How to improve Acceleration/Distance measurement?

I’m experimenting with sensors in Android and decided to make an app to measure the distance by which the device moves, using the linear acceleration sensor. I came up with a following piece of code:

override fun onSensorChanged(e: SensorEvent?) {
   if (e != null) {
      when (e.sensor.type) {
         Sensor.TYPE_LINEAR_ACCELERATION -> {
            var time = if (dta != 0L) (e.timestamp - dta) * 10f.pow(-9) else 0f

            for (i in 0..2) {
               acceleration[i] = e.values[i]
               position[i] += acceleration[i] * time * time / 2
            }
            dta = e.timestamp
         }
      }
   }
}

where dta is the time of the last sensor update and acceleration and position are mutable state lists, displayed in the activity.

However, I noticed that the measurements are very inaccurate. To reduce error, I decided to set acceleration[i] to 0f if the corresponding event value is below a threshold. But still, even if the reading seem correct, I don’t have a good way to at least partially accurately convert raw acceleration data to position changes.
I don’t really know how to cope with that, for example because of the acceleration characteristic of the human steps (they keep once increasing once decreasing), as shown on the graph plotted in the activity:

Where red means X acceleration, green – Y, blue – Z and black is the “total” acceleration – the square root of the sum of squared single-axis accelerations.

What I find noteworthy is that the idea of the app is to measure the distance traveled in the range of 1 to 5 meters, at the rate of a person’s normal walking pace (he presses a button, walks over, puts the phone down and goes back to the original location), so the period of movement should not be longer than a minute. Given such orders of magnitude, sensor drift shouldn’t mess that much, but at cost of no possibility to use GPS to correct the results.
I’d like to achieve accuracy of 15-20 centimeters. Is this possible, and if so, how to achieve such effect? And if not, are there any other ways to effectively measure the user’s distance from the device? I’ve heard of Google ARCore that should be theoretically able to calculate distance between two points (called Hit Records) but the quality of the readings heavily depend on the camera quality and lighting conditions. I’ve also read (here,
here,
here,
here and
here) advice about “implementing Kalman filters” and “fusing sensors” – what does it mean? Maybe it could help?

I truly apprectiate every answer!

This is as much an applied maths or physics problem as anything else. Your code for updating the position is only correct for a sensor at rest. Classical mechanics the two most useful equations that are relevant here are:

v = u + a*t
s = u*t + a*t^2/2

Where 

u = velocity at start of timestep
a = acceleration (assumed constant during timestep)
v = velocity after timestep
s = distance travelled after time t (assumed uniform acceleration)

Your code is assuming that u=0 for all t.

  var time = if (dta != 0L) (e.timestamp - dta) * 10f.pow(-9) else 0f
  for (i in 0..2) {
      acceleration[i] = e.values[i]
      position[i] += acceleration[i] * time * time / 2
  }
  dta = e.timestamp

And has a possible systematic error bias that is proportional to the time spent doing the calculation. e.timestamp may change between first and second usage.

I don’t speak the language you are using for coding this but based on the code that you have shown then the following should be much closer to working (obviously you have to declare velocity[] in the right scope. I have introduced a new variable dt = time - otime... and renamed dta as otime because it is the previous timestamp value and not a time difference.

 var dt, time = e.timestamp
 if (otime != 0L) dt = (time - otime) * 10f.pow(-9) else 0f
 otime = time
 for (i in 0..2) {
           acceleration[i] = e.values[i]
           position[i] += dt*(velocity[i]+ acceleration[i] * dt / 2)
           velocity[i] += dt*acceleration[i]
        }

I do wonder if the scaling of the time interval might also be wrong and whether the sensor really returns acceleration in SI m/s^2 units. Is the timestamp value really measured in nanoseconds? Various sensor calibration scale factors will be important so you need to check the manual for those.

Filed under: Kiến thức lập trình - @ 01:11

Thẻ: androidkotlinaccelerometerandroid-sensors

How to improve Acceleration/Distance measurement?

override fun onSensorChanged(e: SensorEvent?) {
   if (e != null) {
      when (e.sensor.type) {
         Sensor.TYPE_LINEAR_ACCELERATION -> {
            var time = if (dta != 0L) (e.timestamp - dta) * 10f.pow(-9) else 0f

            for (i in 0..2) {
               acceleration[i] = e.values[i]
               position[i] += acceleration[i] * time * time / 2
            }
            dta = e.timestamp
         }
      }
   }
}

where dta is the time of the last sensor update and acceleration and position are mutable state lists, displayed in the activity.

I truly apprectiate every answer!

v = u + a*t
s = u*t + a*t^2/2

Where 

u = velocity at start of timestep
a = acceleration (assumed constant during timestep)
v = velocity after timestep
s = distance travelled after time t (assumed uniform acceleration)

Your code is assuming that u=0 for all t.

  var time = if (dta != 0L) (e.timestamp - dta) * 10f.pow(-9) else 0f
  for (i in 0..2) {
      acceleration[i] = e.values[i]
      position[i] += acceleration[i] * time * time / 2
  }
  dta = e.timestamp

And has a possible systematic error bias that is proportional to the time spent doing the calculation. e.timestamp may change between first and second usage.

 var dt, time = e.timestamp
 if (otime != 0L) dt = (time - otime) * 10f.pow(-9) else 0f
 otime = time
 for (i in 0..2) {
           acceleration[i] = e.values[i]
           position[i] += dt*(velocity[i]+ acceleration[i] * dt / 2)
           velocity[i] += dt*acceleration[i]
        }

Filed under: Kiến thức lập trình - @ 01:11

Thẻ: androidkotlinaccelerometerandroid-sensors

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How to improve Acceleration/Distance measurement?

How to improve Acceleration/Distance measurement?