Gyroscope drift meter with Allan deviation

A working-or-not test answers a yes-or-no question: do the axes respond when you turn the phone. This answers a how-much question that nobody can see by turning anything: with the phone perfectly still, how quickly does the reported heading walk away from the truth. Those are different failures. A gyroscope can pass every functional test and still be too drifty to hold an augmented-reality anchor for thirty seconds, and no amount of waving the phone about would reveal it.

Because the thing being measured only exists over time. White noise shows up in the first seconds; the slow wander of the bias — the part that decides whether averaging helps — only becomes visible over tens of seconds, and the minimum of the Allan curve is usually somewhere between ten and a hundred seconds of averaging. A ten-second recording would give you the noise and tell you nothing about the floor, which is the number that matters.

Angle random walk in degrees per square root of hour is white noise: it says that after t hours of integrating, the heading has wandered by that many degrees times the square root of t. Bias instability in degrees per hour is the floor — the level below which averaging for longer stops improving anything. Both are the units an inertial-sensor datasheet uses, which is what makes your phone comparable with a real part. A good consumer MEMS gyroscope is around 0.5 to 3 °/√h with a floor of tens of degrees per hour; a navigation-grade unit is a thousand times better and costs accordingly.

Then something the table was standing on moved. Footsteps on a wooden floor, a fridge compressor, a washing machine two rooms away and a bus outside all show up at this sensitivity — a gyroscope resolving thousandths of a degree per second is not a gentle instrument. Try the floor rather than a desk, or a different time of day. The refusal is deliberate: a recording of the building is a perfectly good measurement of the building and a useless one of the sensor.

Almost certainly not, and this page shows you the arithmetic rather than asserting it. A gyrocompass works by sensing the Earth’s own rotation: 15.04 degrees per hour, of which the horizontal component at your latitude is what a level gyroscope would see. Sensing that needs a drift well below it — a few degrees per hour at most. Phone gyroscopes typically settle at tens of degrees per hour, which is a few times the Earth’s horizontal rate rather than the hundredfold you might expect; the trouble is that a floor is not noise, so waiting longer does not bring it down. The page prints both numbers side by side, and if you ever hold a phone where the ratio comes out below one, that is a genuinely remarkable device.

Partly because it should: the bias of a MEMS gyroscope depends on temperature, and a phone that has been in a pocket is still cooling down for several minutes. Partly because the tail of an Allan curve is made of only a handful of averages and is genuinely noisy — which is why each point on the chart carries its own error bar and why the floor is not taken from the far right. Two runs on a settled phone should agree within tens of per cent; if they differ by a factor of several, something in the room is moving.

No, though it tells you what a calibration could buy. The resting offset shown here is exactly what a calibration would subtract — and the page shows the heading error both with and without it, which is usually a difference of an order of magnitude. But the offset drifts with temperature and with time, so subtracting today’s value tomorrow recovers only part of it. The bias instability is the part no calibration can remove, and that is why it is the number to judge a sensor by.