Theory for the ambiguity function method: probability model and global solution P. J. G. Teunissen, L. Massarweh Journal of Geodesy, 2025 In this contribution, we introduce some new theory for the classical GNSS ambiguity function (AF) method. We provide the probability model by means of which the AF-estimator becomes a maximum likelihood estimator, and we provide a globally convergent algorithm for computing the AF-estimate. The algorithm is constructed from combining the branch-and-bound principle, with a special convex relaxation of the multimodal ambiguity function, to which the projected-gradient-descent method is applied to obtain the required bounds. We also provide a systematic comparison between the AF-principle and that of integer least-squares (ILS). From this comparison, the conclusion is reached that the two principles are fundamentally different, although there are identified circumstances under which one can expect AF- and ILS-solutions to behave similarly.
An efficient 'P1' algorithm for dual mixed-integer least-squares problems with scalar real-valued parameters Lotfi Massarweh, Peter J. G. Teunissen Journal of Applied Geodesy, 2025 In this contribution we consider mixed-integer least-squares problems, where the integer ambiguities a ∈ Z n $a\\in {\\mathbb{Z}}^{n}$ and real-valued parameters b ∈ R p $b\\in {\\mathbb{R}}^{p}$ 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 ad hoc ‘P1’ algorithm is introduced, and some geometrical insights are provided. It is demonstrated how the algorithm’s complexity (i.e. number of candidate integer solutions to be evaluated) grows linearly with the ambiguity dimensionality n, differently from the primal formulation where an exponential growth is observed. By means of numerical simulations, here based on Global Navigation Satellite System (GNSS) models, we show the efficiency of this proposed ‘P1’ algorithm, meanwhile also demonstrating its quasi-optimal statistical performance.
Strategies for Ambiguity Resolution in LEO-PNT Systems with Various Frequency Bands Lotfi Massarweh, Sandra Verhagen 2025 IEEE Ion Position Location and Navigation Symposium PLANS 2025, 2025 In this paper, we investigate strategies for ambiguity resolution in Low Earth Orbit Positioning, Navigation, and Timing (LEO-PNT) systems, particularly across multiple frequency bands beyond the traditional L-band used in GNSS. By leveraging the rapid geometric change of LEO satellites, our study examines the feasibility of fast and reliable integer ambiguity resolution (IAR) in Precise Point Positioning with Ambiguity Resolution (PPP-AR). Using end-to-end simulations, we assess the impact of different signal bands on convergence time and positioning accuracy. The methodology incorporates the LAMBDA 4.0 toolbox for mixed-integer estimation models, providing insights into how LEO-PNT enhances PPP-AR performance. Results demonstrate significant improvements in ambiguity resolution success rates and positioning convergence when incorporating LEO signals, highlighting their potential in future PNT application.
New LAMBDA toolbox for mixed-integer models: estimation and evaluation Lotfi Massarweh, Sandra Verhagen, Peter J. G. Teunissen GPS Solutions, 2025 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 evaluation capabilities. The new implementation provides redefined algorithms, such as an improved integer search strategy with a one-order reduction in the computational time, along with additional estimators: Vectorial Integer Bootstrapping (VIB), Integer Aperture Bootstrapping (IAB) and Best Integer Equivariant (BIE). This toolbox aims to become a valuable resource for researchers and/or practitioners dealing with mixed-integer models in high dimensions, e.g., terrestrial-based carrier-phase systems, multi-constellation Global Navigation Satellite Systems (GNSS), or other interferometric applications.
Results and Lessons Learned from the NAVITEC 2024 Resilient GNSS Challenge Lotfi Massarweh, Chengyu Yin, Daniele Borio, Melania Susi, Hakan Uyanik, Daniel Medina, Andrea Bellés Ferreres, Filippo Giacomo Rizzi, Christoph Lass, Tao Lin, Tao Li, Wei Gao, Gerarda De Pasquale, Noori Bni Lam, Ruediger Matthias Weiler, Paolo Crosta Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation Ion Gnss, 2025 At the end of 2024, the ‘Resilient GNSS Challenge’ was organized by the European Space Agency (ESA) and hosted during the 11th ESA Workshop on Satellite Navigation Technologies (NAVITEC 2024). This competition focused on real world challenges, based on a dataset collected in September 2024 during the Norwegian Jammertest campaign. In this contribution, we present the challenge results, thus describing the scenarios and providing details on the solutions developed by the teams ranked in the top three positions of the competition. Different spoofing conditions were considered in two scenarios, with a total of three problems to be solved with static and/or moving receivers tracking spoofed signals. All in all, the analysis of Carrier-To-Noise Power Spectral Density Ratio (C/N0) values turned out to be an essential element for a proper characterization of the different problems, along with providing a correct identification of genuine GNSS signals that could safely be used by the teams.
Primal and dual mixed-integer least-squares: distributional statistics and global algorithm P. J. G. Teunissen, L. Massarweh Journal of Geodesy, 2024 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∈Znand baseline vector$$b \\in {\\mathbb {R}}^{p}$$b∈Rpare estimated. As not the ambiguities, but rather the entries ofbare usually the parameters of interest, the attractiveness of the dual formulation stems from its direct computation ofb. It is shown that this potential advantage relies on the ease with which an implicit integer least-squares problem of the dual can be solved. For the convoluted cases, we introduce two methods of simplifying approximations. To be able to describe their quality, we provide a complete distributional analysis of their estimators, thus allowing users to judge whether or not the approximations are acceptable for their application. It is shown that this approach implicitly introduces a new class of admissible integer estimators of which we also determine the pull-in regions. As the dual function is shown to lack convexity, special care is required to be able to compute its global minimizer$${\\check{b}}$$bˇ. Our proposed method, which has finite termination with a guaranteed$$\\epsilon $$ϵ-tolerance, is constructed from combining the branch-and-bound principle, with a special convex-relaxation of the dual, to which the projected-gradient-descent method is applied to obtain the required bounds. Each of the method’s three constituents are described, whereby special emphasis is given to the construction of the required continuously differentiable, convex lower bounding function of the dual.
A multi-lander New Frontiers mission concept study for Enceladus: SILENUS Erica Nathan, Katiyayni Balachandran, Paolo Cappuccio, Julia Di, Kelsey Doerksen, Alessia Gloder, Monica Li, Lotfi Massarweh, Thomas Peev, Shreya Santra, Marc Rovira-Navarro, Dan Limonchik Frontiers in Astronomy and Space Sciences, 2022 Enceladus, with its subsurface ocean, is amongst the top priority targets in the search for life beyond Earth. Following on discoveries from the Cassini mission that Enceladus possesses a global subsurface ocean containing salt and organic compounds, there are many unconstrained properties of the ocean and ice shell that must be investigated to further assess the habitability of Enceladus and begin the search for biosignatures on Enceladus. In this paper, we present a concept study for a New Frontiers class multi-lander and orbiter mission to Enceladus that investigates if there is or ever was a habitable environment on Enceladus. The mission architecture includes an orbiter for detailed chemical analysis of material erupted from Enceladus’ plumes and four impact landers for geophysical measurements. As part of our mission concept study, we explore key trades for orbital and surface science, as well as assess the scientific potential and hazards of candidate landing sites on Enceladus. The novelty of our mission architecture and consideration of both orbital and surface science elements makes this work directly relevant to a broad range of potential future mission architectures under consideration, such as those identified in the 2023–2032 Planetary Science and Astrobiology Decadal Survey.
On vectorial integer bootstrapping implementations in the estimation of satellite orbits and clocks based on small global networks Lotfi Massarweh, Sebastian Strasser, Torsten Mayer-Gürr Advances in Space Research, 2021 The estimation of satellite orbits and clocks plays a central role in different Global Navigation Satellite System (GNSS) domains, e.g. precise positioning or time transfer. Such products can be computed in the process of Orbit Determination and Time Synchronization (ODTS), which relies on a network of ground-based stations, well distributed around the globe. The mm-level precision of carrier-phase measurements is exploited in this network estimation following a correct resolution of their ambiguities. For several stations, satellites and/or signals, thousands of ambiguities have to be processed, which means having to deal with high-dimensional ambiguity resolution (HDAR) problems. In this research work, we firstly account for the impact of ambiguity resolution in a varying network size, based on GPS-only, Galileo-only and GPS+Galileo configurations. Using 25 or more stations, the accuracy (1D RMS orbital errors) of fixed solutions reaches a plateau at 1–2 cm. Hence, we focus on a small global network of 14 stations, where the model strength decreases, so does the reliability of the ambiguity fixing process and advantages over a float solution might become less evident. In order to allow reliable HDAR, two implementations of the Vectorial Integer Bootstrapping estimator are presented and evaluated with respect to their scalar counterpart. Finally, it is shown how the proposed fixing processes are more robust, still very efficient, and on certain days they provide a large improvement to satellite products. The orbital results are ultimately validated by considering the satellite midnight discontinuity errors over a 3-month period in 2019.
Vectorial integer bootstrapping: flexible integer estimation with application to GNSS P. J. G. Teunissen, L. Massarweh, S. Verhagen Journal of Geodesy, 2021 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-block processing of the ambiguities based on a user-chosen partitioning. In this way, flexibility is created, where for specific choices of partitioning, tailored VIB-estimators can be designed. This wide range of possibilities is discussed, supported by numerical simulations and analytical examples. Further guidelines are provided, as well as the possible extension to other classes of estimators.
Towards sub-meter positioning using android raw GNSS measurements Dimitrios Psychas, Jon Bruno, Lotfi Massarweh, Francesco Darugna Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation Ion Gnss 2019, 2019
A Neural Network approximation of Fixed Failure-rate Ratio Test for PPP Ambiguity Resolution L Massarweh, C Yin, S Verhagen, X Liu, D Odijk, H Visser, D Psychas EGU26 , 2026 2026
Novamoon: A strategic lunar reference station for positioning, timing, and largely enhanced science in the earth-moon system S Molli, A Fienga, P Defraigne, K Sośnica, L Cacciapuoti, L Porcelli, ... arXiv preprint arXiv:2602.08432 , 2026 2026 Citations: 1
Ambiguity-Resolved Kinematic Performance in Low Earth Orbit (LEO) Systems for Positioning, Navigation, and Timing (PNT) L Massarweh, S Verhagen Navigating the Geodetic Landscape: A Tribute to 45 Years of Excellence … , 2025 2025
Systems for Positioning, Navigation, and Timing (PNT) L Massarweh, S Verhagen Navigating the Geodetic Landscape: A Tribute to 45 Years of Excellence … , 2025 2025
Results and Lessons Learned from the NAVITEC 2024 Resilient GNSS Challenge L Massarweh, C Yin, D Borio, M Susi, H Uyanik, D Medina, ... Results and Lessons Learned from the NAVITEC 2024 Resilient GNSS Challenge , 2025 2025
Strategies for Ambiguity Resolution in LEO-PNT Systems with Various Frequency Bands L Massarweh, S Verhagen 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), 450-458 , 2025 2025 Citations: 1
An efficient ‘P1’algorithm for dual mixed-integer least-squares problems with scalar real-valued parameters L Massarweh, PJG Teunissen Journal of Applied Geodesy 19 (2), 311-320 , 2025 2025
Impact of on-board satellite orbits and clocks estimation for LEO-PNT ground positioning J Oduber, L Massarweh, J van den IJssel EGU General Assembly Conference Abstracts, EGU25-19075 , 2025 2025
Theory for the ambiguity function method: probability model and global solution: PJG Teunissen, L. Massarweh PJG Teunissen, L Massarweh Journal of Geodesy 99 (4), 28 , 2025 2025 Citations: 1
Modelling, Uncertainty and Data for Engineers (MUDE) workbook J Ding, R Lanzafame, F van der Meer, T van Woudenberg, S Verhagen, ... Delft University of Technology , 2025 2025
Primal and dual mixed-integer models for global navigation satellite systems L Massarweh 2025 Citations: 3
New LAMBDA toolbox for mixed-integer models: estimation and evaluation L Massarweh, S Verhagen, PJG Teunissen GPS Solutions 29 (1), 14 , 2025 2025 Citations: 29
Kinematic Precise Orbit Determination for real-and near-real-time using Galileo High Accuracy Service–GHASP3 project L Massarweh, S Verhagen, C Deprez, M Dassie, C Trainotti, G Giorgi, ... 2024
Primal and dual mixed-integer least-squares: distributional statistics and global algorithm: PJG Teunissen, L. Massarweh PJG Teunissen, L Massarweh Journal of Geodesy 98 (7), 63 , 2024 2024 Citations: 5
A novel globally convergent maximizer for the multivariate carrier-phase integer ambiguity function L Massarweh, P Teunissen European Geosciences Union General Assembly 2024 (EGU24), 19367 , 2024 2024
LAMBDA 4.0: an advanced tool for integer estimation, validation and success rate simulation L Massarweh, S Verhagen, P Teunissen XXVIII General Assembly of the International Union of Geodesy and Geophysics … , 2023 2023
A multi-lander New Frontiers mission concept study for Enceladus: SILENUS E Nathan, K Balachandran, P Cappuccio, J Di, K Doerksen, A Gloder, ... Frontiers in Astronomy and Space Sciences 9, 995941 , 2022 2022 Citations: 10
On vectorial integer bootstrapping implementations in the estimation of satellite orbits and clocks based on small global networks L Massarweh, S Strasser, T Mayer-Guerr Advances in Space Research 68 (11), 4303-4320 , 2021 2021 Citations: 8
Vectorial integer bootstrapping: flexible integer estimation with application to GNSS PJG Teunissen, L Massarweh, S Verhagen Journal of Geodesy 95 (9), 99 , 2021 2021 Citations: 24
Assessment of real-time multipath detection with Android raw GNSS measurements by using a xiaomi mi 8 smartphone L Massarweh, M Fortunato, C Gioia 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS), 1111-1122 , 2020 2020 Citations: 26
MOST CITED SCHOLAR PUBLICATIONS
Towards sub-meter positioning using Android raw GNSS measurements D Psychas, J Bruno, L Massarweh, F Darugna Proceedings of the 32nd international technical meeting of the satellite … , 2019 2019 Citations: 49
New LAMBDA toolbox for mixed-integer models: estimation and evaluation L Massarweh, S Verhagen, PJG Teunissen GPS Solutions 29 (1), 14 , 2025 2025 Citations: 29
Medium‐scale gravity wave activity in the thermosphere inferred from GOCE data RF Garcia, S Bruinsma, L Massarweh, E Doornbos Journal of Geophysical Research: Space Physics 121 (8), 8089-8102 , 2016 2016 Citations: 28
Assessment of real-time multipath detection with Android raw GNSS measurements by using a xiaomi mi 8 smartphone L Massarweh, M Fortunato, C Gioia 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS), 1111-1122 , 2020 2020 Citations: 26
Vectorial integer bootstrapping: flexible integer estimation with application to GNSS PJG Teunissen, L Massarweh, S Verhagen Journal of Geodesy 95 (9), 99 , 2021 2021 Citations: 24
Statistical Investigation of Android GNSS Data: Case Study Using Xiaomi Mi 8 Dual-Frequency Raw Measurements L Massarweh, F Darugna, D Psychas, J Bruno ION GNSS+ 2019, 3847 - 3861 , 2019 2019 Citations: 14
A multi-lander New Frontiers mission concept study for Enceladus: SILENUS E Nathan, K Balachandran, P Cappuccio, J Di, K Doerksen, A Gloder, ... Frontiers in Astronomy and Space Sciences 9, 995941 , 2022 2022 Citations: 10
On the restricted 3-body problem for the saturn-enceladus system: Mission geometry & orbit design for plume sampling missions L Massarweh, P Cappuccio AIAA Scitech 2020 Forum, 0467 , 2020 2020 Citations: 9
On vectorial integer bootstrapping implementations in the estimation of satellite orbits and clocks based on small global networks L Massarweh, S Strasser, T Mayer-Guerr Advances in Space Research 68 (11), 4303-4320 , 2021 2021 Citations: 8
Primal and dual mixed-integer least-squares: distributional statistics and global algorithm: PJG Teunissen, L. Massarweh PJG Teunissen, L Massarweh Journal of Geodesy 98 (7), 63 , 2024 2024 Citations: 5
Primal and dual mixed-integer models for global navigation satellite systems L Massarweh 2025 Citations: 3
Novamoon: A strategic lunar reference station for positioning, timing, and largely enhanced science in the earth-moon system S Molli, A Fienga, P Defraigne, K Sośnica, L Cacciapuoti, L Porcelli, ... arXiv preprint arXiv:2602.08432 , 2026 2026 Citations: 1
Strategies for Ambiguity Resolution in LEO-PNT Systems with Various Frequency Bands L Massarweh, S Verhagen 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), 450-458 , 2025 2025 Citations: 1
Theory for the ambiguity function method: probability model and global solution: PJG Teunissen, L. Massarweh PJG Teunissen, L Massarweh Journal of Geodesy 99 (4), 28 , 2025 2025 Citations: 1
A Mission Concept Investigating the Habitability of Enceladus: SILENUS K Balachandran, E Nathan, M Rovira-Navarro, P Cappuccio, J Di, ... 51st Annual Lunar and Planetary Science Conference, 1339 , 2020 2020 Citations: 1
A Neural Network approximation of Fixed Failure-rate Ratio Test for PPP Ambiguity Resolution L Massarweh, C Yin, S Verhagen, X Liu, D Odijk, H Visser, D Psychas EGU26 , 2026 2026
Ambiguity-Resolved Kinematic Performance in Low Earth Orbit (LEO) Systems for Positioning, Navigation, and Timing (PNT) L Massarweh, S Verhagen Navigating the Geodetic Landscape: A Tribute to 45 Years of Excellence … , 2025 2025
Systems for Positioning, Navigation, and Timing (PNT) L Massarweh, S Verhagen Navigating the Geodetic Landscape: A Tribute to 45 Years of Excellence … , 2025 2025
Results and Lessons Learned from the NAVITEC 2024 Resilient GNSS Challenge L Massarweh, C Yin, D Borio, M Susi, H Uyanik, D Medina, ... Results and Lessons Learned from the NAVITEC 2024 Resilient GNSS Challenge , 2025 2025
An efficient ‘P1’algorithm for dual mixed-integer least-squares problems with scalar real-valued parameters L Massarweh, PJG Teunissen Journal of Applied Geodesy 19 (2), 311-320 , 2025 2025