Timing Error to Range Error

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Timing Error to Range Error

A tag’s poll-and-response exchange runs from 0 ns to 220 ns, with the responder recording 10 ns and 210 ns, so the round trip reduces to a 20 ns flight time and a worked distance of 3.0 m at 0.30 m/ns. The same conversion shows a 2 ns round-trip timing error becomes about 0.30 m of range error, which the chapter says may be fine for a tool cabinet that only needs to know a device is within about 1.5 m, but not enough for a robot cell that needs a 0.25 m exclusion boundary. This audit asks the question that gap invites: does the chapter’s own arithmetic actually support the worked 3.0 m distance and the 0.30 m error warning, once calibration and clock behavior are accounted for?

Companion to the chapter UWB Ranging Techniques — every number here comes from that chapter.

Ada: UWB ranging is a physics calculation before it is a location claim. The chapter’s examples already give the values needed to check both the timing-error warning and the worked two-way range.

• The chapter states that light travels about 0.30 m/ns.
• A 2 ns round-trip timing error becomes one-way range error after the two-way divide: 0.30 m/ns x 2 ns / 2 = 0.30 m.
• In the worked TWR example, the initiator elapsed time is T4 - T1 = 220 ns - 0 ns = 220 ns.
• The responder delay is T3 - T2 = 210 ns - 10 ns = 200 ns.
• The flight-time part of the round trip is therefore 220 ns - 200 ns = 20 ns.
• One-way flight time is 20 ns / 2 = 10 ns.
• Distance is 10 ns x 0.30 m/ns = 3.0 m.

The audit conclusion is bounded: the arithmetic supports the stated 3.0 m example and the 0.30 m error warning, but only for a measurement record that also proves calibration, clock behavior, and channel quality are good enough for the action using the range.

Every number above is taken from the chapter’s own material and re-derived step by step.