Priyanka Das Rajkakati Aerospace Engineer (Ph.D.) | Artist


Synchronization Performance Limits of GNSS Receivers


Dr. Eric Chaumette (ISAE-Supaéro)
Dr. Silvère Bonnabel (Mines ParisTech)
Dr. Jordi Vilà-Valls (ISAE-Supaéro)

Laboratory and Funding

ISAE-ONERA SCANR (Signal, Communication, Antennae, Navigation & Radar)
CIFRE contract with Safran


The advent of Global Navigation Satellite Systems (GNSS) has revolutionized today's world, with applications in positioning, timing and remote sensing. The principle of GNSS is based on multilateration, which first involves the estimation of both signal propagation time-delay and Doppler effect for each visible satellite. In fact, delay-Doppler synchronization is an active research topic of significant practical importance in many fields, with applications in radar, sonar, ultrasonics, communications and navigation. Now, when designing and assessing estimation techniques, it is of fundamental importance to know the ultimate achievable performance in the mean square error (MSE) sense, information which is brought by the computation of performance lower bounds (LBs) on the MSE.

Compared to other LBs, Cramér-Rao Bounds (CRB) are simple to calculate and give an accurate estimation of the MSE of the maximum likelihood estimator (MLE) in the asymptotic region of operation under certain conditions. Indeed, GNSS receiver architectures rely on a scalar acquisition and tracking approach, which can be seen as particular instances of a MLE solution. However, even if the delay-Doppler CRB literature is abundant, most of these CRB expressions are unnecessarily restrictive and only address the standard narrowband signal model, without considering the impact of the Doppler effect on the baseband signal. Most importantly, a sufficiently generalized and easy-to-use compact CRB for generic band-limited signals is not available, being an important missing point of practical interest.

The primary objective of the present thesis is the characterization of the asymptotic performance of GNSS time-delay and Doppler estimation, i.e., synchronization, within a coherent integration time. The first contribution is the derivation of a new compact closed-form CRB expression for time-delay estimation, considering a generic band-limited transmitted signal and constant transmitter-to-receiver propagation delay, completed with insights on an optimal signal design as well as a performance loss metric. This CRB derivation is then extended to include the joint time-delay and phase estimation, which is of interest for standard precise positioning approaches exploiting the carrier phase, such as PPP and RTK. A complimentary problem is then addressed: the lack of a comprehensive performance analysis of GNSS signals in literature, from an optimal estimation point of view. The work further provides the performance thresholds that require a need for carrier phase-based positioning techniques. Finally, we extend the derivation of the generic compact closed-form CRB expression to include the joint time-delay and Doppler stretch estimation, first for narrowband signals and then for their wideband counterpart, followed by the introduction of a general compact closed-form CRB expression for the amplitude and phase. Such results set the theoretical basis for the full GNSS receiver chain characterization.

Keywords: GNSS signals, GNSS synchronization, Cramér-Rao Bounds, maximum likelihood, parameter estimation, delay-Doppler-phase estimation, GNSS positioning.

Will be uploaded soon.


  1. P. Das, J. Vilà-Valls, E. Chaumette, F. Vincent, L. Davain, and S. Bonnabel. “On the Accuracy Limit of Time-delay Estimation with a Band-limited Signal”. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP). Brighton, UK, May 2019
  2. P. Das, B. Priot, J. Vilà-Valls, and E. Chaumette. “A Signal Processing Approach to GNSS Precise Positioning for Lunar Exploration”. 70th International Astronautical Congress (IAC’19). Washington DC, USA, Nov. 2019 – Awarded the ESA ISEB grant.

Journal papers

  1. P. Das, L. Ortega, J. Vilà-Valls, F. Vincent, E. Chaumette, and L. Davain. “Performance Limits of GNSS Code-Based Precise Positioning: GPS, Galileo & Meta-Signals”. Sensors (2020) Vol. 20, Issue 8
  2. P. Das, J. Vilà-Valls, F. Vincent, L. Davain, and E. Chaumette. “A New Compact Delay, Doppler Stretch and Phase Estimation CRB with a Band-Limited Signal for Generic Remote Sensing Applications”. Remote Sensing (2020) Vol. 12, Issue 18

The International Space Education Board (ISEB) program is a wonderful opportunity for students to have privileged access to events during the International Astronautical Congress (IAC), including interactive sessions with astronauts and top space personnels, such as heads of space agencies.

10 European students were awarded the ESA ISEB sponsorship for attending the IAC 2019 in Washington DC.

More information here.

Laboratory experiment advisor, ISAE-Supaéro | 2019
Course: Experimental Project on GNSS, 1st year engineering class (PREX A1)

Teaching assistant, ISAE-Supaéro | 2019
Course: Applied Mathematics, MSc Aerospace Engineering (MAE1)

Teaching asistant, ISAE-Supaéro | 2018
Course: Signal Processing (for Navigation), 1st year engineering class (1A)