https://github.com/scope-lab/pyest
Python library for adaptive Gaussian mixture state estimation. Useful for navigation and tracking in nonlinear non-Gaussian systems. Capable of incorporating negative information and other imprecise evidence.
https://github.com/scope-lab/pyest
bayesian-filtering gaussian-mixture gaussian-splitting negative-information nonlinear-estimation state-estimation target-tracking uncertainty-propagation
Last synced: 5 months ago
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Python library for adaptive Gaussian mixture state estimation. Useful for navigation and tracking in nonlinear non-Gaussian systems. Capable of incorporating negative information and other imprecise evidence.
- Host: GitHub
- URL: https://github.com/scope-lab/pyest
- Owner: scope-lab
- License: mit
- Created: 2025-03-02T17:22:12.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2025-11-23T03:04:27.000Z (7 months ago)
- Last Synced: 2025-11-23T03:26:26.550Z (7 months ago)
- Topics: bayesian-filtering, gaussian-mixture, gaussian-splitting, negative-information, nonlinear-estimation, state-estimation, target-tracking, uncertainty-propagation
- Language: Python
- Homepage: https://pyest.readthedocs.io/
- Size: 571 KB
- Stars: 4
- Watchers: 4
- Forks: 4
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE.txt
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README
# PyEst: Adaptive Gaussian Mixture State Estimation
[](https://github.com/scope-lab/pyest/actions/workflows/pythonapp.yml)
> **Not pytest**: PyEst is a Python library for **adaptive Gaussian mixture state estimation**.
> For the Python test framework, see [pytest](https://pytest.org).
## 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
```shell
pip install pyest
```
To install packages needed for running the examples, run
```shell
pip install 'pyest[examples]'
```
### OS X (bash), Windows (cmd prompt)
To install, run
```shell
pip install pyest
```
To install packages needed for running the examples, run
```shell
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](http://keithlegrand.com/wp/wp-content/uploads/2023/05/LeGrand-2022-Split-Happens-Imprecise-and-Negative-Information-in-Gaussian-Mixture-Random-Finite-Set-Filtering.pdf)
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](https://pyest.readthedocs.io/en/latest/).