TFiltersPy

Bayesian state estimation for Python — sklearn-compatible, scalable, modular.

---

TFiltersPy provides 5 production-ready Bayesian filters with a unified fit / predict / score API. Built on NumPy/SciPy with optional Dask parallelism for large-scale problems.

pip install tfilterspy

Filters at a Glance

Filter	Best For	Linearity	Jacobians?	Scales To
KalmanFilter	GPS tracking, signal denoising	Linear	N/A	10K+ steps
ExtendedKalmanFilter	Radar, navigation	Nonlinear	Required	10K+ steps
UnscentedKalmanFilter	Highly nonlinear systems	Nonlinear	Not needed	10K+ steps
EnsembleKalmanFilter	Weather, ocean models	Nonlinear	Not needed	High-dim states
ParticleFilter	Robot localization, multimodal	Any	Not needed	Non-Gaussian

Architecture

tfilterspy/
  __init__.py               # Top-level exports
  base_estimator.py          # BaseEstimator (sklearn API: fit/predict/score)
  state_estimation/
    linear_filters.py        # KalmanFilter, DaskKalmanFilter
    extended_kalman.py       # ExtendedKalmanFilter
    unscented_kalman.py      # UnscentedKalmanFilter
    ensemble_kalman.py       # EnsembleKalmanFilter (Dask-parallel)
    particle_filters.py      # ParticleFilter, DaskParticleFilter
  utils/
    optimisation_utils.py    # ParameterEstimator

                    +-----------------+
                    | BaseEstimator   |
                    |-----------------|
                    | fit(X)          |
                    | predict()       |
                    | score(X_true)   |
                    | fit_predict(X)  |
                    | filter_step(z)  |
                    | get_params()    |
                    | set_params()    |
                    +--------+--------+
                             |
          +------------------+-------------------+
          |                  |                   |
  +-------v-------+  +------v--------+  +-------v--------+
  | KalmanFilter  |  | Nonlinear     |  | ParticleFilter |
  |               |  | Filters       |  |                |
  | F, H matrices |  | f(), h()      |  | f(), h() or    |
  | smooth()      |  | callables     |  | F, H matrices  |
  | forecast()    |  |               |  |                |
  +---------------+  +---+-------+---+  | n_particles    |
                         |       |      | ESS monitoring |
              +----------+   +---+---+  +----------------+
              |              |       |
        +-----v-----+  +----v--+ +--v--------+
        |    EKF    |  | UKF   | |   EnKF    |
        | Jacobians |  | Sigma | | Ensemble  |
        | F_jac,    |  | points| | Dask      |
        | H_jac     |  |       | | parallel  |
        +-----------+  +-------+ +-----------+

Quick Start

Kalman Filter — GPS Tracking

A vehicle drives a figure-8. GPS gives noisy 2D position. The Kalman filter estimates the true trajectory, and RTS smoothing refines it further.

import numpy as np
from tfilterspy import KalmanFilter

dt = 0.1  # 10 Hz GPS

# Constant-velocity model: state = [x, vx, y, vy]
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],    # GPS observes position only
              [0, 0, 1, 0]])

Q = np.diag([0.1, 1.0, 0.1, 1.0])   # process noise
R = np.eye(2) * 25.0                  # GPS noise (5m std)^2
x0 = np.zeros(4)
P0 = np.eye(4) * 100.0

kf = KalmanFilter(F, H, Q, R, x0, P0)
kf.fit(gps_measurements)           # shape (n_steps, 2)
filtered = kf.predict()            # shape (n_steps, 4)
smoothed, _ = kf.smooth()          # RTS smoother
forecast, _ = kf.forecast(50)      # 50 steps ahead
score = kf.score(true_states)      # negative MSE

Filter Pipeline:
                                          +----------+
  GPS measurements ──> fit() ──> predict() ──> filtered states
                                     |
                                  smooth() ──> smoothed states (better)
                                     |
                                 forecast(n) ──> future prediction

Extended Kalman Filter — Radar Tracking

An aircraft in a coordinated turn. Radar measures range and bearing (nonlinear). The EKF linearizes at each step using Jacobians.

from tfilterspy import ExtendedKalmanFilter

def f_aircraft(x):
    return np.array([x[0] + dt*x[1], x[1], x[2] + dt*x[3], x[3]])

def h_radar(x):
    r = np.sqrt(x[0]**2 + x[2]**2)
    theta = np.arctan2(x[2], x[0])
    return np.array([r, theta])

def F_jac(x):
    return np.array([[1, dt, 0, 0], [0, 1, 0, 0],
                     [0, 0, 1, dt], [0, 0, 0, 1]])

def H_jac(x):
    px, _, py, _ = x
    r = np.sqrt(px**2 + py**2) + 1e-10
    return np.array([[px/r, 0, py/r, 0],
                     [-py/r**2, 0, px/r**2, 0]])

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(radar_measurements)
states = ekf.predict()
smoothed, _ = ekf.smooth()

Unscented Kalman Filter — No Jacobians Needed

Same radar problem, but the UKF uses sigma points instead of Jacobians. Often more accurate for highly nonlinear systems.

from tfilterspy import UnscentedKalmanFilter

ukf = UnscentedKalmanFilter(
    f=f_aircraft, h=h_radar,
    Q=Q, R=R, x0=x0, P0=P0,
    alpha=1e-3, beta=2.0, kappa=0.0,
)
ukf.fit(radar_measurements)
states = ukf.predict()

Ensemble Kalman Filter — High-Dimensional Systems

Weather models, ocean simulations, and other systems with thousands of state variables. Uses a Monte Carlo ensemble instead of full covariance matrices. Supports Dask for parallel ensemble propagation.

from tfilterspy import EnsembleKalmanFilter

enkf = EnsembleKalmanFilter(
    f=dynamics_fn, h=observation_fn,
    Q=Q, R=R, x0=x0,
    n_ensemble=100,
    use_dask=True,      # parallel ensemble propagation
)
enkf.fit(measurements)
states = enkf.predict()

Particle Filter — Robot Localization

A robot navigates using range measurements to known landmarks. The particle filter handles the nonlinear observation model and can represent multimodal distributions.

from tfilterspy import ParticleFilter

def robot_dynamics(x):
    heading = x[2]
    return np.array([x[0] + 0.5*np.cos(heading),
                     x[1] + 0.5*np.sin(heading),
                     x[2] + 0.05])

def range_to_landmarks(x):
    pos = x[:2]
    return np.sqrt(np.sum((landmarks - pos)**2, axis=1))

pf = ParticleFilter(
    f=robot_dynamics, h=range_to_landmarks,
    Q=Q, R=R, x0=x0,
    n_particles=2000,
    resample_threshold=0.5,
)
pf.fit(range_measurements)
states = pf.predict()
ess = pf.effective_sample_sizes_   # monitor particle health

Online Filtering (Streaming Data)

All filters support step-by-step updates for real-time applications:

kf = KalmanFilter(F, H, Q, R, x0, P0)
for measurement in sensor_stream:
    x_est, P_est = kf.filter_step(measurement)
    print(f"State estimate: {x_est}")

Choosing a Filter

Start
  |
  v
Is the system linear? ──yes──> KalmanFilter
  |                              (fastest, optimal for linear-Gaussian)
  no
  |
  v
Is noise Gaussian? ──no──> ParticleFilter
  |                          (handles any distribution)
  yes
  |
  v
Can you compute Jacobians? ──yes──> ExtendedKalmanFilter
  |                                   (fast, needs analytical derivatives)
  no
  |
  v
Is the state dimension large (>100)? ──yes──> EnsembleKalmanFilter
  |                                             (scales to millions of states)
  no
  |
  v
UnscentedKalmanFilter
  (no Jacobians, sigma-point accuracy)

Memory Efficiency

For long time series, disable covariance storage to save ~80% memory:

kf = KalmanFilter(F, H, Q, R, x0, P0, store_covariances=False)
kf.fit(million_step_data)     # only stores state estimates
states = kf.predict()         # works fine
# kf.smooth()                 # raises error (needs stored covariances)

Examples

Full working examples are included in the repository:

Example	File	Description
GPS Vehicle Tracking	examples/example_gps_tracking.py	KF + RTS smoother on figure-8 trajectory, 86% noise reduction
Radar Target Tracking	examples/example_radar_tracking.py	EKF vs UKF on coordinated-turn aircraft with polar radar
Robot Localization	examples/example_robot_localization.py	Particle filter with range measurements to landmarks

Notebooks

Notebook	Description
Kalman-filters-use-cases.ipynb	Image denoising, EEG filtering, NLP topic smoothing
particle-filters-usecases.ipynb	Computer vision, EEG, topic tracking with particle filters
nonlinear-filters-usecases.ipynb	EKF, UKF, and EnKF on nonlinear problems
benchmarks.ipynb	Speed and accuracy comparison of all 5 filters

Run any example:

python examples/example_gps_tracking.py

API Reference

All filters inherit from BaseEstimator and share this interface:

Method	Description
fit(X)	Run the forward filter pass on measurements X (n_steps, n_obs)
predict()	Return filtered state estimates (n_steps, n_state)
score(X_true)	Negative MSE vs ground truth (higher = better, sklearn convention)
fit_predict(X)	Shorthand for fit(X).predict()
filter_step(z)	Process a single measurement for online/streaming use
get_params()	Get estimator parameters (sklearn-compatible)
set_params(**p)	Set estimator parameters (sklearn-compatible)

KalmanFilter also provides:

Method	Description
smooth()	RTS backward smoother, returns (smoothed_states, smoothed_covs)
forecast(n_steps)	Predict n steps into the future, returns (states, covariances)

ParticleFilter also provides:

Attribute	Description
effective_sample_sizes_	ESS at each time step (monitors particle degeneracy)

Installation

pip install tfilterspy

From source:

git clone https://github.com/ubunye-ai-ecosystems/tfilterspy.git
cd tfilterspy
pip install -e .[dev]

Requirements: Python >= 3.8, NumPy, SciPy, Dask

Development

git clone https://github.com/ubunye-ai-ecosystems/tfilterspy.git
cd tfilterspy
pip install -e .[dev]
pytest tests/

The test suite covers all 5 filters with 37+ tests including edge cases, backward compatibility, and a 10K-step large dataset test.

Contributing

• Found a bug? Open an issue.
• Want to add a feature? Fork, implement, and open a pull request.
• Write tests for any new filter or feature.

License

MIT License. See LICENSE for details.

Documentation

Full documentation: ubunye-ai-ecosystems.github.io/tfilterspy