Logarithmic binning of smartphone sensor measurements

Question

I' measuring linear acceleration (acceleration minus gravity) and gyroscope from Android smartphones on three axis (x,y,z). Becuase the distribution of the measurments is exponential, i.e. there are much more small values than large values, I would like to bin the sensor measurements using logarithmic binning into 96 bins. If I would use linear binning, I would have to clip the sensor measurements very heavy because otherwise most of the measurements will fall into the first few bins.

Right now I'm using the following bin edges (Python):

import numpy as np
bins = np.logspace(np.log10(0.001), np.log10(hi), num=96, base=10)

The problem here is that there are different types of logarithms (base e, 2, 10) and different starting points (here 0.001).

What is the best way to determine the best logarithmic binning?

Second, right now I'm clipping gyroscope values at 5 rad/s and linear acceleration values at 4*g. Is this reasonable or what are common values for clipping?

Answer 1

The problem here is that there are different types of logarithms (base e, 2, 10) and different starting points (here 0.001).

I get the same bins for any base. see below. note the aproprate usage of log10, log and log2 functions which are consistent with the base= parameter.

>>> import numpy as np
>>> np.logspace(np.log10(0.1), np.log10(10), num=11, base=10)
array([ 0.1       ,  0.15848932,  0.25118864,  0.39810717,  0.63095734,
        1.        ,  1.58489319,  2.51188643,  3.98107171,  6.30957344,
       10.        ])

>>> np.logspace(np.log(0.1), np.log(10), num=11, base=2.718)
array([0.10002388, 0.15851959, 0.25122463, 0.39814519, 0.63098747,
       1.        , 1.58481752, 2.51164657, 3.98050148, 6.30836847,
       9.99761287])

>>> np.logspace(np.log2(0.1), np.log2(10), num=11, base=2)
array([ 0.1       ,  0.15848932,  0.25118864,  0.39810717,  0.63095734,
        1.        ,  1.58489319,  2.51188643,  3.98107171,  6.30957344,
       10.        ])

Second, right now I'm clipping gyroscope values at 5 rad/s and linear acceleration values at 4*g. Is this reasonable or what are common values for clipping?

That depends on your application.

5 rad/s is approximately 3/4 rotation per second. A highly agile quad copter would touch this limit. A model aircraft may not. A real aircraft shouldn't. A motor spinning at 100 RPM definitely would get clipped.

Similar for the 4g acceleration. A fighter aircraft may touch it during maneuvres; a civil aircraft (hopefully) won't. A quad copter might.