Hmmm. What about the sensors on my phone? For a while now I've wanted to know my realtime speed in the underground sections of the local rail/metro network.

I suspect the most accurate measurements would be done using wideband SDR, iff I were able to acquire absolute position references for the signals I was seeing. Not likely, especially for something I might like to let others play with and/or generalize.

Everywhere I read about the subject the general consensus is that using accelerometer and gyro data from the average phone is a fool's errand. I have zero experience with the field so I wouldn't know if failure was incorrect signal processing or just had sensors.

Without wheel speed sensors, distance and speed errors quickly accumulate.

With a particle filter and enough computation, that error can be eliminated after the fact. Ie. At the time you won't know where you are, but after you get out of the metro and the particle filter reconverged you'll know where you were with more accuracy at some point in the past.

Ah. I see. Thanks very much for that insight - so that's why it's possible, but not generally interesting and/or widely pursued.

You'd also need to account for slope.

I’ll be overjoyed the day that the compass in the vehicle can tell my phone what direction the vehicle is pointed to avoid making a left instead of a right out of a driveway. Yes, there are solutions to these problems in theory, but in real-world application today they’re still pretty lame / inaccurate, and the solutions still seem far away (try getting a few auto mfgs to agree to a standard way of communicating a compass heading to a phone over CarPlay or Android Auto)

I've used a phone that didn't have a built in compass and one that does. The one that has an actual compass knows which direction I'm facing even without moving. The one that didn't would usually have no idea until I started moving.

They make external GPS units that plug into your car and connect to your phone wirelessly for example Garmin GLO that are supposed to improve accuracy although I haven't used one myself and thus can't vouch for it.

The built in compass in a phone is pretty inaccurate for driving because it can't compensate for the unknown shape of the body shell of the car it's in.

When turn-by-turn directions specify traveling 1 mile down a very steep grade, do they mean 1 mile along the slope, or 1 mile along a flattened map?

Only the former would match the car's odometer, of course.