed into three parts: 1) a float approximate ISB number that can be considered equal to the ISB of code pseudorange observations and thus can be estimated through single point positioning (SPP); 2) a number that is a multiple of the GNSS signal wavelength; and 3) a fractional ISB part, with a magnitude smaller than a single wavelength. Then, the relationship between intra- and inter-system DD ambiguity RATIO values and ISB was investigated by integrating GPS L1 and GLONASS L1 signals. In our numerical analyses with short baselines, the ISB parameter and IIDDA were successfully fixed, even if the number of observed satellites in each system was small.

Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases

Double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can be fixed to integers if the associated differential inter-system biases (DISBs) are well known. In this case, only one common pivot satellite is sufficient for inter-system ambiguity resolution. This will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning especially when only a few satellites are observed. However, for GPS and current operational BDS-2, there are no overlapping frequencies. Due to the influence of different frequencies, the inter-system DD ambiguities still cannot be fixed to integers even if the DISBs are precisely known. In this contribution, we present an inter-system differencing model for combined GPS and BDS single-frequency RTK positioning through real-time estimation of DISBs. The stability of GPS L1 and BDS B1 DISBs is analyzed with different receiver types. Along with parameterization and using the short-term stability of DISBs, the DD ambiguities between GPS and BDS pivot satellites and the between-receiver single-difference ambiguity of the GPS pivot satellite can be estimable jointly with the differential phase DISB term from epoch to epoch. Then the inter-system differencing model can benefit from the near time-constant DISB parameters and thus has better multi-epoch positioning performance than the classical intra-system differencing model. The combined GPS and BDS single-frequency RTK positioning performance is evaluated with various simulated satellite visibilities. It will be shown that compared with the classical intra-system differencing model, the proposed model can effectively improve the positioning accuracy and reliability, especially for severely obstructed situations with only a few satellites observed.

Instantaneous BDS + GPS undifferenced NRTK positioning with dynamic atmospheric constraints

As the Chinese BeiDou Navigation Satellite System (BDS) has become operational in the Asia-Pacific region, it is important to better understand and demonstrate the benefits of combining triple-frequency BDS with dual-frequency GPS observations for network-based real-time kinematic (NRTK) services. Undifferenced NRTK is a new NRTK service mode, it extends the concept of NRTK by not requiring reference station and specified reference satellite at the rover processing. In order to realize the undifferenced NRTK service, a strategy for real-time modeling the undifferenced (UD) augmentation information is given, in which the fixed double-differenced ambiguities are transformed into UD ones with the help of datum settings. Since this strategy is insensitive to existing ephemeris products, it is applicable to the services of current BDS regional reference networks. Furthermore, a processing scheme for ambiguity resolution (AR) with arbitrary-frequency observations is also presented in detail. An instantaneous and reliable BDS + GPS positioning service can be provided to the rovers in undifferenced NRTK processing mode. With the data collected at 31 stations from a continuously operating reference station network in Guangdong Province (GDCORS) of China, the efficiency of the proposed approaches using combined BDS and GPS observations is confirmed. For three rover stations during days 327–329, a total of 12,960 1-min tests were performed separately to demonstrate the performance of AR. Thanks to the dynamically refined priori information of residual tropospheric and ionospheric error, and the availability of more satellites and observations, the AR fixing rates of combined BDS and GPS systems improve by 13 to 65%, compared with those of the GPS-only system using the traditional WL-L1-IF scheme. The positioning accuracy has also significantly improved.

An improved method for multi-GNSS baseline processing using single difference

The rapid development of multi-GNSS (Global Navigation Satellite System) constellations has provided numerous benefits for common PNT (Positioning, Navigation and Timing) services. Generally, DD (Double Difference) observations are used in GNSS baseline processing. However, in traditional DD data processing methods, DD observations are normally not formed between different GNSS systems or the inter-system DD ambiguities are rather difficult to be resolved due to the different wavelength. As a result, DD observations are normally formed in each system or their inter-system ambiguities are left unresolved, which could not be regarded as the optimal baseline processing methods for multi-GNSS. This paper presents an improved algorithm for multi-GNSS short baseline processing where SD (Single Difference) rather than DD observations are formed between two receivers and this method is found to be equivalent to the ideal DD method with inter-system DD observations and resolved inter-system DD ambiguities. Furthermore, an average approach and linear model are proposed to isolate the receiver-dependent Uncalibrated Phase Delays (UPDs) from the SD ambiguities for CDMA (Code Division Multiple Access) and FDMA (Frequency Division Multiple Access) GNSS systems, respectively, to address ambiguity resolution. Experiments show that after removing the UPDs derived by the proposed methods, the fractional parts of the residuals for almost all ambiguities are less than 0.1 cycles for the GPS, BDS, GLONASS and Galileo systems, which confirms the validity of our UPD calibration methods. Experiments also show that the mean differences between the daily solutions derived by GAMIT and the 4-h solutions derived by the proposed SD method are approximately −0.12, −0.33, 1.04 and 0.31cm in the north, east, up and length components, respectively. We also find that the baseline repeatability of the new SD method outperforms that of the DD method with only DD observations formed in each GNSS system by 36% and 26% in the north and up directions, respectively. These improvements are more significant in environments with poor observation conditions. An improvement of 40% and 30% in the north and up directions are, respectively, found when only 5GPS and 4 BDS satellites are available. Therefore, more reliable and precise baselines can be derived with our new baseline processing method in multi-GNSS cases.

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

An inter-system differencing model between two Global Navigation Satellite Systems (GNSS) enables only one reference satellite for all observations. If the associated differential inter-system biases (DISBs) are priori known, double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can also be fixed to integers. This can provide more redundancies for the observation model, and thus will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning. However, for Global Positioning System (GPS) and the regional BeiDou Navigation Satellite System (BDS-2), there are no overlapping frequencies. Tight combination of GPS and BDS needs to process not only the DISBs but also the single-difference ambiguity of the reference satellite, which is caused by the influence of different frequencies. In this paper, we propose a tightly combined dual-frequency GPS and BDS RTK positioning model for medium baselines with real-time estimation of DISBs. The stability of the pseudorange and phase DISBs is analyzed firstly using several baselines with the same or different receiver types. The dual-frequency ionosphere-free model with parameterization of GPS-BDS DISBs is proposed, where the single-difference ambiguity is estimated jointly with the phase DISB parameter from epoch to epoch. The performance of combined GPS and BDS RTK positioning for medium baselines is evaluated with simulated obstructed environments. Experimental results show that with the inter-system differencing model, the accuracy and reliability of RTK positioning can be effectively improved, especially for the obstructed environments with a small number of satellites available.

GLONASS inter-frequency phase bias rate estimation by single-epoch or Kalman filter algorithm

GLONASS double-differenced (DD) ambiguity resolution is hindered by the inter-frequency bias (IFB) in GLONASS observation. We propose a new algorithm for IFB rate estimation to solve this problem. Although the wavelength of the widelane observation is several times that of the L1 observation, their IFB errors are similar in units of meters. Based on this property, the new algorithm can restrict the IFB effect on widelane observation within 0.5 cycles, which means the GLONASS widelane DD ambiguity can be accurately fixed. With the widelane integer ambiguity and phase observation, the IFB rate can be estimated using single-epoch measurements, called the single-epoch IFB rate estimation algorithm, or using the Kalman filter to process all data, called the Kalman filter-based IFB rate estimation algorithm. Due to insufficient accuracy of the IFB rate estimated from widelane observations, the IFB rate has to be further refined with L1 and L2 observations. A new reference satellite selection method is proposed to serve the IFB rate estimation. The experiment results show that the IFB rates on L1 and L2 bands are different, that an accurate IFB rate will help us to obtain more fixed solutions at places with serious occlusion, that the single-epoch IFB rate estimation algorithm can meet the requirements for real-time kinematic positioning with only 8% extra computational time, and that the Kalman filter-based IFB rate estimation algorithm is a satisfactory option for high-accuracy GLONASS positioning.

Improved single‐epoch single‐frequency Par Lambda algorithm with baseline constraints for the BeiDou Navigation Satellite System

A new single-epoch single-frequency algorithm based on partial least-squares ambiguity decorrelation adjustment (Par Lambda) that employs baseline constraints is developed for BeiDou Navigation Satellite System (BDS) called Improved Par Lambda, based on the characteristics of building deformation monitoring. The floating solution of double-difference ambiguities is obtained by means of double-difference observations and least-squares method. The double-difference observation equations with baseline length constraint are composed of the equations of BDS single-frequency pseudo-range observations and carrier phase observations and the baseline length constraint equation. The least-squares principle is used to compute floating solution of double-difference ambiguities and the corresponding cofactor matrix. Based on the precision of double-difference ambiguities, the ambiguities will be divided into different levels (2, 1, 1,..., 1) and then be fixed based on the Lambda method progressively. The 1, 5 and 10 s short baseline data of BDS single-epoch single-frequency based on B 1 band carrier phase were computed through this method. The results showed that, for BDS single-epoch single-frequency, the success rate and the search efficiency of fixing ambiguities of Improved Par Lambda were all better than the traditional methods and the success rate was more than 98%.

The study and realization of BDS un-differenced network-RTK based on raw observations

A BeiDou Navigation Satellite System (BDS) Un-Differenced (UD) Network Real Time Kinematic (URTK) positioning algorithm, which is based on raw observations, is developed in this study. Given an integer ambiguity datum, the UD integer ambiguity can be recovered from Double-Differenced (DD) integer ambiguities, thus the UD observation corrections can be calculated and interpolated for the rover station to achieve the fast positioning. As this URTK model uses raw observations instead of the ionospheric-free combinations, it is applicable for both dual- and single-frequency users to realize the URTK service. The algorithm was validated with the experimental BDS data collected at four regional stations from day of year 080 to 083 in 2016. The achieved results confirmed the high efficiency of the proposed URTK for providing the rover users a rapid and precise positioning service compared to the standard NRTK. In our test, the BDS URTK can provide a positioning service with cm level accuracy, i.e., 1cm in the horizontal components, and 2–3cm in the vertical component. Within the regional network, the mean convergence time for the users to fix the UD ambiguities is 2.7s for the dual-frequency observations and of 6.3s for the single-frequency observations after the DD ambiguity resolution. Furthermore, due to the feature of realizing URTK technology under the UD processing mode, it is possible to integrate the global Precise Point Positioning (PPP) and the local NRTK into a seamless positioning service.

IRNSS/NavIC L5 Attitude Determination.

The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) become fully-operational and has been provided with the operational name of NavIC (Navigation with Indian Constellation). It has been developed by the Indian Space Research Organization (ISRO) with the objective of offering positioning, navigation and timing (PNT) to the users in its service area. This contribution provides for the first time an assessment of the IRNSS L5-signal capability to achieve instantaneous attitude determination on the basis of data collected in Perth, Australia. Our evaluations are conducted for both a linear array of two antennas and a planar array of three antennas. A pre-requisite for precise and fast IRNSS attitude determination is the successful resolution of the double-differenced (DD) integer carrier-phase ambiguities. In this contribution, we will compare the performances of different such methods, amongst which the unconstrained and the multivariate-constrained LAMBDA method for both linear and planar arrays. It is demonstrated that the instantaneous ambiguity success rates increase from 15% to 90% for the linear array and from 5% to close to 100% for the planar array, thus showing that standalone IRNSS can realize 24-h almost instantaneous precise attitude determination with heading and elevation standard deviations of 0.05° and 0.10°, respectively.