Free-Inertial Displacement Envelope for Authenticated GNSS Between Authentication Marks: An Illustrative Fixed-Bias Model

This technical note presents a simplified free-inertial displacement envelope for authenticated Global Navigation Satellite System (GNSS) operation between authentication marks. Selected inertial-sensor class values-lower endpoints for numerical ranges and tabulated boundary values for inequalities are propagated as fixed, same-sign biases over a 180-second interval corresponding to the standalone slow authentication channel considered in the cited Chimera literature. Under the stated assumptions, the modeled same-sign fixed-bias displacement envelopes at 180 seconds are 8.4 m for navigation-grade sensors, 205.1 m for tactical-grade sensors, 2.05 km for industrial-grade sensors, and 12.56 km for consumer-grade sensors. The results are illustrative model outputs. They do not establish a detector threshold, a statistically calibrated confidence bound, a formally guaranteed worst-case limit, or a guaranteed limit of distinguishability. Actual receiver behavior depends on sensor characteristics, calibration, filter covariance, geometry, gating logic, environmental conditions, and integration architecture. The accompanying Python script, displacement_bound.py, reproduces the calculations and reported output table using only the Python standard library.