Error Budget and Airtime Load

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

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Ada ADA · CALCULATION AUDIT

Error Budget and Airtime Load

A 30 m x 20 m work area places anchors at known coordinates and mounts a tag on a cart, where a geometry factor of 3 can turn a 0.20 m range error into about 0.60 m of position uncertainty. A fuller error budget of range 0.15 m, geometry factor 2.5, environment bias 0.20 m, and filter lag 0.10 m sums to about 0.675 m, which clears a room-level need but fails a 0.30 m robot-safety boundary, while a TWR design with 80 tags, 4 anchors, and 1 update per second asks for 320 ranging exchanges per second. This audit asks the question those sums invite: are the geometry-amplified error budget and the TWR airtime load really additive bookkeeping the way the chapter claims, and which decision do they actually clear?

Companion to the chapter UWB Indoor Positioning Systems — every number here comes from that chapter.

Ada: This chapter builds two kinds of number: a position error budget and an airtime load. Both are just sums, and both decide whether a design is honest. Let me total them with the chapter’s own values.

Geometry amplification, from the GDOP example: a 0.20 m range error under a geometry factor of 3 becomes 0.20 x 3 = 0.60 m of position uncertainty before any other term is added.

The full error budget (range 0.15 m, geometry factor 2.5, environment bias 0.20 m, filter lag 0.10 m):

  • 0.15 x 2.5 = 0.375 m from range times geometry.
  • 0.375 + 0.20 + 0.10 = 0.675 m total.
  • That clears a room-level 1.0 m need but fails a 0.30 m robot-safety boundary – the same evidence is adequate or inadequate only relative to the decision.

Airtime load, TWR versus TDoA:

  • TWR at 80 tags, 4 anchors, 1 Hz: 80 x 4 x 1 = 320 ranging exchanges per second.
  • A 10-tool commissioning fleet at 2 Hz: 10 x 4 x 2 = 80 exchanges per second – fewer requests, stronger per-anchor evidence each.
  • Relaxing 200 tags from 1 Hz to 0.2 Hz: 200 x 0.2 = 40 reports per second.
  • TDoA at 80 tags, 1 Hz: one blink each, so 80 x 1 = 80 transmissions – there is no x anchors factor, which is exactly why it scales.

The audit shows both budgets are bookkeeping, not a rating: geometry multiplies the error term by term, and the anchor factor is the single line separating TWR airtime from TDoA – so the honest release states which sum was met, and under what geometry and load.

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