A Transit-Phase Ranging Unit: Distance Measurement by Phase-Step Counting with Computed Resolution and Ambiguity Range

Ranging by phase has a characteristic two-scale structure: a fine interpolation within one period and a coarse ambiguity across periods, and most practical systems bolt the two together from separate waveforms. A waveform organised by the transit law's phase steps carries both scales natively, whole steps for the coarse count and intra-step phase for the fine interpolation. This paper specifies a ranging unit on that principle. Its phase subdivision of one part in 65536 of a 4.50-metre step gives a quantisation resolution of 68.7 micrometres; its 2048-step code gives an unambiguous range of 9216 metres; and its noise-limited accuracy is 20.2 millimetres at one kilometre, degrading to 186 millimetres at full range as the carrier signal-to-noise ratio falls to 8.7 decibels. Step-slip probability at full range is computed at 9.4e-34 per measurement. SIMULATED, NOT MEASURED: all figures are computed from the stated assumptions.