Math Bridge: IMU and Barometer Calibration

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Math BridgeSensorsStruggle-friendly runway

How does a floor become counts and pressure?

One thread from a physical change to IMU codes, gyro drift, and barometric evidence.

Phoebe, the physics guidePhoebe guides
The one targetTurn two sensor scales into checks.
The chapter case16,384 counts/g and 12 Pa/m.
What it buys youReject motion and floor claims that do not clear noise.

A field team faces an unresolved physical question: How does a floor become counts and pressure? They must answer it before changing height step in metres 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 height step in metres. The middle card applies this page's relationship. The green card is 0.1 g threshold. 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.

Height step in metres changes 0.1 g threshold An input card leads through the page relationship to the 0.1 g threshold result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. A smaller height step reduces barometric evidence without changing IMU scale. That is why each claim needs its own calibrated quantity and noise comparison.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for height step in metres is 3.

  2. 2

    Name the relationship. N=ag·S; ΔP=gPΔh; SNR=ΔP/σP; drift=bgt

  3. 3

    Substitute the chapter fixture. Set height step in metres to 3. The page ledger gives 0.1 g threshold as 1638 counts.

  4. 4

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

Predict, then change height step in metres

Try Predict the direction of 0.1 g threshold. Move one control, calculate, then check your prediction.

3
Chapter baseline
0.1 g threshold

Observe A smaller height step reduces barometric evidence without changing IMU scale. That is why each claim needs its own calibrated quantity and noise comparison. Reset the control to 3 and compare 0.1 g threshold.

Explain Only height step in metres moves here. The other chapter fixtures remain fixed.

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 height step in metres moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only height step in metres. It replays the chapter fixture; it is not a field prediction.

1. Start with two rulers

The IMU ruler measures acceleration in counts. The barometer ruler measures a height change through pressure. Neither raw number is yet a trustworthy event.

Phoebe: Calibration tells firmware where zero is and how long each ruler mark is.

2. Map gravity to counts

N = ag × 16,384 counts/g

At the chapter's +/-2 g setting, a still upright Z axis should be near 16,384 counts. A 0.1 g motion threshold is therefore about 1,638 counts away from the 1 g reference.

3. Map height to pressure

ΔP ≈ 12 Pa/m × Δh; Δh ≈ ΔP/(12 Pa/m)

For small changes near sea level, a 3 m floor gives 36 Pa, or 0.36 hPa. Compare that result with the stated +/-0.12 hPa relative accuracy before calling a floor.

4. Try a height step

N=ag·S; ΔP=gPΔh; SNR=ΔP/σP; drift=bgt

TryMove the height while the chapter's IMU scale, pressure slope, pressure accuracy, and gyro bias stay fixed.

Still 1 g code
0.1 g threshold
Pressure step
Pressure step
Step / accuracy
Gyro drift per minute

ObserveAt 3 m, the pressure step is 36 Pa (0.36 hPa), three times the stated accuracy figure. The IMU threshold stays 1,638 counts because it belongs to a different ruler.

ExplainA smaller height step reduces barometric evidence without changing IMU scale. That is why each claim needs its own calibrated quantity and noise comparison.

Technical boundaries.

The count mapping assumes the +/-2 g range and a correct signed-axis conversion.

The 12 Pa/m pressure rule is a local near-sea-level approximation
Needs separate evidence
Weather, airflow, mounting stress, temperature, vibration, bias, and correlated noise can dominate these simple checks
Needs separate evidence

Use field evidence or a deeper model before release.

5. Keep drift separate

0.01 deg/s × 60 s = 0.6 deg/min

A constant gyro offset accumulates with time. A pressure scale check cannot repair it; the IMU needs a still reference or another long-term orientation source.

6. Decide what passes

First verify the still count and sign. Then verify the pressure step against a known height. Finally record the range, offsets, time, weather, and mounting state that make those checks repeatable.

7. Check yourself

Why is 0.1 g about 1,638 counts?
Answer: Multiply 0.1 by the configured 16,384 counts/g scale.
Why is a 3 m floor about 0.36 hPa?
Answer: 3 m × 12 Pa/m = 36 Pa, and 100 Pa = 1 hPa.
Does a 3.0 ratio prove the floor every time?
Answer: No. It compares only the ideal step with one accuracy figure; weather, airflow, filtering, and reference drift still need evidence.
Honesty boundary.

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

16,384 counts/g
Sensor scale, pressure, or digital result
0.1 g
Chapter input or worked result
12 Pa/m
Distance, wavelength, or size
+/-0.12 hPa
Sensor scale, pressure, or digital result
0.01 deg/s
Time, interval, or service-life value

They support a calibration runway, not a complete MPU6050 or BMP280 error model and not a guarantee of floor detection.

Return to the chapter with the maths unpacked →