An implementation of the Kalman Filter, Kalman Smoother, and EM algorithm in Python

# pykalman

Welcome to pykalman, the dead-simple Kalman Filter, Kalman Smoother, and EM library for Python.

## Installation

For a quick installation::

pip install pykalman


Alternatively, you can setup from source:

pip install .


## Usage

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

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

## Project details

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