====================================== 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)

---

Installation

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

Examples of all of pykalman's functionality can be found in the scripts in the examples/ folder.