P. J. G. Teunissen

Delft University of Technology | TU

In this contribution we consider mixed-integer least-squares problems, where the integer ambiguities a ∈ ℤ^n and real-valued parameters b ∈ ℝ^p are estimated. Both a primal and a dual formulation can be considered, with the latter concerning the ambiguity resolution process taking place into the parameters' domain. We study the p = 1 case, where an...

In this work we introduce the LAMBDA 4.0 toolbox, which provides an enhanced implementation for integer estimation, validation, and success rate evaluation. This free and open-source toolbox is a major update to LAMBDA 3.0 (2012), while it also integrates the functionalities from Ps-LAMBDA 1.0 (2013), thus respectively merging both estimation and e...

In this paper inversion-free formulae are derived for the adjustment and testing of the models of the Affine and Similarity transformation. For the Affine transformation we assume the covariance matrices of the plane coordinates in the two coordinate systems to be block diagonal with equal 2x2 blocks. The coordinate covariance structure for the Sim...

GNSS-based positioning plays an important role in safety-critical applications (e.g., automotive, aviation, shipping, rail) where positioning safety is paramount. Safety analyses typically include a probability-based formulation, such as calculating the probability that the position estimator falls outside a safety region (probability of positionin...

In this contribution, we introduce the ambiguity-resolved (AR) detector and study its distributional characteristics. The AR-detector is a new detector that lies in between the commonly used ambiguity-float (AF) and ambiguity-known (AK) detectors. As the ambiguity vector can seldomly be known completely, usage of the AK-detector is questionable as...

The geodetic method of positional data processing is usually not one of position estimation only, nor one of model testing only, but usually one in which estimation and testing are combined. The Detection, Identification and Adaptation (DIA)-estimator captures the statistical intricacies of this combination, providing a unifying framework for rigor...

In this contribution we introduce the dual mixed-integer least-squares problem and study it in relation to its primal counterpart. The dual differs from the primal formulation in the order in which the integer ambiguity vector $$a \in {\mathbb {Z}}^{n}$$ a ∈ Z n and baseline vector $$b \in {\mathbb {R}}^{p}$$ b ∈ R p are estimated. As not the ambig...

In this contribution, we introduce, in analogy to penalized ambiguity resolution, the concept of penalized misclosure space partitioning, with the goal of directing the performance of the DIA-estimator towards its application-dependent tolerable risk objectives. We assign penalty functions to each of the decision regions in misclosure space and use...

To accommodate the presence of bounded biases in mixed-integer models, Khodabandeh (2022) extended integer estimation theory by introducing a new admissible integer estimator. The estimator follows the principle of integer least squares estimation and is computed via the integer search method of BEAT. In this contribution, we present the probabilit...

PPP-RTK corrections, aiding GNSS users to achieve single-receiver integer ambiguity-resolved parameter solutions, are often estimated in a recursive manner by a provider. Such recursive, multi-epoch, estimation of the corrections relies on a set of \(\mathcal {S}\)-basis parameters that are chosen by the provider so as to make the underlying measur...

The present contribution aims to address why the stochastic model of the PPP-RTK user-filter is misspecified, and how one can limit the precision-loss associated with user parameter solutions. By developing tools for measuring the stated precision-loss under existing formulations of the user’s Kalman filter, we propose an alternative formulation th...

Statistical testing procedures employed in geodetic quality control often consist of two steps: detection and identification. In the detection step, the null hypothesis (working model) $$\mathcal {H}_0$$ ℋ 0 undergoes a validity check. If the outcome of the detection step is the rejection of $$\mathcal {H}_0$$ ℋ 0 , identification of potential sour...

In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GNSS carrier phase ambiguity residuals, thereby assuming that the GNSS data belong to the very general class of elliptically contoured (EC) distributions. Examples of distributions belonging to this class are the multivariate n...

It is common practice to use the well-known concept of the minimal detectable bias (MDB) to assess the performance of statistical testing procedures. However, such procedures are usually applied to a null and a set of multiple alternative hypotheses with the aim of selecting the most likely one. Therefore, in the DIA method for the detection, ident...

Carrier phase signals are considered among the key observations in global navigation satellite systems (GNSSs) and several other high-precision interferometric measurement systems. However, these ultra-precise measurements are not fully exploited when the integerness of their inherent ambiguities is discarded during the estimation process. Provided...

To obtain single-receiver Global Navigation Satellite System (GNSS) parameter solutions, the PPP-RTK user-filter combines measurements with time-correlated corrections that are separately computed by the filter of an external provider. The consequence of exercising such double-filtering is that the Kalman filter’s standard assumption of having unco...

In this contribution, we generalize PPP–RTK theory by allowing the transmitters to transmit on different frequencies. The generalization is based on the integer-estimability theory of Teunissen (A new GLONASS FDMA model. GPS Solutions, 2019). As the theory and associated algorithms provided are generally applicable, they apply to satellite-based ca...

Customary confidence regions do not truly reflect in the majority of our geodetic applications the confidence one can have in one’s produced estimators. As it is common practice in our daily data analyses to combine methods of parameter estimation and hypothesis testing before the final estimator is produced, it is their combined uncertainty that h...

The corrections needed to realize integer ambiguity resolution-enabled precise point positioning (PPP-RTK) at a single-receiver user are often treated as if they are deterministic quantities. The present contribution aims to study and analyze the effect the neglected uncertainty of these corrections, which are subject to time delay, has on the PPP-...

The best integer equivariant (BIE) estimator for the multivariate t-distribution was introduced in Teunissen (J Geod, 2020. https://doi.org/10.1007/s00190-020-01407-2), where it was shown that the BIE-weights will be different from that of the normal distribution. In this contribution, we analyze these BIE estimators while making use of multi globa...

Smartphone accelerometers and low-cost Global Navigation Satellite System (GNSS) equipment have faced rapid and important advancement, opening a new door to deformation monitoring applications such as landslide, plate tectonics and structural health monitoring (SHM). The precision potential and operational feasibility of the equipment play an impor...

Although ionosphere-weighted GNSS parameter estimation is a popular technique for strengthening estimator performance in the presence of ionospheric delays, no provable rules yet exist that specify the needed weighting in dependence on ionospheric circumstances. The goal of the present contribution is therefore to develop and present the ionospheri...

In this contribution, we introduce a generalized Kalman filter with precision in recursive form when the stochastic model is misspecified. The filter allows for a relaxed dynamic model in which not all state vector elements are connected in time. The filter is equipped with a recursion of the actual error-variance matrices so as to provide an easy-...

In this contribution, we extend the principle of integer bootstrapping (IB) to a vectorial form (VIB). The mathematical definition of the class of VIB-estimators is introduced together with their pull-in regions and other properties such as probability bounds and success rate approximations. The vectorial formulation allows sequential block-by-bloc...

The single-receiver integer ambiguity resolution-enabled variant of precise point positioning (PPP), namely PPP-RTK, has proven to be crucial in reducing the long convergence time of PPP solutions through the recovery of the integerness of the user-ambiguities. The proliferation of global navigation satellite systems (GNSS) supports various improve...

An assessment of standalone GLONASS RTK performance is provided using its FDMA and CDMA signals. The new integer-estimable GLONASS FDMA model (Teunissen 2019), which guarantees the integer-estimability of its ambiguities, is employed. We introduce the combined integer-estimable GLONASS FDMA+CDMA model and compare its strength against the FDMA model...

Precise point positioning (PPP) is a modeling and processing method that uses global navigation satellite system (GNSS) pseudorange and carrier‐phase observations, along with precise satellite orbit and clock products, for single‐receiver static or kinematic positioning with centimeter precision. As such it offers an attractive alternative to diffe...

In [1] a new integer-estimable GLONASS FDMA model was introduced. The new model is generally applicable and guarantees, independent of the actual channel number entries, the integer-estimability of the new GLONASS ambiguities. As the model has a close resemblance with CDMA models, available CDMA software is easily modified and existing methods of i...

The goal of this contribution is to assess the impact statistical model selection has on confidence levels of parameter estimators in linear(ized) GNSS models. In the processing of observational data, parameter estimation and statistical testing are often combined. A testing procedure is exercised to select the most likely observational model among...

The key to precise global navigation satellite system (GNSS) positioning is carrier phase integer ambiguity resolution with a high success rate. On the other hand when the success rate is too low, the user will normally prefer the float solution. The alternative can be to use the best integer equivariant (BIE) estimator, since it is optimal in the...

This contribution extends the theory of integer equivariant estimation (Teunissen in J Geodesy 77:402–410, 2003) by developing the principle of best integer equivariant (BIE) estimation for the class of elliptically contoured distributions. The presented theory provides new minimum mean squared error solutions to the problem of GNSS carrier-phase a...

A single-receiver integer ambiguity resolution-enabled precise point positioning (PPP-RTK) user experiences a long convergence time when the rather weak single-constellation dual-frequency ionosphere-float model is used. Nowadays, the rapid development of Global Navigation Satellite Systems (GNSS) provides a multitude of available satellites and fr...

In this contribution, we propose a method for statistically evaluating the risk in a deformation monitoring system. When the structure under monitoring moves beyond tolerance, the monitor system should issue an alert. Only a very small probability is acceptable of the system telling us that no change beyond a critical threshold has taken place, whi...

Ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP) are two popular scalar-diagnostics used in Global Navigation Satellite System (GNSS) positioning. Where the ADOP is a predictor for carrier-phase ambiguity resolution performance, the PDOP is meant to predict the receiver-satellite geometry’s capability for precise pos...

In safety-critical applications, deformation monitoring systems are required to issue timely alerts when a deformation beyond a critical threshold occurs. Only a very small probability of failing to issue an alert when in fact one should have been given, is acceptable. This probability is referred to as integrity risk. In this contribution, we show...

Successful implementation of integer ambiguity resolution enabled precise point positioning (aka PPP-RTK) algorithms is inextricably linked to the ability of a user to perform near real-time positioning by quickly and reliably resolving the integer carrier-phase ambiguities. In the PPP-RTK technique, a major barrier to successful ambiguity resoluti...

Estimability and \(\mathcal {S}\)-systems are important concepts when dealing with rank-defect models. In this contribution, we generalize the concept of estimability to integer estimability and determine the necessary and sufficient conditions that need to be satisfied for parameter functions to be integer estimable. This is then worked out and ap...

A new integer-estimable GLONASS FDMA model is studied and analysed. The model is generally applicable, and it shows a close resemblance with the well-known CDMA models. The analyses provide insights into the performance characteristics of the model and concern a variety of different ambiguity-resolution critical applications. This will be done for...

We introduce a new formulation of the double-differenced GLONASS FDMA model. It closely resembles that of CDMA-based systems and it guarantees the estimability of the newly defined GLONASS ambiguities. The formulation is made possible because of our defining new concept of integer-estimability and the analytical construction of a special integer ma...

The DIA-method, for the detection, identification and adaptation of modeling errors, has been widely used in a broad range of applications including the quality control of geodetic networks and the integrity monitoring of GNSS models. The DIA-method combines two key statistical inference tools, estimation and testing. Through the former, one seeks...

In view of the recent proliferation of low-cost mass-market receivers, the number of network receivers and GNSS users will be growing rapidly, demanding an efficient way of data processing in terms of computational power and capacity. One way of improving the computational capacity is to decentralize the underlying data processing and distribute th...

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,...

As parameter estimation and statistical testing are often intimately linked in the processing of observational data, the uncertainties involved in both estimation and testing need to be properly propagated into the final results produced. This necessitates the use of conditional distributions when evaluating the quality of the resulting estimator....

In this contribution, we study the phase-only ambiguity resolution and positioning performance of GPS for short baselines. It is well known that instantaneous (single-epoch) ambiguity resolution is possible when both phase and code (pseudorange) data are used. This requires, however, a benign multipath environment due to the severe effects multipat...

In this contribution we analyze the single-frequency L5 positioning capabilities of the two regional satellite navigation systems IRNSS and QZSS, stand alone as well as combined. The positioning analysis is done for two different baselines, having a mix of receivers, providing ambiguity-float and ambiguity-fixed positioning for models with and with...

Various studies have been performed to investigate the accuracy of troposphere zenith wet delays (ZWDs) determined from GPS. Most of these studies use dual-frequency GPS data of large-scale networks with long baselines to determine the absolute ZWDs. For small-scale networks the estimability of the absolute ZWDs deteriorates due to high correlation...

The emerging GNSSs make single-frequency (SF) RTK positioning possible. In this contribution two different types of low-cost (few hundred USDs) RTK receivers are analyzed, which can track L1 GPS, B1 BDS, E1 Galileo and L1 QZSS, or any combinations thereof, for a location in Dunedin, New Zealand. These SF RTK receivers can potentially give competiti...

The Japanese Quasi-Zenith Satellite System (QZSS) has recently (October 2017) reached its first 4-satellite constellation. In this contribution, the standalone performance of this 4-satellite QZSS constellation is assessed by means of its triple-frequency (L1 + L2 + L5) real-time kinematic (RTK) integer ambiguity resolution and precise positioning...

In PPP-RTK network processing, the wet component of the zenith tropospheric delay (ZTD) cannot be precisely modelled and thus remains unknown in the observation equations. For small networks, the tropospheric mapping functions of different stations to a given satellite are almost equal to each other, thereby causing a near rank-deficiency between t...

For long-baseline over several hundreds of kilometers, the ionospheric delays that cannot be fully removed by differencing observations between receivers hampers rapid ambiguity resolution. Compared with forming ionospheric-free linear combination using dual- or triple-frequency observations, estimating ionospheric delays using uncombined observati...

The integer ambiguity resolution-enabled precise point positioning (PPP) method, the so-called PPP-RTK, is a state-of-the-art Global Navigation Satellite Systems (GNSS) technique that allows to determine position solutions with high accuracy in a short amount of time. The main idea behind PPP-RTK is to extend the PPP technique by providing single-r...

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 the DIA estimator. We di...

Precise point positioning (PPP) and its integer ambiguity resolution-enabled variant, PPP-RTK (real-time kinematic), can benefit enormously from the integration of multiple global navigation satellite systems (GNSS). In such a multi-GNSS landscape, the positioning convergence time is expected to be reduced considerably as compared to the one obtain...

Sensing the ionosphere with the Global Positioning System (GPS) involves two sequential tasks, namely, the ionospheric observable retrieval and the ionospheric parameter estimation. A prominent source of error has long been identified as short-term variability in receiver Differential Code Bias (rDCB). We modify the Carrier-to-Code Leveling (CCL),...

The Minimal Detectable Bias (MDB) is an important diagnostic tool in data quality control. The MDB is traditionally computed for the case of testing the null hypothesis against a single alternative hypothesis. In the actual practice of statistical testing and data quality control, however, multiple alternative hypotheses are considered. We show tha...

The real-time kinematic precise point positioning (PPP-RTK) technique enables integer ambiguity resolution by providing single-receiver users with information on the satellite phase biases next to the standard PPP corrections. Using undifferenced and uncombined observations, rank deficiencies existing in the design matrix need to be eliminated to f...

Kalman filtering in its distributed information form is reviewed and applied to a network of receivers tracking Global Navigation Satellite Systems (GNSS). We show, by employing consensus-based data-fusion rules between GNSS receivers, how the consensus-based Kalman filter (CKF) of individual receivers can deliver GNSS parameter solutions that have...

Abstract With the combination of the emerging GNSSs, single-frequency (SF) precise RTK positioning becomes possible. In this contribution we evaluate such low-cost ublox receiver and antenna performance when combining real data of four CDMA systems, namely L1 GPS, E1 Galileo, L1 QZSS, and B1 BDS. Comparisons are made to more expensive dual-frequenc...

Integer ambiguity resolution (IAR) is the key to fast and precise GNSS positioning and navigation. Next to the positioning parameters, however, there are several other types of GNSS parameters that are of importance for a range of different applications like atmospheric sounding, instrumental calibrations or time transfer. As some of these paramete...

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...

Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary...

In PPP-RTK processing, the network corrections including the satellite clocks, the satellite phase biases and the ionospheric delays are provided to the users to enable fast single-receiver integer ambiguity resolution. To solve the rank deficiencies in the undifferenced observation equations, the estimable parameters are formed to generate full-ra...

The current Galileo constellation in April 2017 comprises both in-orbit validation and full operational capability satellites transmitting signals on five frequencies, i.e., E1, E5a, E5b, E5, and E6. We analyze the power, multipath and noise of these signals using the data collected by four short baselines of various lengths and receiver/antenna ty...

The DIA method for the detection, identification and adaptation of model misspecifications combines estimation with testing. The aim of the present contribution is to introduce a unifying framework for the rigorous capture of this combination. By using a canonical model formulation and a partitioning of misclosure space, we show that the whole esti...

The integration of the Chinese BDS with other systems, such as the American GPS, makes precise RTK positioning possible with low-cost receivers. We investigate the performance of low-cost ublox receivers, which cost a few hundred USDs, while making use of L1 GPS + B1 BDS data in Dunedin, New Zealand. Comparisons will be made to L1 + L2 GPS and surv...

As the navigation solution of exclusion-based RAIM follows from a combination of least-squares estimation and a statistically based exclusion-process, the computation of the integrity of the navigation solution has to take the propagated uncertainty of the combined estimation-testing procedure into account. In this contribution, we analyse, theoret...

The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) reached its full operational capability. In this contribution, we provide the very first L5 attitude determination analyses of the fully operational IRNSS as a standalone system and also in combination with the fully operational GPS Block IIF along with the correspondin...

Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISB...

A first assessment of GLONASS CDMA L3 ambiguity resolution and positioning performance is provided. Our analyses are based on GLONASS L3 data from the satellite pair SVNs 755-801, received by two JAVAD receivers at Curtin University, Perth, Australia. In our analyses, four different versions of the two-satellite model are applied: the geometry-free...

The GPS carrier-phase and code data have proven to be valuable sources of measuring the Earth’s ionospheric total electron content (TEC). With the development of new GNSSs with multi frequency data, many more ionosphere-sensing combinations of different precision can be formed as input of ionospheric modelling. We present the general way of interpr...

The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) become fully operational. In this contribution, for the fully operational IRNSS as a stand-alone system and also in combination with GPS, we provide a first assessment of L5 integer ambiguity resolution and positioning performance. While our empirical analyses are based...

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 th...

This chapter is a primer on global navigation satellite systems (GNSS s). It assumes no prior knowledge of the systems or how they work. All of the key concepts of satellite-based positioning, navigation, and timing (PNT ) are introduced with pointers to subsequent chapters for further details. The chapter begins with a history of PNT using satelli...

This chapter presents the estimation and filtering principles as used in global navigation satellite system (GNSS ) data processing. Estimation and filtering are concerned with retrieving or recovering parameters of interest from noisy measurements. The least-squares (LS) principle is the standard approach for estimating unknown parameters from unc...

Modeling errors, when passed unnoticed, may seriously deteriorate the final results of any estimation process. It is therefore of importance to have quality control procedures in place so as to be able to judge and validate the outcome of estimation. This chapter presents such methods for global navigation satellite system (GNSS ) model validation...

Global Navigation Satellite System (GNSS ) carrier-phase integer ambiguity resolution is the process of resolving the carrier-phase ambiguities as integers. It is the key to fast and high-precision GNSS parameter estimation and it applies to a great variety of GNSS models that are currently in use in navigation, surveying, geodesy and geophysics. T...

As a first step towards