Sensors & Measurement · Study deck

IMU and Barometric Calibration

Picture a delivery cart that must detect a turn and a change of floor.

Physics Phoebe is your guide for this deck.

sensormotionbarometric

After studying this chapter

Learning objectives

You will be able to:

Explain how a MEMS capacitive accelerometer turns proof-mass deflection into acceleration readings.
Convert analog and digital IMU readings into physical units while preserving full-scale and offset evidence.
Diagnose why accelerometers confuse gravity, tilt, vibration, and horizontal acceleration without fusion.
Use BMP280 pressure changes as relative altitude evidence while accounting for weather drift and baseline freshness.

Major section

Start With the Measurement Story

Its motion sensor reports gravity as well as movement.

A changing number is not yet proof of a real move.
If the reference is old or the sensors disagree, lower confidence instead of forcing an answer.
One indoor check cannot promise accuracy on every vehicle or day.

Major section

Overview: A Tiny Mass on Silicon Springs

The accelerometer in a phone, a drone, or an IoT motion tag is a MEMS device — a micro-electro-mechanical system etched from silicon.

Inside is a microscopic proof mass suspended on flexible silicon beams that act as springs.
When the device accelerates, inertia makes the mass lag behind, deflecting on its springs.
The sensor measures that tiny deflection and reports it as acceleration.

Major section

Deflection to Volts

The package converts proof-mass deflection into three analogue outputs; the breakout only makes those supply and signal pins accessible.

The mechanics are a mass on a spring.
That same equation is also the whole story of why MEMS accelerometers can be shrunk onto a chip in the first place.
A miniaturized accelerometer therefore needs a small mass and a proportionally weak spring — it is the ratio, not the size, that is being designed.

A blue ADXL335 three-axis analog accelerometer breakout board shows its central sensor chip, printed X, Y and Z markings, and labeled connection pads. A separate strip of six metal header pins lies to the right on a white background.

Major section

Gravity, Brownian Noise, Bandwidth

The accelerometer gives a gravity guide but is noisy in motion.

Their joint path can estimate roll and pitch.
This split also explains why pressure needs its own check.

IMU sensor fusion architecture combining gyroscope, accelerometer, and magnetometer inputs with calibration to estimate roll, pitch, and yaw.

Deck summary

Key takeaways

Its motion sensor reports gravity as well as movement.

The accelerometer in a phone, a drone, or an IoT motion tag is a MEMS device — a micro-electro-mechanical system etched from silicon.
The package converts proof-mass deflection into three analogue outputs; the breakout only makes those supply and signal pins accessible.
The accelerometer gives a gravity guide but is noisy in motion.

Retrieval practice

Recall check 1 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q1What physically moves inside a MEMS capacitive accelerometer when the device accelerates?

AA spinning disc changes speed in proportion to acceleration.

BA crystal generates a steady voltage proportional to constant acceleration.

CA microscopic proof mass on silicon springs deflects.

DNothing moves; the chip measures temperature changes instead.

Show answer

Answer: C Inertia deflects the proof mass, and the resulting capacitance change is the readout.

Retrieval practice

Recall check 2 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q2A digital accelerometer uses ±2 g full scale and 16,384 counts per g. Its raw axis value is 9,216 counts, including a +1,024 count zero offset. What acceleration remains after offset correction?

A0.5625 g, dividing the uncorrected 9,216 count reading.

B1.0 g, treating the zero offset as a full gravity unit.

C2.0 g, mistaking the full-scale range for the reading.

D0.5 g, after offset correction and count-to-g conversion.

Show answer

Answer: D Correct: remove the zero offset in counts, then divide by counts per g.

Retrieval practice

Recall check 3 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q3An ADXL335 outputs 300 mV/g with 0 g at 1.5 V. Its axis reads 1.20 V while stationary. What is happening?

AIt needs a zero-offset correction to 1.5 V, since the device is not translating.

BThe axis senses about -1 g: (1.20 - 1.50) / 0.300 = -1.0 g.

CIt reads +1 g, using the magnitude of the 1.20 V deviation from 1.5 V.

DIt suggests supply drift, so restore the zero-g level before interpreting the 1.20 V reading.

Show answer

Answer: B The 0.30 V offset below the 1.5 V zero-g level corresponds to -1 g, i.e. gravity along that axis. (Also: consistent with that axis pointing straight down so gravity acts along it.).

Retrieval practice

Recall check 4 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q4Why can a single MEMS accelerometer not distinguish a slow tilt from a genuine horizontal acceleration?

AIt cannot sense gravity, making slow tilt invisible to the device.

BTilt and horizontal acceleration differ only in temperature.

CIt senses gravity and linear acceleration together as specific force.

DQuantization noise always erases the distinction between them.

Show answer

Answer: C Gravity reoriented by tilt and genuine linear acceleration both contribute to the same measured specific force, so separating them requires extra information such as fusion with a gyroscope.

Retrieval practice

Recall check 5 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q5A fixed BMP280 reports a pressure change that looks like a floor change. What should the system check before claiming movement?

ATreat every pressure change as a true height change.

BUse a fresh local baseline and a second movement clue.

CReplace the baseline with a permanent absolute altitude label.

DAverage away all pressure changes before checking movement.

Show answer

Answer: B Relative pressure needs a recent baseline and corroboration before it becomes a movement claim.

Print reference

Answers 1 of 2

Answer key.

C · Inertia deflects the proof mass, and the resulting capacitance change is the readout.
D · Correct: remove the zero offset in counts, then divide by counts per g.
B · The 0.30 V offset below the 1.5 V zero-g level corresponds to -1 g, i.e. gravity along that axis. (Also: consistent with that axis pointing straight down so gravity acts along it.).

Print reference

Answers 2 of 2

Answer key.

C · Gravity reoriented by tilt and genuine linear acceleration both contribute to the same measured specific force, so separating them requires extra information such as fusion with a gyroscope.
B · Relative pressure needs a recent baseline and corroboration before it becomes a movement claim.