Motion-Consistent Reciprocal TDCP for Cooperative UAV Localization

Directed inter-UAV Time-Differenced Carrier Phase (TDCP) couples an inter-node distance increment with a relative clock-bias increment, while phase differencing produces temporally correlated noise and near-planar formations retain a weak relative-height mode. We formulate a fixed-lag factor graph that combines reciprocal TDCP, Time-of-Arrival (TOA), Global Positioning System (GPS), clock dynamics, and calibrated navigation-frontend motion and altitude outputs. An invertible sum-and-difference transformation exposes geometry and clock-bias-increment-rate channels while full covariance propagation preserves the reciprocal-pair likelihood. Local information analysis shows that the reverse observation removes the single-direction geometry–clock-increment rank deficiency, and phase-level modeling yields the first-order moving-average covariance retained by block whitening. A causal motion-consistency test (MCT) compares the whitened geometry channel with an independent motion prediction before the current pair enters optimization; a flagged pair is assigned negligible information and its detector–estimator phase arc is reset. Implementation checks verify the exact four-bias-state residual, covariance-normalized reciprocal innovations, and operation under sparse single-direction ambiguity changes. Across ten paired runs at ps=5%, MCT detected all 770 injected events with a pair-level false-alarm rate of 0.169% and reduced the mean position RMSE by 96.6% relative to DCS.