API Overview

PyRecEst exposes most user-facing classes through package-level imports such as pyrecest.distributions, pyrecest.filters, pyrecest.models, pyrecest.protocols, pyrecest.sampling, pyrecest.smoothers, pyrecest.evaluation, and pyrecest.utils.

Use backend-compatible arrays from pyrecest.backend in examples and user code when the same code should run on more than one numerical backend.

from pyrecest.backend import array, diag
from pyrecest.distributions import GaussianDistribution
from pyrecest.filters import KalmanFilter
from pyrecest.models import LikelihoodMeasurementModel

See Shapes and conventions for the expected vector, matrix, batch, measurement-set, and manifold-coordinate shapes used by common APIs.

Package Map

pyrecest.backend

Dynamic backend facade used by the rest of the project. The default backend is NumPy. PyTorch and JAX support are selected through PYRECEST_BACKEND before importing pyrecest. See backend compatibility for backend-specific support notes and known limitations.

pyrecest.protocols

Public capability contracts for PyRecEst extension points. Protocols describe what an object can do without requiring it to inherit from a specific PyRecEst base class.

The current seed exposes common dimension protocols:

  • SupportsDim for objects with an intrinsic state-space dimension;
  • SupportsInputDim for objects with an ambient or input coordinate dimension.

See public protocols, custom distribution extensions, and custom filter extensions for protocol-oriented extension examples.

pyrecest.distributions

Probability distributions and density representations on linear spaces, periodic spaces, spheres, hyperspheres, hypertori, Cartesian-product spaces, and rigid-body state spaces.

Common starting points include:

  • GaussianDistribution for Euclidean Gaussian states;
  • GaussianMixture and LinearMixture for mixtures on linear spaces;
  • VonMisesDistribution and wrapped distributions for circular states;
  • VonMisesFisherDistribution, BinghamDistribution, and related classes for hyperspherical states;
  • HypertoroidalFourierDistribution and hypertoroidal grid or wrapped-normal distributions for toroidal states.

Use pyrecest.distributions.conversion.convert_distribution(...) to convert between analytic, Dirac/particle, grid, Fourier, and moment-matched representations. The target may be a concrete class or an alias such as "particles", "gaussian", "grid", or "fourier". See representation conversion.

pyrecest.models

Reusable transition and measurement model objects that describe model capabilities independently of a concrete filter. The initial model layer focuses on likelihood-based measurement models and transition models that can either sample next states or evaluate transition densities.

Common starting points include:

  • LikelihoodMeasurementModel for particle-filter or grid-filter style measurement likelihoods;
  • SampleableTransitionModel for transition models that can draw samples from a next-state distribution;
  • DensityTransitionModel for transition models that can evaluate transition densities.

See model objects for usage patterns and conventions.

pyrecest.filters

Recursive Bayesian estimators and trackers. The package includes standard linear and unscented Kalman filters, particle filters, grid filters, manifold-specific filters, multi-target trackers, extended-object trackers, and track-management utilities.

Common starting points include:

  • KalmanFilter for linear Gaussian Euclidean state estimation;
  • AssociationHypothesis, NISGate, CostThresholdGate, TopKGate, and linear_gaussian_association_hypotheses for reusable association diagnostics, gating, and cost-matrix conversion;
  • OutOfSequenceKalmanUpdater, OutOfSequenceParticleUpdater, FixedLagBuffer, and MeasurementTimeBuffer for fixed-lag delayed measurement handling;
  • UnscentedKalmanFilter and UKFOnManifolds for nonlinear models;
  • ManifoldExponentialMovingAverage for streaming manifold-valued samples;
  • EuclideanParticleFilter and manifold-specific particle filters;
  • VonMisesFilter, VonMisesFisherFilter, and Fourier or grid filters for directional estimation;
  • MultiBernoulliTracker, GlobalNearestNeighbor, JPDAF, and TrackManager for tracking workflows.

pyrecest.smoothers

Backward-pass smoothers that refine filter estimates after a measurement sequence has been processed.

Common starting points include:

  • RauchTungStriebelSmoother;
  • UnscentedRauchTungStriebelSmoother.

pyrecest.sampling

Samplers and grid generators for Euclidean and manifold domains.

Common starting points include:

  • GaussianSampler;
  • MerweScaledSigmaPoints and JulierSigmaPoints;
  • FibonacciGridSampler;
  • FibonacciRejectionSampler;
  • SobolGridSampler;
  • HaltonGridSampler;
  • SphericalFibonacciSampler;
  • HealpixHopfSampler;
  • LeopardiSampler;
  • get_grid_hypersphere.

pyrecest.evaluation

Simulation, measurement generation, evaluation, plotting, and result summary helpers for filter and tracker experiments.

Common starting points include:

  • generate_groundtruth;
  • generate_measurements;
  • perform_predict_update_cycles;
  • evaluate_for_variables;
  • summarize_filter_results;
  • plot_results.

pyrecest.utils

Reusable utility helpers for assignment, association models, history recording, multi-session assignment, generic track-matrix evaluation, Gaussian/covariance pairwise features, and point-set registration.

Common starting points include:

  • murty_k_best_assignments;
  • LogisticPairwiseAssociationModel;
  • pairwise_mahalanobis_distances;
  • pairwise_covariance_shape_components;
  • HistoryRecorder;
  • solve_multisession_assignment;
  • normalize_track_matrix;
  • score_track_links;
  • track_error_ledger;
  • estimate_thin_plate_spline.

Where To Look Next

  • Use the examples guide for small runnable workflows.
  • Use public protocols and the custom extension guides when you want user-defined objects to interoperate with generic PyRecEst utilities.
  • Use the generated API reference for package-level reference pages built from docstrings.
  • Use tests/ as executable reference coverage for APIs that do not yet have dedicated tutorials.
  • Use module docstrings and class docstrings for detailed mathematical notes where they are available.