[chris (OP)]

How do the accelerometers in mobile devices, like phones, actually work, and what is their accuracy?

According to my phone I've walked the length of England on a stroll out with my next door neighbour this morning...

[Halc]

How do the accelerometers in mobile devices, like phones, actually work, and what is their accuracy?

According to my phone I've walked the length of England on a stroll out with my next door neighbour this morning...

The accelerometer on a phone is usually used to detect which way is up so it knows which way to orient the display.  In some apps, it might use the information to detect your local motion, i.e. changes in gait and orientation.
An app tracking the length of a walk should be using GPS, not the accelerometer, which lacks absolute references.

You may well have move the length of England on your stroll, as the spin of Earth will carry you that distance.  Maybe for some reason the phone was computing distance relative to the center of Earth instead of relative to the local surface of it.

[chris (OP)]

But how does it actually work? Are there little weights that are inertially measured to detect movement?

[Halc]

But how does it actually work? Are there little weights that are inertially measured to detect movement?

If it is counting steps, it feels you bounce up and down as you walk.  It then multiplies that by your stride length, which is probably based on some configuration info you provided it when setting it up.
False readings can be had if it mistakes other motion for steps such as dancing or shaking it.  It should be in your pocket to get a good reading for counting steps.

[Halc]

As for how it actually works, moving parts are discouraged.  They have crystals that get stressed under acceleration and conduct electricity differently, which is detected by the electronics attached to the crystals.

They detect axis motion more than up and down motion, so the swing of your arm or hip is detected more than the vertical bouncing.

[Bored chemist]

But how does it actually work? Are there little weights that are inertially measured to detect movement?

Yes.
https://www.siliconsensing.com/technology/mems-accelerometers/

[evan_au]

The tiny, mass-produced sensors in a smartphone or smartwatch use MicroElctroMechanical Systems (MEMS).

These use micromachining to produce a tiny sensor on a silicon chip.

See: https://en.wikipedia.org/wiki/Microelectromechanical_systems#Applications
...the same article mentions how they are made - just search for accelerometer, eg:
https://en.wikipedia.org/wiki/Microelectromechanical_systems#Surface_micromachining

[evan_au]

Traditionally, this function was carried out by a pedometer, worn at the waist. This mostly responds to the up-and-down motion while walking.

However, a smartphone can be used in any orientation - in a pocket, held in the hand, texting while walking (dangerous!), or in a bag, and so they must sense motion on any axis.

A fitness tracker on your wrist is an even more challenging environment, as your hand is moving when typing, making/eating dinner, reading a book, etc. My fitness tracker even asked whether it was on my dominant or non-dominant hand (I guess this might allow them to correct for inaccuracies between left and right-handers?).

So  the MEMS sensor is surrounded by layers of software that (I imagine) do functions like:
- Turn several single-axis measurements from the sensor into a magnitude measurement
- Filter the software in several frequency bands related to walking, running, etc
- Apply thresholds for amplitude and duration in these frequency bands
- Combine with inputs from other sensors like barometer (atmospheric pressure) and GPS (absolute location)
- Classify the results into categories like walking, running, climbing stairs, driving, sleeping, or even using an elliptical exercise machine at the gym, etc
- These categories are not always accurate - a recent update to my smartphone OS tries to discourage you from doing anything on the phone when it thinks you might be driving. However, it can't tell the difference between a car and a train, so I always have to tap "No I'm not driving" when I try to fill in my activities for the day, while commuting on the train.
- I assume that some of the vendors use Machine Learning/AI techniques to train their classifier algorithms, using traces from people doing various known activities, and apply corrections for spurious readings from various sources...

Overall, a device on your waist or hip pocket would be best for measuring steps. But smartphones & fitness trackers do a remarkable job of tracking activities.
- I get a weekly email reporting on how I did that week - it's good for keeping you conscious of general activity levels and sleep quality, so it doesn't matter if it is wrong by 1-5%
- My tracker once told me that I had walked the length of Italy - but that was after I had used it for a reasonable amount of time (not 1 day!).

[alancalverd]

I use visual recognition signals and integrated velocity computation referred to solar azimuth via an electromechanical analog display.  If I set out from A, T_A and recognise my arrival at B, T_B, then I calculate that I have walked (B-A) miles in (T_B - T_A) hours. The ratio gives me my average speed, and multiplying distance by 1760 tells me how many steps I have taken.

The only error source is Alzheimers, but it is self correcting - if I don't know where I am, or what time it is, I probably don't care, and the number of steps is always irrelevant: if I am at B, n must have been optimal.

Similar systems work for other modes of transport.

[Bored chemist]

I use visual recognition signals and integrated velocity computation referred to solar azimuth via an electromechanical analog display.  If I set out from A, T_A and recognise my arrival at B, T_B, then I calculate that I have walked (B-A) miles in (T_B - T_A) hours. The ratio gives me my average speed, and multiplying distance by 1760 tells me how many steps I have taken.

The only error source is Alzheimers, but it is self correcting - if I don't know where I am, or what time it is, I probably don't care, and the number of steps is always irrelevant: if I am at B, n must have been optimal.

Similar systems work for other modes of transport.

When I first read this post a few hours ago I was sat in this chair.
I am sat in it now.
So, by distance travelled is zero and my speed is zero.
And the number of steps is also zero.
Which is odd, considering that I went shopping.
My phone thinks I took 7000 steps this morning.
I trust it better than I trust Alan's method.

[alancalverd]

The key words are "set out" and "arrival" If you sat in the chair continuously, ΔT = 0 and B-A = 0, but a loop integral locus is not zero. You might have been abducted by an alien whilst asleep.

Some of us know where we have been for the last few hours, others are merely grateful to have got back to where they started. The first rule of nursing is to know what diagnosis you are dealing with.

[Bored chemist]

Roughly speaking, I set out about 11:00 and arrived about 12:45
I know that the loop integral's non zero

But that's now what you said to calculate is it?
Do you remember?
You said " I calculate that I have walked (B-A) miles in (TB - TA) hours. "
And that gives the wrong answer.


" The first rule of nursing is to know what diagnosis you are dealing with."
Interesting, but obviously not always possible. A bit like your calculation.

[kaynan]

I think so far I have not thought about it. I wear a fitness bracelet for several years. Sensors are built into smart bracelets, each of which registers a certain indicator. For example, calculating the speed, pulse rate and duration of physical activity, the gadget calculates calories expended or the duration of sleep.

The device syncs with my smartphone via Bluetooth.