Bandwidth-Efficient TDOA Estimation in Generalized Differential Positioning With OFDM Satellite Signals of Opportunity

Orthogonal Frequency Division Multiplexing (OFDM) modulation has been used in Starlink, OneWeb and considered for using in many emerging low earth orbit (LEO) satellite communication systems. The explosive growth of OFDM satellite signals provides a plethora of satellite signals of opportunity (SOOPs) for intelligent vehicle systems positioning. In this work, we extend the differential positioning in GNSS to generalized differential positioning with OFDM satellite SOOPs, and propose a bandwidth-efficient framework to estimate the time difference of arrival (TDOA) at the reference node and the rover node. In this framework, the reference node estimates its own time of arrival (TOA) and shares partial subcarrier and symbol information with the rover node to help it achieve a better TOA estimation when its received signal is not strong enough, and the TDOA is obtained via subtraction. Then, a TOA estimation algorithm using only partial subcarriers and symbols of OFDM signals is proposed and the Cramer-Rao lower bound (CRLB) of TOA estimation with parital data is derived. Subsequently, a data compression algorithm is proposed to minimize the transmission bits under the expected TDOA estimation accuracy and rover node's signal-to-noise ratio (SNR). Simulations with Starlink downlink signals and 5 G non-terrestrial network (NTN) downlink New Radio (NR) singals are conducted. The results show that the TOA estimation performance approaches the CRLB and a 10 picosecond-level TDOA performance is achievable with merely using 13<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> bits of the Starlink signal or using 34<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> bits of the 5G NR signal, which will bring about centimeter-level positioning if enough quantity of TDOAs are available.