An unexpected behaviour with speed-based filtering

[ghost]

Hi!

I started using your library lately and came across an unexpected behaviour in speed-based filtering function: https://github.com/scikit-mobility/scikit-mobility/blob/master/skmob/preprocessing/filtering.py#L115

Consider a case where we move along the equator. For the simplicity sake the trajectory points are reported at 1 hour intervals. The trajectory is as follows:

• starting at lat=0 deg and lon=0 deg
• flying to lat=0 deg and lon=7.186609624 deg, i.e. 800 km/h w.r.t. the previous point
• driving to lat=0 deg and lon=7.5458541615 deg, i.e. 40 km/h w.r.t. the previous point
• continue the trajectory along the equator at 40 km/h.

With a speed limit set at 50 km/h it is expected to remove only the second point, where the limit was exceeded.

This scenario is represented with the following code snippet

from skmob.preprocessing.filtering import _filter_array
import numpy as np
import pandas as pd

degs_800_km = 7.186609624  # math.degrees(800/6371)
degs_40_km = 0.3592445375  # math.degrees(40/6371)

 lat_lng_time = ([np.array([0.0, 0.0, pd.Timestamp('2008-10-23 05:00:00')])]
            + [np.array([0.0, degs_800_km + i*degs_40_km, pd.Timestamp('2008-10-23 06:00:00') + pd.Timedelta(hours=i)]) for i in range(10)])

_filter_array(lat_lng_time, max_speed=50, include_loops=False, speed=50., max_loop=6, ratio_max=0.25)

Out: 
[array([0.0, 0.0, Timestamp('2008-10-23 06:00:00')]),
 array([0.0, 10.4198104615, Timestamp('2008-10-23 15:00:00')])]

Which does not meet the expectation.

Having studied the code, it appears that the continue in line https://github.com/scikit-mobility/scikit-mobility/blob/master/skmob/preprocessing/filtering.py#L142 is responsible for this behaviour.

Let's follow the execution of the loop:

• i = 0, compare i+1 with i, the speed is 800 km/h, above the limit, remove i+1 point, continue without incrementing index i
• i = 0, compare i+1 with I (so i=2 and i=0 of the original array), the speed is 420 km/h, above the limit, remove i+1 point, continue without incrementing index I
• i = 0, compare i+1 with I (so i=3 and i=0 of the original array), the speed is 293 km/h, above the limit, remove i+1 point, continue without incrementing index I
• ...

It seems that the filtering algorithm was designed to eliminate singular points that moved at high speed. However, the same method fails if the high-speed movement was permanent, e.g., flying or traveling on a highway.

Could you please confirm my findings? If that is the case, then I'll happily work on the issue.