Maximum Likelihood Time of Arrival and Doppler Estimation for Precise Starlink-Based PNT

We present a maximum likelihood (ML) Doppler and time-of-arrival (TOA) estimation framework for opportunistic tracking of Starlink downlink signals. Extending previous approaches that rely solely on known pilot symbols, we incorporate full-frame ML estimation to harness the data payload, significantly improving Doppler and TOA estimation accuracy. Using live Starlink transmissions, we validate our ML estimator and compare its performance against pilot-based cross-ambiguity function (CAF) and pilot-only ML estimation methods. Results show that the full-frame ML estimator achieves a 10³ factor improvement in Doppler accuracy over the pilot-only CAF method and 10² factor improvement over the pilot-only ML method, reducing post-fit residual RMSE from 1469.20 Hz and 752.43 to 6.34 Hz, respectively. TOA estimation sees a smaller improvement. The findings highlight the value of leveraging the entire OFDM frame for estimation. Additionally, we newly identify two OFDM symbol modulation schemes in use by Starlink.