Examples

TFiltersPy includes Python scripts and Jupyter notebooks demonstrating each filter on real-world problems.

Python Examples

Run any example directly:

python examples/example_gps_tracking.py

Example	Filter	Description
`example_gps_tracking.py`	KF	Vehicle tracks a figure-8 at 10 Hz GPS. Demonstrates `fit`, `predict`, `smooth`, `forecast`, `score`, and `filter_step`. Achieves 86% noise reduction (filtered), 96% (smoothed).
`example_radar_tracking.py`	EKF, UKF	Aircraft in a coordinated turn observed by radar (range + bearing). Compares EKF vs UKF accuracy. EKF smoothing reaches 81% improvement.
`example_robot_localization.py`	PF	Robot navigates using range measurements to 3 landmarks. Compares 100, 500, and 2000 particles. Shows ESS monitoring and online `filter_step` demo.

GPS Tracking (KalmanFilter)

import numpy as np
from tfilterspy import KalmanFilter

dt = 0.1
F = np.array([[1, dt, 0,  0],
              [0,  1, 0,  0],
              [0,  0, 1, dt],
              [0,  0, 0,  1]])
H = np.array([[1, 0, 0, 0],
              [0, 0, 1, 0]])
Q = np.diag([0.1, 1.0, 0.1, 1.0])
R = np.eye(2) * 25.0
x0 = np.array([0, 10, 0, 10], dtype=np.float64)
P0 = np.eye(4) * 100.0

kf = KalmanFilter(F, H, Q, R, x0, P0)
kf.fit(measurements)
filtered = kf.predict()
smoothed, _ = kf.smooth()
forecast_states, forecast_covs = kf.forecast(50)

RESULTS
==================================================
MSE raw GPS:    24.465 m^2
MSE filtered:   3.495 m^2  (86% reduction)
MSE smoothed:   0.990 m^2  (96% reduction)
Log-likelihood: -6193.8

Radar Tracking (EKF vs UKF)

from tfilterspy import ExtendedKalmanFilter, UnscentedKalmanFilter

ekf = ExtendedKalmanFilter(
    f=f_aircraft, h=h_radar,
    F_jacobian=F_jac, H_jacobian=H_jac,
    Q=Q, R=R, x0=x0, P0=P0,
)
ekf.fit(measurements)
ekf_states = ekf.predict()
ekf_smoothed, _ = ekf.smooth()

ukf = UnscentedKalmanFilter(
    f=f_aircraft, h=h_radar,
    Q=Q, R=R, x0=x0, P0=P0,
)
ukf.fit(measurements)
ukf_states = ukf.predict()

POSITION RMSE COMPARISON
=======================================================
Raw radar:      42.84 m
EKF filtered:   33.68 m  (21% improvement)
EKF smoothed:    8.01 m  (81% improvement)
UKF filtered:   33.66 m  (21% improvement)

Robot Localization (ParticleFilter)

from tfilterspy import ParticleFilter

pf = ParticleFilter(
    f=robot_dynamics, h=range_observation,
    Q=Q, R=R, x0=x0,
    n_particles=2000,
    resample_threshold=0.5,
)
pf.fit(measurements)
states = pf.predict()
print(f"Mean ESS: {np.mean(pf.effective_sample_sizes_):.0f}")

PARTICLE FILTER RESULTS
============================================================
Particles    RMSE (m)    Mean ESS     ESS %
-----------------------------------------------
     100       0.777       62.3     62.3%
     500       0.437      304.2     60.8%
    2000       0.320     1193.2     59.7%

Jupyter Notebooks

Interactive notebooks with visualizations are in examples/notebooks/.

Notebook	Description
`Kalman-filters-use-cases.ipynb`	Image denoising (digits), EEG time series filtering, NLP topic smoothing with KalmanFilter
`particle-filters-usecases.ipynb`	Same three domains with ParticleFilter. Includes ESS monitoring and comparison to KF
`nonlinear-filters-usecases.ipynb`	Pendulum tracking (EKF vs UKF), radar with RTS smoothing, high-dimensional coupled oscillator (EnKF vs UKF)
`benchmarks.ipynb`	Speed and accuracy comparison of all 5 filters on the digits dataset. Includes classification accuracy with LogisticRegression

Browse notebooks on GitHub

Filter Pipeline Diagram

                                        +-----------+
measurements ──> fit() ──> predict() ──>| filtered  |
                               |        | states    |
                               |        +-----------+
                               |
                           smooth() ──> smoothed states (KF, EKF only)
                               |
                         forecast(n) ──> future prediction (KF only)
                               |
                        filter_step(z) ──> online / streaming mode (all filters)