High precision positioning using Global Navigation Satellite Systems relies on techniques such as Precise Point Positioning or Real Time Kinematic. In order to achieve accuracies and precisions at the centimeter level, these techniques require the use of precise products: GNSS satellite orbits and clocks, as well as satellite hardware biases and in some cases atmospheric products. In addition to the accuracy of such products, new applications of real-time PP such as autonomous driving systems require the integrity of the solution to be assured. The integrity is the trust that can be placed in the solution and includes the ability to detect gross errors which could compromise safety. 

The integrity of such PPP solutions depends upon the integrity of the products employed, that is the confidence in the solution depends upon the confidence of the input data, including the precise PPP products available from various providers (both organizational e.g. IGS and commercial e.g. Trimble, Swift). An integrity flag is raised if a feared event has been detected on a monitored satellite or constellation or within other parts of the system (e.g. the corrections service ground segment) with a predefined maximum time to alert as defined by the application. The integrity algorithm should encompass the fault detection of the raw measurement issued by the GNSS satellites, as well as the possible problems encountered in the precise products generation. Possible sources of fault, or gross errors, includes issues with measurement data at the ground stations used to compute the PPP products or leading to issues in the ambiguity resolution needed for such estimation processes. 

In addition to fault detection, integrity also requires error bounding in order to provide the ‘confidence’, undertaken either in the user domain through the calculation of protection levels or measurement domain through range bounding and one of the key objectives of this thesis is to provide both aspects of integrity (FD and bounding) for the precise orbit and clock products employed in PPP. Furthermore, precise positioning solutions must also be provided with estimated code and phase biases that are mandatory in order to perform the integer ambiguity resolution that is a pre-requisite for achieving centimeter level accuracy. Therefore, the first objective also includes the means to ensure the integrity of the real-time code and phase biases generation in PPP products. 

The interest in the integrity of the products used for precise positioning has grown in the recent years with the anticipated arrival of new services related to use of LEO satellites complementary to the GNSS satellites in MEO orbits. Recent studies have investigated some integrity algorithms in order to detect faults in the products by analyzing the impact of a missed detection in the PPP products on the navigation solution performance, whilst other studies apply RAIM techniques to receivers in LEO. 

In the case where the LEO-layer is used as flying ground stations, their orbits have to be determined together in addition to estimation and prediction of the MEO satellites from the GNSS core constellations. It is likely, or perhaps necessary, that GNSS signals from MEO and the measurements then derived must be used for the LEO Orbit Determination and Time Synchronization (ODTS) solution. A secondary challenge of the proposed thesis is thus to handle the potential dependency between the LEO ODTS and the LEO based integrity solution (fault detection and range bounding of MEO measurement). Multiple potential solutions are envisaged. Firstly, a joint estimation and detection may be envisaged based on assumptions of the types of faulty measurements that could occur. Secondly, a two stream solution whereby the MEOs are partitioned into two subsets A and B, used to determined two LEO ODTS solutions which are then employed for the Fault Detection and integrity bounding of the other solution (i.e. LEO ODTS MEOs ‘A’  FD of MEOs ‘B’ & LEO ODTS MEOs ‘B’  FD of MEOs ‘A’). Finally, separation in time may be used, such that measurements are employed for the LEO ODTS over an interval [t0,t1], whilst used for FD and integrity bounding (also possibly MEO GNSS measurement corrections) over the later interval [t1+T,t]. It is envisaged to test these various solutions as part of the PPP integrity concept that includes LEO flying stations. 

This PhD proposal therefore has the objective to define a new integrity concept for the precise orbits, clocks and code/phase biases estimated as part of precise positioning products used for PPP. The work will address both the fault detection and error bounding aspects of integrity applied to GNSS constellations (primary focus on Galileo and GPS) whilst also treating the case of flying ground stations in LEO orbit. 

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - milner@recherche.enac.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online before March 13th, 2026 Midnight Paris time!