A magnetometer measures the magnetic field vector B in microteslas, reporting three orthogonal components in the phone's body frame. Earth's field ranges from roughly twenty-five to sixty-five microteslas depending on latitude and local geomagnetic anomalies — strong enough to orient a compass outdoors, yet fragile enough that a steel parking column two meters away can rotate the apparent north direction by forty to ninety degrees without the phone moving at all. Wheria's heading pipeline treats the compass as guilty until proven innocent: magnetometer measurements enter the fusion filter only when field magnitude and inclination fall within expected Earth bands, and the user interface surfaces distrust explicitly rather than drawing a confident arrow toward a wall.

Calibration literature distinguishes two distortion mechanisms that matter in practice. Hard iron errors produce constant offsets on each sensor axis — a speaker magnet, a ferrous phone case, or permanent magnetization of nearby steel shifts the center of the magnetometer's measurement ellipsoid away from the origin. Users can partially correct hard iron by tracing a figure-eight motion that samples the field across orientations, allowing an algebraic fit to estimate the offset vector. Soft iron errors arise when ferromagnetic material nearby distorts the field itself, stretching the ellipsoid into an ellipse rather than translating it. Parking pillars, rebar in concrete, and the body of your own car create soft iron distortion that varies with position, meaning calibration valid at one row may fail three meters later.

Fusion when the field lies

Textbook three-by-three soft-iron calibration requires diverse phone orientations sampled over time — excellent in a laboratory, unrealistic when someone is walking through a basement trying to remember whether they turned left at pillar forty-seven. Our approach calibrates slowly during straight walking segments, accumulating samples only when the gyroscope reports low turn rate, and discarding measurements when the user turns sharply because the magnetic field direction should not change at the rate a quick pivot produces. Between detected steps, the gyroscope integrates heading at one hundred to two hundred hertz with drift on the order of one to three degrees per minute without correction — acceptable over the half-second gap between footfalls but unacceptable over a two-minute walk without magnetometer assistance.

When variance of heading residuals spikes — the telltale signature of entering a steel zone near EV charging stations where DC cables and transformers superimpose local fields — the Extended Kalman Filter inflates magnetometer measurement noise R by an order of magnitude, effectively reducing to gyro-only dead reckoning until the field stabilizes. The interface responds with a yellow or red compass confidence chip and widens the augmented-reality arrow's cone of uncertainty. If heading standard deviation exceeds twenty-five degrees, Find mode shifts to distance-first presentation: walk approximately sixty meters, then rescan compass in a clearer area. We would rather under-instruct than confidently navigate you into structural concrete.

Real-world offenders and platform parity

ktuyen's regression matrix documents the worst environments: electric vehicle charging bays with heavy DC cabling, structural steel within two meters of the walking path, and the occasional second phone in a back pocket creating a moving hard-iron source. iOS and Android report magnetometer axes with different native conventions; we normalize to a consistent north-east-down or east-north-up frame in shared logic modules before either SwiftUI or Compose renders direction. Phyzix shows raw and calibrated magnetometer vectors side by side, letting students watch the ellipsoid flatten as they walk into Landmark 81's basement — the same data Wheria uses, presented as physics rather than navigation.

We do not promise five-degree compass accuracy in all garages because physics does not permit that promise. We promise not to navigate you confidently into a wall, and we promise that when the instrument distrusts itself, you see that distrust on screen. The Kalman fusion mathematics are detailed in Kalman filters for parking; step-based position updates that heading feeds into are covered in step detection and IMU odometry; the broader indoor context lives in indoor navigation when GPS dies.