Every smartphone carries an inertial measurement unit — a cluster of tiny MEMS chips that report how the device accelerates and rotates. The accelerometer measures specific force in meters per second squared; the gyroscope measures angular rate in radians per second. Together they form what engineers call an IMU. The tempting first project in any sensor course is to integrate those signals into position: double-integrate acceleration for displacement, integrate gyroscope for heading, and draw a trail on a map. Within thirty seconds the trail has wandered into the next building. Consumer MEMS biases sit at milligram scale, and integration squares time — small errors become large distances very quickly.

Wheria does not try to be a general-purpose inertial navigator. Underground, where GPS horizontal error often exceeds thirty meters, we use pedestrian dead reckoning: a method that treats each footfall as a discrete event rather than a continuous integral. Detect a step, multiply by an estimated stride length, rotate by current heading, and advance a point on a local map. Error still accumulates, but it grows roughly with the square root of step count instead of exploding exponentially with elapsed time. That difference is what makes a four-minute garage walk usable instead of absurd.

What a step looks like to an accelerometer

When you walk at a normal pace of about 1.2 to 1.5 meters per second, your body produces a rhythmic vertical bounce. That bounce repeats at a cadence of roughly 1.5 to 3 hertz — one complete up-down cycle every third to two-thirds of a second. The accelerometer magnitude, computed as the square root of the sum of squared axis values, shows clear peaks in that band even when the phone sits in a pocket at an odd angle.

Our step detector band-passes that magnitude signal around the walking band, then hunts for peaks. The threshold is not fixed: over a sliding two-second window we compute the local mean and standard deviation, then declare a step when a peak exceeds mean plus k times sigma, where k ranges from about 1.2 to 1.8 depending on whether the phone is in a trouser pocket or held in hand. A minimum interval of 280 milliseconds between accepted steps filters out shuffling false positives. Between steps, the gyroscope z-axis — rotation about the vertical axis when the phone is upright — helps confirm that the user actually turned rather than merely jostled the device.

iOS and Android deliver IMU samples at different native rates, anywhere from fifty to two hundred hertz depending on device and power mode. Before the detector runs, shared logic resamples both platforms to a fixed one-hundred hertz so the same peak-picking code produces the same step count on an iPhone and a Pixel given identical motion.

Stride length is the hidden variable

A detected step tells you that the user moved, but not how far. That distance comes from stride length — the horizontal span of one footfall. Wheria starts with a default of about 0.72 meters, which matches average adult walking on flat ground. If the user enters height in settings, we apply a common anthropometric estimate: stride approximately equals 0.415 times height in meters. For users who want tighter accuracy, an optional calibration walk asks them to traverse a known distance — twenty meters in a straight corridor works well — and we solve stride as distance divided by step count.

Some research papers tie stride to step frequency through power-law models such as Weinberg's relation, where stride scales with the fourth root of cadence. We expose a modest version of that tie-in, but it is not magic: a five percent stride error on an eighty-meter walk with a hundred and ten steps produces four meters of longitudinal error before heading is even considered. That is why Wheria shows distance bands instead of fake precision, and why we encourage calibration for users who regularly park in large structures.

Building an honest error budget

Suppose you walk eighty meters through a spiral ramp with a hundred and ten detected steps. Stride is wrong by five percent: you are four meters off along the path. Heading at the end is wrong by ten degrees: lateral error is eighty times sine of ten degrees, roughly fourteen meters in the worst geometry. These numbers are not pessimistic fiction — they are what ktuyen's garage test matrix produces when compass trust is low and the user skipped calibration. The UI responds with a fading polyline whose older segments dim, a confidence chip derived from fusion covariance, and language like "about 45 m" rather than "44.7 m." Each new parked event resets the odometry state so errors stay bounded per trip instead of compounding across weeks of history.

PDR has hard limits we do not hide. Escalators increment step count without equivalent horizontal travel. Moving walkways decouple footfalls from ground speed. Running breaks the cadence band the detector expects. A phone clamped to a shopping cart handle produces an acceleration profile that looks nothing like walking. When accelerometer variance spikes in ways that do not match normal gait, Wheria flags unusual motion rather than silently drawing a path that pretends the user walked.

Step detection is only one layer of the indoor stack. Heading comes from gyroscope and magnetometer fusion described in our compass post; floor hints from the barometer in barometer math; and the full pipeline in indoor navigation. The Kalman filter in Kalman filters for parking ties those measurements together so a single step update does not overconfidence the map. Phyzix exposes raw accelerometer and gyroscope traces if you want to see the peaks yourself before trusting an app to count them.