A Sequence Matching Approach for GNSS-Based Orbit Determination Using Dynamic Time Warping

Accurate navigation in deep space and lunar environments poses significant challenges due to limited GNSS signal availability and the need for robust state estimation that may take advantage of additional trajectory information. This paper investigates the application of sequence matching (SM) techniques to align a GNSS-based trajectory with a pre-designed aiding trajectory (AT), a crucial step in enhancing GNSS-based Position, Navigation, and Timing (PNT) solutions. We formulate the SM problem as a generalized constrained optimization problem and introduce, as a solution, a locally weighted Dynamic Time Warping (DTW) method tailored for GNSS state estimation fusion in challenging environments. The proposed approach is validated through comparisons with an exhaustive search benchmark and extended to assess different local cost functions---based on quasi-norm operators and angular distance---within both classical DTW and the locally weighted DTW framework. Performance analysis, conducted using realistic RF signal simulations for the cislunar environment and trajectories with error-affected sampling rate, demonstrates the effectiveness of the proposed method in handling signal degradation and time misalignment. These findings contribute to advancing autonomous space navigation, reducing reliance on ground-based tracking, and supporting future deep-space missions.