PyEst: Adaptive Gaussian Mixture State Estimation

Not pytest: PyEst is a Python library for adaptive Gaussian mixture state estimation. For the Python test framework, see pytest.

Basic Usage

Import the gm module of PyEst as well as numpy and matplotlib

import numpy as np
import matplotlib.pyplot as plt
import pyest.gm as gm

Create a three-mixand two-dimensional Gaussian mixture:

# mixand means (nc,nx)
m = np.array([[0,0], [1,2], [0,-1]])
# mixand covariance matrices (nc,nx,nx)
P = np.array([[[1,0], [0,1]],
              [[2, 0.5], [0.5,3]],
              [[0.5, -0.1], [-0.1, 1]]])
# mixand weights (nc,)
w = gm.equal_weights(3)
# contruct the Gaussian mixture
p = gm.GaussianMixture(w, m, P)

Compute the mean and covariance of the distribution:

# compute and print the mean
print(p.mean())
# compute and print the covariance
print(p.cov())

Plot the Gaussian mixture

pp, XX, YY = p.pdf_2d()
fig = plt.figure()
ax = fig.add_axes(111)
ax.contourf(XX,YY,pp,100)

Apply a linear transformation to the mixture

dt = 5
F = np.array([[1, dt], [0, 1]])
my = np.array([F@m for m in p.m])
Py = np.array([F@P@F.T for P in p.P])
py = gm.GaussianMixture(p.w, my, Py)

Plot the transformed Gaussian mixture

pp, XX, YY = py.pdf_2d()
fig = plt.figure()
ax = fig.add_axes(111)
ax.contourf(XX,YY,pp,100)
plt.show()

Installation

OS X (zsh)

To install, run

pip install pyest

To install packages needed for running the examples, run

pip install 'pyest[examples]'

OS X (bash), Windows (cmd prompt)

To install, run

pip install pyest

To install packages needed for running the examples, run

pip install pyest[examples]

Citing this work

If you use this package in your scholarly work, please cite the following articles:

K.A. LeGrand and S. Ferrari, “Split Happens! Imprecise and Negative Information in Gaussian Mixture Random Finite Set Filtering,” Journal of Advances in Information Fusion, Vol 17, No. 2, December, 2022

J. Kulik and K.A. LeGrand, “Nonlinearity and Uncertainty Informed Moment-Matching Gaussian Mixture Splitting,” https://arxiv.org/abs/2412.00343

@article{legrand2022SplitHappensImprecise,
  title = {Split {{Happens}}! Imprecise and Negative Information in {G}aussian Mixture Random Finite Set Filtering},
  author = {LeGrand, Keith A. and Ferrari, Silvia},
  year = {2022},
  month = dec,
  journal = {Journal of Advances in Information Fusion},
  volume = {17},
  number = {2},
  eprint = {2207.11356},
  primaryclass = {cs, eess},
  pages = {78--96},
  doi = {10.48550/arXiv.2207.11356},
}
@misc{kulik2024NonlinearityUncertaintyInformed,
  title = {Nonlinearity and {{Uncertainty Informed Moment-Matching Gaussian Mixture Splitting}}},
  author = {Kulik, Jackson and LeGrand, Keith A.},
  year = {2024},
  month = nov,
  number = {arXiv:2412.00343},
  eprint = {2412.00343},
  primaryclass = {stat},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2412.00343},
  urldate = {2025-01-01},
  archiveprefix = {arXiv}
}

Documentation

For more information about PyEst, please see the documentation.