Kalman Filter, Smoother, and EM Algorithm for Python
Kalman Filter, Smoother, and EM Algorithm for Python
The dead-simple Kalman Filter, Kalman Smoother, and EM library for Python.
pykalman is a Python library for Kalman filtering and smoothing, providing efficient algorithms for state estimation in time series. It includes tools for linear dynamical systems, parameter estimation, and sequential data modeling. The library supports the Kalman Filter, Unscented Kalman Filter, and EM algorithm for parameter learning.
Originally created by Daniel Duckworth (@duckworthd).
:rocket: Version 0.11.2 out now! Check out the release notes here.
| Documentation · Tutorials | |
|---|---|
| Open Source | |
| Community | |
| Code | |
| Downloads | ) |
Questions and feedback are extremely welcome! We strongly believe in the value of sharing help publicly, as it allows a wider audience to benefit from it.
| Type | Platforms |
|---|---|
| :bug: Bug Reports | GitHub Issue Tracker |
| :sparkles: Feature Requests & Ideas | GitHub Issue Tracker |
| :woman_technologist: Usage Questions | Stack Overflow |
| :speech_balloon: General Discussion | Discord |
| :factory: Contribution & Development | dev-chat channel · Discord |
| :globe_with_meridians: Meet-ups and collaboration sessions | Discord - Fridays 13 UTC, dev/meet-ups channel |
For a quick installation::
pip install pykalmanAlternatively, you can setup from source:
pip install .from pykalman import KalmanFilter
import numpy as np
kf = KalmanFilter(transition_matrices = [[1, 1], [0, 1]], observation_matrices = [[0.1, 0.5], [-0.3, 0.0]])
measurements = np.asarray([[1,0], [0,0], [0,1]]) # 3 observations
kf = kf.em(measurements, n_iter=5)
(filtered_state_means, filtered_state_covariances) = kf.filter(measurements)
(smoothed_state_means, smoothed_state_covariances) = kf.smooth(measurements)Also included is support for missing measurements:
from numpy import ma
measurements = ma.asarray(measurements)
measurements[1] = ma.masked # measurement at timestep 1 is unobserved
kf = kf.em(measurements, n_iter=5)
(filtered_state_means, filtered_state_covariances) = kf.filter(measurements)
(smoothed_state_means, smoothed_state_covariances) = kf.smooth(measurements)And for the non-linear dynamics via the UnscentedKalmanFilter:
from pykalman import UnscentedKalmanFilter
ukf = UnscentedKalmanFilter(lambda x, w: x + np.sin(w), lambda x, v: x + v, transition_covariance=0.1)
(filtered_state_means, filtered_state_covariances) = ukf.filter([0, 1, 2])
(smoothed_state_means, smoothed_state_covariances) = ukf.smooth([0, 1, 2])And for online state estimation:
for t in range(1, 3):
filtered_state_means[t], filtered_state_covariances[t] = \
kf.filter_update(filtered_state_means[t-1], filtered_state_covariances[t-1], measurements[t])And for numerically robust "square root" filters
from pykalman.sqrt import CholeskyKalmanFilter, AdditiveUnscentedKalmanFilter
kf = CholeskyKalmanFilter(transition_matrices = [[1, 1], [0, 1]], observation_matrices = [[0.1, 0.5], [-0.3, 0.0]])
ukf = AdditiveUnscentedKalmanFilter(lambda x, w: x + np.sin(w), lambda x, v: x + v, observation_covariance=0.1)Examples of all of pykalman's functionality can be found here.
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