UX Uma guidesA field team faces an unresolved physical question: Why does one microsecond become three hundred metres? They must answer it before changing clock error on the real device. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is clock error. The middle card applies this page's relationship. The green card is signal travel time. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline for clock error is 1.
- 2
Name the relationship. travel time=20,200,000/299,792,458=67.4 ms 1 us error→299,792,458x10⁻⁶=299.8 m 3.00 m target→3/299,792,458=10.0 ns 1 ns/day→0.300 m/day of uncorrected range creep
- 3
Substitute the chapter fixture. Set clock error to 1. The page ledger gives signal travel time as 67.38 ms.
- 4
Read the result. Keep ms beside the value. Use it only inside the technical boundary on this page.
Predict, then change clock error
Try Predict the direction of signal travel time. Move one control, calculate, then check your prediction.
Observe The huge multiplier is light speed, not a software defect; the receiver must estimate clock bias with position. Reset the control to 1 and compare signal travel time.
Explain Only clock error moves here. The other chapter fixtures remain fixed.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Begin with distance equals speed times time
Radio signals travel at nearly the speed of light. A receiver estimates distance from travel time, so any receiver-clock error looks like extra or missing distance on every satellite measurement.
2. Name every algebra move
Convert orbit distance20,200 km=20,200,000 m.
Divide for travel timeΔt=d/c.
Convert microseconds1 µs=10⁻⁶ s.
Multiply clock errorΔρ=cΔtclock.
Count unknownsx, y, z, and clock bias b need four independent equations.
3. Reproduce the chapter timing
1 µs error→299,792,458×10⁻⁶=299.8 m
3.00 m target→3/299,792,458=10.0 ns
1 ns/day→0.300 m/day of uncorrected range creep
Three coordinates are not the only unknowns. Clock bias is the fourth, so three satellites cannot solve the full receiver state.
4. Try the clock error
TryMove receiver-clock error from nanosecond-scale toward microsecond-scale.
ObserveRange error changes linearly: halve the timing error and the pseudorange error halves.
ExplainThe huge multiplier is light speed, not a software defect; the receiver must estimate clock bias with position.
The calculator isolates clock arithmetic from the rest of GNSS estimation.
- Path
- Actual satellite-to-receiver distance is not simply orbital altitude
- Signals
- Ionosphere, troposphere, ephemeris, multipath, and noise add errors
- Geometry
- Four equations need independent, well-spread satellites to be useful
Validate receiver error and user-facing fallback in the target environment.
5. Test degraded sky view
Record fixes under open sky, partial obstruction, urban reflection, motion, cold start, stale corrections, and loss of satellites. Check the product response, not only coordinates.
6. Record the location state
Store receiver, firmware, constellation, satellite geometry, corrections, timestamp, fix age, uncertainty, environment, action, fallback, and retest triggers.
7. Check yourself
Why does 1 µs create about 300 m?
Why is a fourth satellite needed?
Do four satellites guarantee 3 m accuracy?
The distance, clock-error, target, and atomic-clock values reproduce the chapter's teaching case.
- 20,200 km
- Orbit-scale illustration, not exact slant range
- 1 µs
- Clock-error scale used to expose the multiplier
- Four equations
- Solvability floor, not an accuracy guarantee
Correct, not complete: pseudorange timing alone does not qualify an outdoor position.