A Computationally Efficient Approach for Acquisition and Doppler Tracking for PNT With LEO Megaconstellations

Abstract

A computationally efficient approach for acquisition and Doppler tracking for positioning, navigation, and timing (PNT) with unknown low Earth orbit (LEO) megaconstellation satellite signals is developed. The acquisition is based on a sequential matched subspace detector (MSD), whose complexity is reduced via: (i) reducing the detector's projection matrix calculation from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N^{2}_{s})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N_{s})$</tex-math></inline-formula>, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ N_{s}$</tex-math></inline-formula> is typically on the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{5}$</tex-math></inline-formula>; and (ii) exploiting the computational efficiency of the fast Fourier transform (FFT) to mechanize the likelihood function calculation. The Doppler Cramér-Rao lower bound as a function of the signal-to-noise ratio is derived and the performance of the proposed approach is analyzed. A Kalman filter is developed to track the LEO Doppler frequency. The significance of utilizing sequential MSD to acquire multiple LEO satellites is experimentally demonstrated with OneWeb LEO signals. Experimental results are presented with Starlink LEO satellite signals, showing successful acquisition and Hz-level Doppler tracking. Positioning results with six Starlink LEO satellites are presented showing a two-dimensional error of 9.52 m, starting from an initial estimate 179 km away.

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