On the Fundamental Tracking Performance and Design Considerations of Radio Navigation

The fundamental tracking performance in radio navigation is characterized, leading to optimal receiver design considerations. First, a generalized beacon model is proposed and its sufficient, salient parameters are defined. Second, closed-form approximations of the delay, Doppler, Doppler stretch, and Doppler rate ambiguity functions (AFs) and a generalized coherent integration efficiency model are proposed. Third, design considerations and optimal coherent processing interval (CPI) length selection are presented, based on the complete navigation framework, entailing the: (i) beacon's parameters, (ii) channel dynamics between the transmitter and receiver, (iii) employed clocks by the transmitter and receiver, (iv) search space adopted in the acquisition stage, and (v) dynamical model's order employed in the tracking stage. Fourth, the acquisition and tracking stages of the navigation receiver architecture are discussed. Fifth, three sets of experimental results are presented validating the proposed closed-form approximation of the Doppler stretch and Doppler rate AFs and demonstrating the performance of a receiver tuned by the proposed design considerations in acquiring, tracking, and localization, namely: (i) aircraft tracking of terrestrial 4G signals, (ii) stationary receiver tracking of Starlink low Earth orbit (LEO) signals, and (iii) stationary receiver localization with Starlink and OneWeb LEO signals. For the Starlink and OneWeb receiver localization experiment, the receiver was capable of tracking the Doppler and carrier phase of 5 Starlink and 3 OneWeb LEO satellites. Starting from an initial estimate 50 km away from its true position, the receiver converged to a final two-dimensional (2D) position error of 30.3 m.