Thèse Integrity-Aware Factor Graph Optimization Estimation And Statistical Testing For Gnss-Based Multi-Sensor Navigation H/F Doctorat.Gouv.Fr

Établissement : Ecole Nationale de l'Aviation Civile École doctorale : EDMITT - Ecole Doctorale Mathématiques, Informatique et Télécommunications de Toulouse Laboratoire de recherche : ENAC-LAB - Laboratoire de Recherche ENAC Direction de la thèse : Paul THEVENON ORCID 0000000296001029 Début de la thèse : 2027-09-01 Date limite de candidature : 2026-11-16T23:59:59 See English section. The proposed PhD project combines two state-of-the-art techniques, namely Factor Graph Optimization (FGO) as well as Detection, Identification, and Adaptation (DIA) for integrity-aware navigation in the context of positioning of UAV. The study will focus on satellite navigation (GNSS), which is the domain of expertise of the two host institutions (ENAC and TU Delft), with a possible inclusion of inertial sensors. In this section, for each domain, we briefly provide an overview of recent advances, current limitations and the existing research gaps. Some of these gaps will be tackled during this PhD project.

FGO is an estimation framework particularly well adapted to dynamic system state estimation, such as in positioning or navigation applications, where the observation of the system over long period is beneficial. Compared to other filtering techniques, FGO has proved additional benefits in terms of positioning accuracy by considering a larger temporal window and correctly modeling time-correlated parameters, such as sensor biases and atmospheric states. Additionally, inclusion of multi-epoch observations within the same estimation process allows us to efficiently mitigate outliers by means of robust statistical methods [Das 2022, Xia 2024]. However, a rigorous integrity monitoring, i.e. reliably bounding the user positioning error with an application-driven required guarantee, is still an open issue in FGO literature. Finally, FGO is a flexible modelling framework, which scales nicely to large estimation problems, such as in multi-sensor fusion such as GNSS/INS integration [Suzuki 2024], or multi-agent positioning for a fleet of UAVs [Zhang 2022, Yang 2025]

DIA is a rigorous framework for statistical testing, suitable for fault detection and exclusions, while being generally applicable to least-squares estimation problems, as well as Kalman filtering (e.g. recursive quality control in dynamic systems). The DIA method combines estimation with testing, with the latter aiming at validating the estimation results to avoid potential biased solutions due to misspecifications of the functional model. It follows that the whole estimation-testing scheme can be captured in one single estimator, i.e. the DIA estimator, which depends on the alternative hypotheses (e.g. potential faults) being considered in the model. Unfortunately, with higher redundancy, also the computational complexity grows since the combination of candidate biases increases exponentially. Hence, in the context of high-dimensional estimation problems, such as those ones considering factor graphs over a large temporal window, this framework has not yet been fully explored, whereas still very promising for rigorous integrity monitoring.

Ultimately, after defining FGO as a batch least-squares problem, the goal is to apply existing DIA procedures to bring an integrity layer to FGO solutions. This is expected to enhance detectability of faults, as well as benefit their correct identification to ensure integrity performance in safety-critical applications, in particular concerning UAVs' navigation as the main case study.
The main objective of this project is to establish a rigorous integrity-monitoring framework based on Detection, Identification and Adaptation (DIA) Theory for multi-epoch navigation via Factor Graph Optimization (FGO).

The specific objectives are:
- Develop a statistically rigorous DIA formulation for the linearized multi-epoch FGO, including suitable iterative identification procedures.
- Quantify how observation-window length, graph structure, temporal dependencies or model parametrization can affect fault detectability and fault distinguishability.
- Extend the analysis from a single to multiple simultaneous faults and investigate some computationally efficient strategies for managing the large resulting set of alternative hypotheses.
- Integrate the proposed integrity DIA framework within tightly coupled GNSS/INS FGO and investigate how inertial sensor information, along with how relinearization and marginalization can affect fault detection and integrity performance.
- Potentially extend the framework to collaborative multi-UAV navigation by incorporating shared information, thence determining under which conditions temporal and spatial diversity might improve integrity.
- Investigate the main limitations associated with common-mode faults, or poorly distinguishable fault signatures, and effects of heterogeneous measurement quality across the UAVs' fleet.
- Validate the theoretical developments using Monte Carlo simulations, controlled fault injection and representative UAV experiment(s).
- Derive quantitative procedure guidelines describing trade-offs among accuracy, continuity and integrity, along with other relevant KPIs.
The research will follow a progressive methodology in which each stage could provide some independently valuable scientific results.

1. Requirements, use cases and fault models
a. Define representative operational scenarios for a low-altitude single or multiple UAVs.
b. Define potential accuracy, integrity, continuity and availability requirements relevant to the selected applications.
c. Specify sensor configurations and stochastic models for GNSS and INS, along with a fault taxonomy including, but not limited to, GNSS multipath, NLOS delays, signal faults, spoofing-like biases, INS failures, etc.

2. DIA formulation for multi-epoch FGO estimators
a. Formulate a relationship between the linearized FGO and batch weighted least-squares estimation.
b. Derive DIA detection and identification statistics in the context of multi-epoch graphs.
c. Investigate both fault detectability and fault distinguishability as functions of the batch window length, graph structure, temporal correlation and model parametrization.
d. Extend the analysis towards multiple simultaneous faults and a study strategy for reducing DIA computational complexity.

3. Application of the method to UAV navigation
a. Consider GNSS observation and integrate inertial observations and INS stochastic states into the FGO framework.
b. Analyze how inertial information affects fault detectability and integrity performance during degraded GNSS conditions.
c. Investigate consequences of temporal correlation, linearization and marginalization for statistically calibrated testing.
d. Subject to PhD time constraints, possibly extend the study to a collaborative FGO architecture, thus combining GNSS and INS information from a fleet of multiple UAVs.
e. Quantify how fleet geometry, network connectivity, and visibility of heterogeneous satellites and/or sensors might affect integrity performance.
f. Investigate the local and common-mode faults, thus potentially assessing centralized versus decentralized implementations.

4. Data acquisition and validation campaign
a. Perform Monte Carlo simulations and controlled fault-injection experiments with known fault types, e.g. magnitude and location based on previously reviewed literature.
b. Acquire representative GNSS/INS datasets from UAVs under a few different operating conditions, i.e. using ENAC experimental facilities.
c. Validate theoretical predictions on integrity performances and relevant KPIs against empirical positioning results, i.e. using an independent reference trajectory.

5. Performance assessment and design analysis
a. Quantify positioning accuracy, integrity and continuity, along with the computational complexity requirements.
b. Perform a sensitivity analysis with respect to relevant metrics, such as observation-window length, inertial sensor quality, fault magnitude, and other environmental conditions.
c. Derive practical design guidelines identifying the key conditions under which temporal and spatial diversity provide a significant integrity benefit for collaborative positioning.