Math Bridge: Location Accuracy and Task Fit

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Math BridgeSensor ApplicationsStruggle-friendly runway

When is a browser location accurate enough?

One thread from radio loss and timing scale to a simple decision: compare uncertainty with the task.

Phoebe, the physics guidePhoebe guides
The one targetJudge a confidence radius against the task.
The chapter case25 m vs 5 m; 40 m vs 10 m.
What it buys youDefer decisions the fix cannot support.

Try this in the phone motion and tilt lab, where you change the phone tilt and see the orientation reading and level indicator.

1. Accuracy is an uncertainty radius

coords.accuracy is the provider's 95% uncertainty estimate in metres. The browser does not promise which radios, cached values, inertial inputs, or databases produced it.

Phoebe: Keep the radius as evidence. Do not turn it into an unsupported label such as “GPS fix.”

2. See why radio scale is difficult

1

Spread power over areaS=Pt/(4πd²).

2

Express the ratio as lossFSPL=(4πd/λ)², or 20log10(4πd/λ) dB.

1575.42 MHz across about 20,200 km ⇒ FSPL ≈ 182.5 dB

3. Bound timing without overclaiming

3

Invert the chip rate1/(1.023 Mchip/s)=0.978 µs per chip.

4

Multiply by light speed0.978 µs × 3.00×10⁸ m/s ≈ 293 m.

Receivers estimate sub-chip timing and combine several corrected pseudoranges. One chip's travel distance is a physical scale, not a final position-accuracy guarantee.

4. Reproduce the chapter decisions

25 m / 5 m = 5×; 40 m / 10 m = 4×

Both fixes are much coarser than the stated distinction. Request a better fix or defer; do not make the location decision anyway.

5. Preserve what the API actually says

Record coordinates, timestamp, radius, permission state, request settings, and whether the value was fresh enough for the task. enableHighAccuracy is a hint, not a promise of GNSS or a particular precision.

6. Check yourself

What does a 25 m accuracy value mean here?
Answer: A provider-reported 95% uncertainty radius of 25 m, not a guaranteed error and not a source label.
Can a 40 m radius answer a 10 m nearest-point question?
Answer: No. Its uncertainty scale is four times larger than the distinction.
Does 293 m per C/A chip set GPS accuracy?
Answer: No. Receivers estimate sub-chip timing and combine several pseudoranges with geometry and corrections.
Honesty boundary.

These are the chapter inputs, worked results, and named teaching assumptions.

1575.42 MHz carrier
Frequency, sample rate, or event rate
about 20,200 km path
Distance, wavelength, or size
182.5 dB free-space loss
Gain, loss, margin, or level ratio
1.023 Mchip/s timing scale
Time, interval, or service-life value
293 m chip travel
Distance, wavelength, or size
25/5 plus 40/10 task ratios reproduce the chapter
Percentage, ratio, or gain

They do not identify the browser's hidden provider or predict its position error; Under the Hood keeps those system limits.