The Hidden 3x Inside the E911 Tiers

The Hidden 3x Inside the E911 Tiers

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

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Ada ADA · CALCULATION AUDIT

The Hidden 3x Inside the E911 Tiers

When you dial 911 from a mobile phone, FCC E911 rules force the carrier to report where you are — and the chapter tabulates how accurately. Handset-based A-GPS must reach 50 m for 67% of calls and 150 m for 95%; network-based positioning, 100 m and 300 m. The chapter’s design rule is to spec to the 95% number and expect roughly 3x worse than the brochure figure, so this audit asks whether that 3x is a loose rule of thumb or something the regulation actually encodes.

Companion to the chapter Location Privacy and Regulations — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is typical accuracy bound. The middle card applies the page rule. The green card is dependable accuracy bound. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Typical accuracy bound changes dependable accuracy bound An input card leads through the rule 95% bound = 3 x 67% bound to the dependable accuracy bound result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A safety promise should use the dependable bound, not the brochure-like typical value.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 50 m.

  2. 2

    Name the relationship. 95% bound = 3 x 67% bound

  3. 3

    Substitute with units. 3 x 50 = 150.00 m

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change typical accuracy bound

Try Predict the direction of 95% bound = 3 x 67% bound. Test another typical accuracy bound, then compare dependable accuracy bound.

50 m
Chapter baseline
Dependable accuracy bound

Observe A safety promise should use the dependable bound, not the brochure-like typical value. Reset typical accuracy bound to 50 and compare dependable accuracy bound.

Explain A safety promise should use the dependable bound, not the brochure-like typical value.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only typical accuracy bound moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only typical accuracy bound. It is not a field prediction.

TryRecompute Handset-based (A-GPS): 150 m / 50 m = 3.0.
ObserveTrack Network-based: 300 m / 100 m = 3.0.
ExplainA ratio of 3.0 means the stated coarse accuracy radius is three times the finer radius in each method. It compares spatial uncertainty tiers; it does not imply that either estimate identifies the handset's exact position.

Ready: use the stated baseline inputs, then compare each displayed result.

Ada: The E911 table gives two accuracy tiers for each technology, and the chapter’s design rule is to spec to the 95% number and expect roughly 3x worse than the advertised figure. Let me check whether that 3x is a loose rule of thumb or something the regulation actually encodes.

Take the ratio of the 95%-of-calls bound to the 67%-of-calls bound for each technology:

  • Handset-based (A-GPS): 150 m / 50 m = 3.0
  • Network-based: 300 m / 100 m = 3.0

They are not merely close, they are both exactly 3.0. The FCC set the worst-case (95%) requirement at precisely three times the typical-case (67%) requirement, and it did so identically for two physically different positioning methods. So the chapter’s heuristic is not folklore; it is reading a constant straight out of the mandate. That is why the “advertised 5 m -> expect 15-20 m in hard environments” guidance (a 3x to 4x spread) is well founded: a location system’s typical accuracy and its dependable accuracy differ by a roughly fixed multiple, and safety-critical design should budget for the 3x-worse number rather than the brochure number.

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

Technical boundaries. This arithmetic deliberately does not simulate a population's movement, re-identification attacks, or consent decisions. It compares the stated E911 accuracy tiers and their fixed threefold scale relationship only.