Geometric Analysis and Optimization of Doppler-Based Navigation with Low Earth Orbit Satellites
| Doppler-only navigation using low-Earth orbit satellite constellations is a promising complement to Global Navigation Satellite Systems (GNSS), yet the geometric principles governing satellite selection for Doppler positioning differ fundamentally from those established for pseudorange-based navigation prevalent in GNSS. Volume-based satellite selection, effective for pseudorange-based geometric dilution of precision (GDOP) minimization, shows weak correlation with Doppler GDOP, but the mechanism responsible for this failure has not been identified thus far. In this talk, we will develop the theoretical framework needed to explain this phenomenon. Analytical parameterization of the eight-state Doppler Jacobian measurement matrix reveals that clock bias sensitivity creates a functional collinearity with the vertical-velocity column, which has no pseudorange analogue, and cannot be eliminated by any geometric arrangement. A Schur-complement framework quantifies the resulting covariance inflation, and a systematic experimental campaign validates the predictions, confirming that altitude diversity is the primary decorrelation mechanism. The main contribution is the analysis and explanation of why volume-based satellite selection fails, and why common heuristic GDOP proxies remain limited in effectiveness. Implications for optimal satellite selection for Doppler-based navigation are outlined.
This work is towards a Ph.D. degree under the supervision of Prof. Pini Gurfil, Shirley and Burt Harris Professor of Aerospace Engineering.
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