To smooth trajectories, we can use a Kalman filter. The implemented KalmanSmootherCV is based on the assumption of a nearly-constant velocity (CV) model. To use KalmanSmootherCV, the optional dependency StoneSoup
needs to be installed.
A closely related type of operation is trajectory generalization which is coverd in a separate notebook.
import pandas as pd
import geopandas as gpd
import movingpandas as mpd
import shapely as shp
import hvplot.pandas
import matplotlib.pyplot as plt
from geopandas import GeoDataFrame, read_file
from shapely.geometry import Point, LineString, Polygon
from datetime import datetime, timedelta
from holoviews import opts, dim
import warnings
warnings.filterwarnings('ignore')
plot_defaults = {'linewidth':5, 'capstyle':'round', 'figsize':(9,3), 'legend':True}
opts.defaults(opts.Overlay(active_tools=['wheel_zoom']))
hvplot_defaults = {'tiles':'CartoLight', 'frame_height':320, 'frame_width':320, 'cmap':'Viridis', 'colorbar':True}
mpd.show_versions()
gdf = read_file('../data/geolife_small.gpkg')
tc = mpd.TrajectoryCollection(gdf, 'trajectory_id', t='t')
split = mpd.ObservationGapSplitter(tc).split(gap=timedelta(minutes=15))
split.plot(column='trajectory_id', **plot_defaults)
This smoother operates on the assumption of a nearly-constant velocity (CV) model. The process_noise_std
and measurement_noise_std
parameters can be used to tune the smoother:
process_noise_std
governs the uncertainty associated with the adherence of the new (smooth) trajectories to the CV model assumption; higher values relax the assumption, therefore leading to less-smooth trajectories, and vice-versa.measurement_noise_std
controls the assumed error in the original trajectories; higher values dictate that the original trajectories are expected to be noisier (and therefore, less reliable), thus leading to smoother trajectories, and vice-versa.Try tuning these parameters and observe the resulting trajectories:
smooth = mpd.KalmanSmootherCV(split).smooth(process_noise_std=0.1, measurement_noise_std=10)
print(smooth)
kwargs = {**hvplot_defaults, 'line_width':4}
(split.hvplot(title='Original Trajectories', **kwargs) +
smooth.hvplot(title='Smooth Trajectories', **kwargs))
kwargs = {**hvplot_defaults, 'c':'speed', 'line_width':7, 'clim':(0,20)}
smooth.add_speed()
(split.trajectories[2].hvplot(title='Original Trajectory', **kwargs) +
smooth.trajectories[2].hvplot(title='Smooth Trajectory', **kwargs))
traj = split.trajectories[2]
cleaned = traj.copy()
cleaned.add_speed(overwrite=True)
for i in range(0,10):
cleaned = mpd.OutlierCleaner(cleaned).clean({'speed': 1})
smoothed = mpd.KalmanSmootherCV(cleaned).smooth(process_noise_std=0.1, measurement_noise_std=10)
(traj.hvplot(title='Original Trajectory', **kwargs) +
cleaned.hvplot(title='Cleaned Trajectory', **kwargs) +
smoothed.hvplot(title='Cleaned & Smoothed Trajectory', **kwargs))