🖇️Track Interpolation
Track interpolation with AISdb involves generating estimated positions of vessels at specific intervals when actual AIS data points are unavailable. This process is important for filling in gaps in the vessel's trajectory, which can occur due to signal loss, data filtering, or other disruptions.
In this tutorial, we introduce different types of track interpolation implemented in AISdb with usage examples.
Example data preparation
First, we defined functions to transform and visualize the track data (a generator object), with options to view the data points or the tracks:
import plotly.graph_objects as go
import plotly.express as px
import pandas as pd
def track2dataframe(tracks):
data = []
for track in tracks:
times = track['time']
mmsi = track['mmsi']
lons = track['lon']
lats = track['lat']
# Iterate over the dynamic arrays and create a row for each time point
for i in range(len(times)):
data.append({
'mmsi': mmsi,
'time': times[i],
'longitude': lons[i],
'latitude': lats[i],
})
return pd.DataFrame(data)
def plotly_visualize(data, visual_type='lines'):
if (visual_type=='scatter'):
# Create a scatter plot for the vessel data points using scatter_geo
fig = px.scatter_geo(
data,
lat="latitude",
lon="longitude",
color="mmsi", # Color by vessel identifier
hover_name="mmsi",
hover_data={"time": True},
title="Vessel Data Points"
)
else:
# Create a line plot for the vessel trajectory using line_geo
fig = px.line_geo(
data,
lat="latitude",
lon="longitude",
color="mmsi", # Color by vessel identifier
hover_name="mmsi",
hover_data={"time": True},
title="Vessel Trajectory"
)
# Set the map style and projection
fig.update_geos(
projection_type="azimuthal equal area", # Change this to 'natural earth', 'azimuthal equal area', etc.
showland=True,
landcolor="rgb(243, 243, 243)",
countrycolor="rgb(204, 204, 204)",
)
# Set the layout to focus on a specific area or zoom level
fig.update_layout(
geo=dict(
projection_type="azimuthal equal area",
),
width=1200, # Increase the width of the plot
height=800, # Increase the height of the plot
)
fig.show()We will use an actual track retrieved from the database for the examples in this tutorial and interpolate additional data points based on this track. The visualization will show the original track data points:
Linear interpolation
Linear interpolation estimates the vessel's position by drawing a straight line between two known points and calculating the positions at intermediate times. It is simple, fast, and straightforward but may not accurately represent complex movements.
With equal time window intervals
This method estimates the position of a vessel at regular time intervals (e.g., every 10 minutes). To perform linear interpolation with an equal time window on the track defined above:
With equal distance intervals
This method estimates the position of a vessel at regular spatial intervals (e.g., every 1 km along its path). To perform linear interpolation with equal distance intervals on the pseudo track defined above:
Geodesic Track Interpolation
This method estimates the positions of a vessel along a curved path using the principles of geometry, particularly involving great-circle routes.
Cubic Spline Interpolation
Given a set of data points, cubic spline interpolation fits a smooth curve through these points. The curve is represented as a series of cubic polynomials between each pair of data points. Each polynomial ensures a smooth curve at the data points (i.e., the first and second derivatives are continuous).
Custom Track Interpolation
In addition to the standard interpolation methods provided by AISdb, users can implement other interpolation techniques tailored to their specific analytical needs. For instance, B-spline (Basis Spline) interpolation is a mathematical technique that creates a smooth curve through data points. This smoothness is important in trajectory analysis as it avoids sharp, unrealistic turns and maintains a natural flow.
Here is an implementation and example of using B-splines interpolation:
Then, we can apply the function just implemented on the vessel tracks generator:
The visualization of the interpolation shows as:
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