Peter Teunissen

During the last decade the technique of CORS-based Network RTK has been proven capable of providing cm-level positioning accuracy for rovers receiving GNSS correction data from the CORS network. The technique relies on successful integer carrier-phase ambiguity resolution at both network and user level: at the level of the CORS network, ambiguity resolution is a prerequisite in order to determine very precise atmospheric corrections for (mobile) users, while these users need to resolve their integer ambiguities (with respect to a certain CORS network master reference station) to obtain precise cm-level positioning accuracy. In case of Network RTK a user thus needs corrections from the network, plus the GNSS data of one of the CORS stations. In practice, there exists a variety of implementations of the Network RTK concept, of which VRS, FKP and MAC are best known [1, 2, 3, 4]. In this contribution we discuss a closely related concept, PPP-RTK, and show its performance on two CORS net...

This contribution addresses the effect of having a triple frequency Global Navigation Satellite System (GNSS) on ambiguity resolution of long baselines, i.e. baselines for which the differential ionospheric delays cannot be ignored. Although it is recognized that a combination of GNSS’s is more effective for integer ambiguity resolution –the key to highly accurate positioning– than the use of three frequencies, it is still of interest to investigate single GNSS triple-frequency ambiguity resolution, especially since it is expected that the quality of the code data of Galileo triplefrequency signals will be better than of current dual-frequency GPS. For this purpose we have simulated triple-frequency Galileo signals using ESA’s Galileo Signal Validation Facility for a Wide Area network of permanent stations and user stations receiving Wide Area RTK (WARTK)ionospheric corrections from this network. The three user stations are located at 100-400 km from the network’s master reference s...

SUMMARY A newly developed GNSS (Global Navigation Satellite System) carrier phase ambiguity resolution method to determine the full attitude and dynamic draught of ships is analysed. GNSS receivers placed onboard a ship can provide both absolute vertical motions relative to a fixed vertical reference on earth, to be used (in combination with nautical chart datum) to estimate the UKC (Under-Keel Clearance), and relative baseline measurements which are employed to estimate the attitude of the ship. The advantage of the GNSS-RTK (Real Time Kinematic) solution compared to other techniques (e.g. Inertial sensors) is that it is driftless and, if carrier phase observations are used, still of high accuracy. The difficulties of using such method lie mostly in the ambiguity nature of the phase observations: in order to fully exploit their higher precision compared to the code measurements, the ambiguities must be solved. To apply the RTK technique for the application of this study, it is nece...

The winner of the Journal of Spatial Science award for the Best Research and Review Paper in 2014 is for a series of two papers: First combined COMPASS/BeiDou-2 and GPS positioning results in Australia. Part I: Single-receiver and relative code-only positioning and Part II: Singleand multiplefrequency single-baseline RTK positioning. Both parts were published in Volume 59 Number 1. The Editorial Board and Taylor & Francis Group are pleased to support this award for the authors – Robert Odolinski, Peter Teunissen and Dennis Odijk. The award comprises a certificate and a cheque for AUS$750. The biography of each of the authors follows.

In the theory of integer least-squares ambiguity estimation and validation, a central role is played by the ambiguity search space. In this contribution, the significance of the volume of the ambiguity search space is discussed and analyzed. It is shown how the volume can be used as an estimate for the number of grid points inside the GPS ambiguity search space. This is done for various measurement scenarios, each characterized by the use of different types of data redundancies. For these measurement scenarios, it is also shown how the volume can be used to appropriately scale the size of the ambiguity search space. This analysis is presented in the context of the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method. In particular the low correlation and high precision of the transformed ambiguities as provided by the LAMBDA method, allow an appropriate down scaling of the search space. As a result, only a few candidate grid points are left in the ambiguity search space.

A key issue with GNSS carrier phase ambiguity resolution is that often the full set of ambiguities cannot be fixed fast and reliably. A possible strategy is then to resolve only a subset of ambiguities, one for which the probability of correct fixing, the so-called success rate, is sufficiently close to 1. However, a proper subset selection criterion is still lacking. This criterion should on the one hand guarantee an acceptably high success rate, and at the same time result in a significant performance improvement with respect to the remaining parameters, like the baseline parameters. The second requirement is important and has not yet been addressed in literature. As an extreme example consider the case where the float ambiguities are not correlated with the other float parameters. Ambiguity resolution would then be useless, since it will then not allow for an improvement of these other parameters. This indicates that resolving a subset of ambiguities (in the extreme example, an e...

In this contribution, we present and analyze datasnooping in the context of the DIA method. As the DIA method for the detection, identification and adaptation of mismodelling errors is concerned with estimation and testing, it is the combination of both that needs to be considered. This combination is rigorously captured by theDIA estimator. We discuss and analyze the DIA-datasnooping decision probabilities and the construction of the corresponding partitioning of misclosure space. We also investigate the circumstances under which two or more hypotheses are nonseparable in the identification step. By means of a theorem on the equivalence between the nonseparability of hypotheses and the inestimability of parameters, we demonstrate that one can forget about adapting the parameter vector for hypotheses that are nonseparable. However, as this concerns the complete vector and not necessarily functions of it, we also show that parameter functions may exist for which adaptation is still p...

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 m...

ABSTRACT: As an improvement over ‘conventional’ PPP, Real-Time Kinematic Precise Point Positioning (PPP-RTK) is a promising technique for high-precision (cm-level) carrier-phase based remote sensing platform positioning. The key to obtain these very precise positions is that the user should be able to resolve the ambiguities in the phase data to their integer values, as then his phase data starts to act as if they were very precise code data. In order to do so, the user needs to apply corrections to his GPS data. In addition to corrections for the satellite clocks and ionospheric delays, as with ‘conventional’ PPP, crucial to restore the integerness of the ambiguities is that the PPP-RTK user needs appropriate corrections for the satellite phase hardware biases. In our approach these corrections are determined by a regional network of CORS stations. To provide the most precise corrections to the PPP-RTK user, the corrections should be based on a solution in which the network ambigui...

Best integer equivariant (BIE) estimators provide minimum mean squared error (MMSE) solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Their accuracy is therefore always better or the same as that of Integer Least-Squares (ILS) estimators and Best Linear Unbiased Estimators (BLUEs).

One of the major problems in processing GPS phase observations is estimating the double-difference (DD) ambiguities as integers. Based on carrier phase data only, short observational time spans result in strongly correlated ambiguities and in very elongated ambiguity confidence ellipsoids. As a result the estimation of the integer least-squares ambiguities becomes an extremely time consuming task, when traditional search-methods are applied. In this contribution, it will be shown both analytically as well as numerically, that this can be explained by the distinctivediscontinuity that is present in the spectrum of conditional variances of the DD-ambiguities. In [1] a method has been introduced, that allows an efficient estimation of the integer ambiguities over short observational time spans. This method removes the discontinuity from the spectrum, thereby returning transformed ambiguities that are much less correlated and that show a dramatic improvement in precision. In this contri...

Het Global Positioning System (GPS) is een wereldwijd plaatsbepalingssysteem op basis van satellieten. De eerste plannen en ontwerpen voor het systeem dateren uit de vroege jaren zeventig in de vorige eeuw; reeds in februari van 1978 werd de eerste GPS-satelliet gelanceerd. De nominale constellatie omvat 24 satellieten, die elk in ongeveer 12 uur om de aarde cirkelen. Daardoor kunnen overal ter wereld, doorgaans minstens vier satellieten tegelijkertijd waargenomen worden. Peter Teunissen, hoogleraar mathematische geodesie en positiebepaling aan de Technische Universiteit Delft verzorgde in de zomer van 2003 colleges over Global Positioning Systems in het kader van de, door het CWI georganiseerde, vakantiecursus voor wiskundeleraren.

ABSTRACT: Global Navigation Satellite Systems (GNSS)-based attitude determination is a valuable technique for the estimation of platform orientation. Precise attitude determination using multiple GNSS receivers/antennas mounted on a remote sensing platform relies on successful resolution of the carrier phase integer ambiguities. The LAMBDA method has proven to be an efficient method to solve integer least squares problems. This method is, however, only applicable to unconstrained and/or linearly constrained models, but not to quadratically constrained models such as the GNSS attitude model. For a set of GNSS antennas rigidly mounted on a platform, a number of nonlinear geometrical constraints can be exploited for the purpose of strengthening the underlying observation model and subsequently improving the capacity of fixing the correct set of integer ambiguities. In this contribution, we describe and test the Multivariate Constrained (MC-) LAMBDA method, which effectively makes use o...

The LAMBDA method is very suitable for Multi-Carrier Ambiguity Resolution (MCAR), which is of interest with the coming of Galileo and the modernisation of GPS. Ambiguity resolution involves, however, not only integer estimation, but often also a decision on whether or not to accept the estimated integers. In this contribution, we show the relevance of this decision-step and show that integer aperture estimation is the proper theory for handling the combined integer estimation/acceptance problem. With this approach the user sets his/her own failure rate (irrespective of the strength of the underlying model), thus generating an aperture space which forms the basis of the decision process: the integer solution is chosen as output if the float solution resides inside the aperture space, otherwise the float solution is maintained. We show how the various approaches as used in the literature fit in the framework of integer aperture estimation and we also present the optimal integer apertu...

GPS ambiguity resolution is the key to fast and high precision relative GPS positioning. Since unsuccessful ambiguity resolution, when passed unnoticed, will often lead to unacceptable errors in the positioning results, very high success rates are required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower the level of the ambiguity success rate and thus increase the chance of unsuccessful ambiguity resolution. In this contribution we present a general formula that enables one to evaluate the success rates in the presence of such biases. As an example the formula is applied to the geometry-free GPS model and used to evaluate the model’s robustness against ionospheric biases. This will be shown for the single-, the dualand the future triple-frequency case.

An efficient way for the real-time GNSS data processing of CORS stations is to make use of a Kalman filter implementation. Using dual-frequency un-differenced carrier phase and code data as observations, the state vector consists of troposphere zenith delays, differential ionosphere delays, receiver and satellite clock errors and phase ambiguities. Satellite positions are computed in real time based on the predicted part of the ultrarapid IGS orbits. No receiver positions are present in the state vector since these are precisely known for permanent reference stations. In the Kalman filter time-update the float ambiguities are predicted to be constant (provided that no cycle slips occur). The integer ambiguities are then resolved by means of the LAMBDA method, but only after the precision of the float ambiguity solution has sufficiently converged.

ABSTRACT In Teunissen (1999) we introduced the class of admissible integer estimators. Members from this class are defined by their so-called pull= in regions. These pull-in regions satisfy the following three conditions. They are integer translational invariant and cover the ...

Array-aided precise point positioning (A-PPP) is a measurement concept that uses Global Navigation Satellite System (GNSS) data, from multiple antennas in an array of known geometry, to realize the improved GNSS parameter estimation. In this contribution the ambiguity resolution benefits of A-PPP for antenna-array equipped CORS stations is explored. To demonstrate the performance of array-aided ambiguity resolution between-station, an 80 km baseline experiment, equipped with a 6-antenna array at each CORS station, was conducted. We formulate the underlying model, show how the array-data to be reduced and present numerical results on the ambiguity resolution performance. The results show that the use of antenna-arrays can significantly improve the CORS network ambiguity resolution.

In this contribution we analyze the integrity of the GNSS array model through the so-called uniformly most powerful invariant (UMPI) test-statistics and their corresponding minimal detectable biases (MDBs). The model considered is characterized by multiple receivers/satellites with known coordinates where the multi-frequency carrier-phase and pseudo-range observables are subject to atmospheric (ionospheric and tropospheric) delays, receiver and satellite clock biases, as well as instrumental delays. Highlighting the role played by the model’s misclosures, analytical multivariate expressions of a few leading test-statistics together with their MDBs are studied that are further accompanied by numerical results of the three GNSSs GPS, Galileo and BeiDou.

... We also introduce a new ambiguity dilution of precision measure to express the intrinsicprecision of the ambiguities and show why it is preferred over the more traditional measures. Measurements and model ... Ambiguity dilution of precision. ...

<p><strong>G1.1 Session: Recent Developments in Geodetic Theory</strong></p><p><strong> </strong></p><p><strong>Estimability in Rank-Defect Mixed-Integer Models: Theory and Applications</strong></p><p><strong> </strong></p><p>PJG Teunissen<sup>1,2</sup></p><p><sup>1</sup>GNSS Research Centre, Curtin University, Perth, Australia</p><p><sup>2</sup>Geoscience and Remote Sensing, Delft University of Technology, The Netherlands</p><p>Email: p.teunissen@curtin.edu.au; p.j.g.teunissen@tudelft.nl</p><p><strong> </strong></p><p>Although estimability is one of the foundational concepts of todays’ estimation theory, we show that the current concept of estimability is not adequately equipped to cover the estimation requirements of mixed-integer models, for instance like those of interferometric models, cellular base transceiver network models or the carrier-phase based models of Global Navigation Satellite Systems (GNSSs). We therefore need to generalize the estimability concept to that of integer-estimability. Next to being integer and estimable in the classical sense, functions of integer parameters then also need to guarantee that their integerness corresponds with integer values of the parameters the function is taken of. This is particularly crucial in the context of integer ambiguity resolution. Would this condition not be met, then the integer fixing of integer functions that are not integer-estimable implies that one can fix the undifferenced integer ambiguities to non-integer values and thus force the model to inconsistent and wrong constraints.</p><p>In this paper we present a generalized concept of estimability and one that now also is applicable to mixed-integer models. We thereby provide the operationally verifiable necessary and sufficient conditions that a function of integer parameters needs to satisfy in order to be integer-estimable. As one of the conditions we have that estimable functions become integer-estimable if they can be unimodulair transformed to canonical form. Next to the conditions, we also show how to create integer-estimable functions and how a given design matrix can be expressed in them. We then show how these results are to be applied to interferometric models, cellular base transceiver network models and FDMA GNSS models.</p><p> </p><p><strong>Keywords: </strong>Estimability, S-system theory, Mixed-integer Models, Integer-Estimability, Admissible Ambiguity Transformation, Interferometry, Global Navigation Satellite Systems (GNSSs)</p><p> </p>

<p><strong>G1 – Geodetic Theory and Algorithms</strong></p> <p><strong>G1.3 High-precision GNSS: methods, open problems and Geoscience applications</strong></p> <p><strong> </strong></p> <p><strong>Instantaneous Ambiguity Resolved GLONASS FDMA Attitude Determination</strong></p> <p><strong> </strong></p> <p>PJG Teunissen<sup>1,2</sup>, A. Khodabandeh<sup>3</sup>, S. Zaminpardaz<sup>4</sup></p> <p><sup>1</sup>GNSS Research Centre, Curtin University, Perth, Australia</p>…

The Japanese Quasi-Zenith Satellite System (QZSS) satellite system has placed in orbit four satellites by October 2017. The Indian Regional Navigation Satellite System (IRNSS) system has launched the new satellite IRNNSS-11 in April 2018, completing seven operational satellites. Together with the GPS block IIF satellites and the Galileo satellites, four different global navigation satellite systems (GNSSs) are providing precise L5 signals on the frequency of 1176.45 MHz. In this contribution, we challenge the strength of the multi-GNSS model by analysing its single-frequency (L5), single-epoch (instantaneous) precise positioning capabilities under high-elevation masking (up to 40 degrees). With more satellites available, multi-GNSS real time kinematic (RTK) positioning is possible using L5-only signals with a high customary elevation mask. This helps to enable positioning in areas with constrained measurement geometry, and could significantly reduce the multipath effects in difficul...