Fast and reliable multi-GNSS precise point positioning with integer ambiguity resolution

Research output: ThesisDissertation (TU Delft)

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Precise Point Positioning (PPP) is a Global Navigation Satellite Systems (GNSS) modelling and processing method that provides single-receiver users with high positioning accuracy anywhere on the globe, without the explicit dependence on reference receivers. The realization of PPP is based on undifferenced code and phase measurements, a priori correction models, as well as on precise satellite orbits and clocks. Although PPP delivers highly accurate positioning results, a relatively long timespan is needed to achieve such accurate results. This long convergence time is mainly due to the presence of the carrier-phase ambiguities and ionospheric delays, and can be significantly reduced if one can do away with these unknown parameters using integer-estimation and external corrections, respectively. The integer ambiguity resolution-enabled variant of PPP, namely PPP-RTK, is the GNSS positioning mode that is capable of delivering ambiguity-resolved parameter solutions on the basis of single-receiver user data and state-space corrections, which include, next to satellite orbits and clocks, information about the satellite phase and code biases. These corrections, when properly provided from either a multi- or a single-station setup, enable recovery of the integer property of the user ambiguities, thus enabling single-receiver integer ambiguity resolution and, therefore, reduced convergence times compared to those experienced with ambiguity-float PPP. A considerable observational time span of 30-60 min is, however, still needed to integer-resolve the ambiguities with sufficiently large success rate in the presence of ionospheric delays, which cannot compete with that achieved with relative positioning techniques over short baselines. The lack of any ionospheric information necessitates that the user utilizes the ionosphere-float model – a model that treats the slant ionospheric delays as unknown parameters – that is known to be relatively weak in the sense of its ambiguity resolution capabilities. Faster ambiguity resolution and, therefore, improved convergence time are expected when such information can be provided to the user’s model. The augmentation with ionospheric information, though, requires dense network infrastructure that is often not available either because of spatial restrictions or due to the high-cost and complex operation requirements involved. In such cases, a user’s model strengthening can be alternatively substantiated through the integration of multi-constellation multi-frequency measurements. The increased number of satellites and frequencies paves the way for accelerating successful ambiguity resolution and, therefore, convergence times. Next to the rapid centimeter-level convergence that is of top priority to the users, positioning reliability is critical as well for the user performance. The commonly used practice in PPP-RTK to neglect the correctional uncertainty may have considerable effects not only on the ambiguity resolution performance but, most importantly, on the precision description the user is provided with to judge his real-time performance. To obtain the optimal positioning performance, the users need to incorporate the quality description of the corrections into their estimation process. Obviously, the PPP-RTK user positioning convergence time and reliability are still open problems. In order to overcome the aforementioned limitations, three approaches are investigated in this PhD thesis. The first method utilizes ionospheric information from regional multi-scale networks to aid the user model in increasing its redundancy, thus allowing for faster PPP-RTK ambiguity resolution. An extensive formal analysis revealed that such an acceleration would be possible only if the precision of the provided ionospheric corrections is equal to or better than 5 cm. It was observed, though, that this quality level may not be achieved with a function-based two-dimensional ionosphere model that considers a single-layer model and a slant-to-vertical mapping function. To overcome this, a methodology was introduced that uses the slant delays directly as estimated from the PPP-RTK network processing and predicts, by means of the best linear unbiased prediction framework, the slant ionospheric corrections per satellite and per epoch at the user’s location. It was shown how the user’s model needs to be extended to its ionosphere-weighted variant in order to incorporate these corrections, and how their quality can be reliably evaluated. The empirical analysis of a sufficiently large number of positioning solution samples showed that near-instantaneous centimeter-level positioning is feasible in case the corrections are provided by a small-scale network. Further analysis of networks with varying density revealed, for the first time in terms of PPP-RTK, the impact the network density has on the achieved convergence times and their linear relationship with the mean inter-station distance. Then, the approach of integrating multi-GNSS multi-frequency data, as an alternative to the ionospheric corrections augmentation, was analyzed for improving PPP-RTK convergence. The advantage of this approach compared to the previous is that it dispenses with the stringent requirement of operating a dense network infrastructure and also the necessity for the user to be located within the network’s operating range to utilize the provided ionospheric signals. A formal performance analysis of globally distributed user stations showed the impact of the increased number of satellites and frequencies on the expected ambiguity resolution and positioning performance. Although both factors bring considerable improvements, it was revealed that the satellite redundancy plays a more crucial role in speeding up the convergence time due to the improved geometry strength. Analysis of various simulated datasets revealed that the sensitivity of the user’s performance, in response to changes in the measurement precision, becomes less pronounced for multi-GNSS multi-frequency models. In addition, the impact of the number and spacing of frequencies on the multi-frequency PPP-RTK user performance was investigated, for the first time in terms of PPP-RTK. It was both formally and empirically evidenced that frequency spacing contributes to a larger extent, compared to the number of frequencies, to the user ambiguity resolution and, therefore, to the convergence times. The role of the estimable satellite code biases in multi-frequency data processing was highlighted and their impact on the achieved performance was evaluated. The positioning results using multi-frequency Galileo-plus-GPS data showed that centimeter-level positioning can be achieved almost instantaneously, even in the absence of ionospheric information. Finally, the PPP-RTK user positioning reliability was analyzed in terms of the precision description the user is provided with when the user stochastic model is misspecified. A generalized Kalman-filter was introduced that is capable of, first, rigorously processing dynamic systems when only a subset of the state-vector elements are linked in time and, second, recursively providing the actual precision in case of a misspecified stochastic model as is the case when neglecting the uncertainty of PPP-RTK corrections. Analysis of the behavior of the filter-precision indicated that the actual error-variance, in response to changes in the assumed stochastic model, is difficult to predict a priori. The effects of such a misspecification on the data quality control mechanisms was discussed and analyzed with illustrative examples. The impact of the neglected PPP-RTK correctional uncertainty on the user ambiguity resolution and positioning performance was empirically evaluated for nonzero correction latencies. It was evidenced that, apart from the reduced ambiguity success rates, the inconsideration of the corrections’ quality may lead to significant deviation between the formal and empirical positioning errors, thereby misleading the users with incorrect standard deviations. Mitigation methods were developed and their performance was numerically demonstrated for varying latency and for both single- and multi-constellation models.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Teunissen, P.J.G., Supervisor
  • Verhagen, A.A., Advisor
Award date20 Jan 2022
Print ISBNs978-94-6458-027-3
Electronic ISBNs978-94-6458-035-8
Publication statusPublished - 2022


  • Global navigation satellite systems (GNSS)
  • Precise point positioning (PPP)
  • Integer ambiguity resolution (IAR)
  • Fast convergence
  • Ionospheric corrections
  • Multi-GNSS
  • Multi-frequency
  • Stochastic model
  • Generalized Kalman-filter


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