====================================== pykalman
Welcome to pykalman, the dead-simple Kalman Filter, Kalman Smoother, and EM library for Python
>>> 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)
For a quick installation::
$ easy_install pykalman
pykalman depends on the following modules,
numpy(for core functionality)scipy(for core functionality)Sphinx(for generating documentation)numpydoc(for generating documentation)nose(for running tests)
All of these and pykalman can be installed using easy_install
$ easy_install numpy scipy Sphinx numpydoc nose pykalman
Alternatively, you can get the latest and greatest from github::
$ git clone git@github.com:pykalman/pykalman.git pykalman
$ cd pykalman
$ sudo python setup.py install
Examples of all of pykalman's functionality can be found in the scripts in
the examples/ folder.