Smoothing trajectories

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.

Documentation

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()

MovingPandas 0.17.0

SYSTEM INFO
-----------
python     : 3.10.12 | packaged by conda-forge | (main, Jun 23 2023, 22:34:57) [MSC v.1936 64 bit (AMD64)]
executable : H:\miniconda3\envs\mpd-ex\python.exe
machine    : Windows-10-10.0.19045-SP0

GEOS, GDAL, PROJ INFO
---------------------
GEOS       : None
GEOS lib   : None
GDAL       : 3.7.0
GDAL data dir: None
PROJ       : 9.2.1
PROJ data dir: H:\miniconda3\pkgs\proj-9.0.0-h1cfcee9_1\Library\share\proj

PYTHON DEPENDENCIES
-------------------
geopandas  : 0.13.2
pandas     : 2.0.3
fiona      : 1.9.4
numpy      : 1.24.4
shapely    : 2.0.1
rtree      : 1.0.1
pyproj     : 3.6.0
matplotlib : 3.7.2
mapclassify: 2.5.0
geopy      : 2.3.0
holoviews  : 1.17.0
hvplot     : 0.8.3
geoviews   : 1.9.6
stonesoup  : 1.0

gdf = read_file('../data/geolife_small.gpkg')
tc = mpd.TrajectoryCollection(gdf, 'trajectory_id', t='t')

split = mpd.ObservationGapSplitter(tc).split(gap=timedelta(minutes=15))

KalmanSmootherCV

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)

TrajectoryCollection with 11 trajectories

kwargs = {**hvplot_defaults, 'line_width':4}
(split.hvplot(title='Original Trajectories', **kwargs) + 
 smooth.hvplot(title='Smooth Trajectories', **kwargs))