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Research and Academic Papers

This page provides a curated collection of influential research papers on Kalman and Bayesian filtering, from foundational works to modern advancements.

Foundational and Tutorial Works

An Elementary Introduction to Kalman Filtering

Authors: Yan Pei et al. Institution: University of Texas at Austin Year: 2017

Offers a clear conceptual and mathematical introduction to Kalman filtering with examples in robotics and control systems. Excellent starting point for newcomers to the field.

Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond

Author: Zhe Chen Year: 2003

A highly cited tutorial and survey paper that traces the evolution from Kalman filters to modern Bayesian and particle filtering methods. Provides comprehensive historical context and theoretical foundations.

A Study about Kalman Filters Applied to Embedded Sensors

Authors: Valade et al. Year: 2017

Explains how standard and extended Kalman filters can be applied effectively in embedded and constrained environments like drones and smartphones. Practical focus on real-world implementation challenges.

Hybrid and Modernized Approaches

A Review of Kalman Filter with Artificial Intelligence Techniques

Author: Kim Institution: Cranfield University

Reviews methods integrating Kalman filters with neural networks, providing a taxonomy of AI-augmented Kalman filter approaches. Covers emerging trends in learning-based filtering.

A Hybrid Bayesian Kalman Filter and Applications to Numerical Models

Authors: Galanis et al. Year: 2017

Presents a hybrid systems approach combining nonlinear Kalman filters and Bayesian models for robust prediction tasks. Applications in meteorology and environmental modeling.

Developments of Inverse Analysis by Kalman Filters and Bayesian Filtering

Author: Murakami Year: 2023

Reviews evolving strategies in engineering using Kalman, Extended Kalman, Ensemble Kalman, and Particle Filters from a Bayesian perspective. Focus on inverse problems and parameter estimation.

Cutting-Edge and Application-Driven Research

State of the Art on State Estimation: Kalman Filter Driven by Artificial Neural Networks

Publisher: ScienceDirect Year: 2023

Summarizes advanced variants of Kalman filters that incorporate learning and adaptive mechanisms for enhanced performance. Comprehensive review of neural-network-augmented filtering.

The Discriminative Kalman Filter for Bayesian Filtering with Nonlinear and Non-Gaussian Models

Authors: Burkhart et al., Casco-Rodriguez et al. Years: 2020, 2024

Introduces and replicates a modified Kalman filter using discriminative modeling suitable for complex neural decoding and non-Gaussian environments. Applications in neuroscience and biomedical signal processing.

Quantitative Verification of Kalman Filters

Author: Evangelidis Year: 2021

Evaluates and compares various Kalman filter variants using formal quantitative verification techniques. Rigorous analysis of filter performance and stability.

Filter Comparison and Selection

Comparing Filter Types for Nonlinear Systems

Different filtering approaches excel in different scenarios. Here's a comprehensive comparison to guide your choice:

Kalman Filter (KF)

  • Best for: Linear systems with Gaussian noise
  • Accuracy: Optimal for linear models
  • Computational Cost: Low
  • Limitations: Fails in nonlinear settings

Extended Kalman Filter (EKF)

  • Best for: Mildly nonlinear systems
  • Accuracy: Moderate (first-order linearization)
  • Computational Cost: Low
  • Strengths: Computationally efficient baseline
  • Limitations: Can diverge with strong nonlinearities; suboptimal estimation

When to use EKF: - Process noise exceeds measurement noise - Nonlinearities are smooth and mild - Computational resources are limited - Real-time performance is critical

Unscented Kalman Filter (UKF)

  • Best for: Moderately to strongly nonlinear systems
  • Accuracy: High (captures up to 3rd-order Taylor terms)
  • Computational Cost: Moderate to High
  • Strengths: No Jacobian calculation required; more accurate than EKF
  • Limitations: Higher computational cost; requires parameter tuning

When to use UKF: - Nonlinearities are significant - Accurate uncertainty estimation is critical - You want to avoid derivative calculations - Computational resources allow moderate overhead

Particle Filter (PF)

  • Best for: Highly nonlinear, non-Gaussian systems
  • Accuracy: Very high (nonparametric approach)
  • Computational Cost: Very High
  • Strengths: Handles arbitrary distributions; most flexible
  • Limitations: Computationally expensive; particle degeneracy in high dimensions

When to use Particle Filter: - System is highly nonlinear - Noise is non-Gaussian or multimodal - Accurate tail probability estimation needed - Computational resources are available

Performance Comparison Table

Filter Type Nonlinearity Handling Accuracy Computational Cost Robustness Best Use Case
Kalman Filter Only linear Optimal for linear Low Limited to Gaussian linear Linear systems, optimal baseline
Extended KF First-order linearization Moderate Low Stable under mild nonlinearity Mildly nonlinear, real-time systems
Unscented KF Sigma point sampling High Moderate to High More robust than EKF Moderate nonlinearity, better accuracy
Particle Filter Full posterior sampling Very High Very High Handles any nonlinearity/noise Highly nonlinear, non-Gaussian systems

Selection Guidelines

Choose based on your constraints:

  1. Computational Budget:
  2. Very limited → EKF
  3. Moderate → UKF

  4. High → Particle Filter

  5. Nonlinearity Level:

  6. Linear → Kalman Filter
  7. Mild (< 10% deviation from linear) → EKF
  8. Moderate (10-30% deviation) → UKF

  9. Strong (> 30% deviation) → Particle Filter

  10. Noise Characteristics:

  11. Gaussian → KF, EKF, or UKF
  12. Non-Gaussian but unimodal → UKF

  13. Multimodal or arbitrary → Particle Filter

  14. Dimensionality:

  15. Low (< 5 states) → Any filter
  16. Medium (5-20 states) → KF, EKF, UKF
  17. High (> 20 states) → KF, EKF (PF becomes impractical)

Implementation Notes

EKF vs UKF Trade-offs

Use EKF when: - You have analytical Jacobians readily available - Real-time performance is critical - Process noise >> measurement noise - Nonlinearities are smooth and well-behaved

Use UKF when: - Jacobians are difficult or expensive to compute - Nonlinearities are moderate to strong - Accurate covariance estimation is important - You can afford ~3x computational cost vs EKF

Practical Considerations

Filter Stability: - EKF: Can diverge if linearization point is poor - UKF: More stable, but sigma points can become poorly conditioned - PF: Requires careful resampling to avoid particle depletion

Parameter Tuning: - EKF: Tune process and measurement noise covariances - UKF: Additionally tune alpha, beta, kappa parameters - PF: Tune number of particles and resampling threshold

Implementation Status

The following table shows which Bayesian filtering methods are currently implemented in this library:

Filter/Method Implemented Module/Class Documentation
Linear Filters
Kalman Filter (KF) ✅ bayesian_filters.kalman.KalmanFilter Docs
Information Filter ✅ bayesian_filters.kalman.InformationFilter Docs
Square Root Filter ✅ bayesian_filters.kalman.SquareRootKalmanFilter Docs
Fading Memory Filter ✅ bayesian_filters.kalman.FadingMemoryFilter Docs
Nonlinear Filters
Extended Kalman Filter (EKF) ✅ bayesian_filters.kalman.ExtendedKalmanFilter Docs
Unscented Kalman Filter (UKF) ✅ bayesian_filters.kalman.UnscentedKalmanFilter Docs
Cubature Kalman Filter (CKF) ✅ bayesian_filters.kalman.CubatureKalmanFilter API
Ensemble Kalman Filter (EnKF) ✅ bayesian_filters.kalman.EnsembleKalmanFilter Docs
Particle Filters
Particle Filter (Sequential Monte Carlo) ⚠️ bayesian_filters.monte_carlo (resampling only) API
Sequential Importance Resampling (SIR) ❌ - -
Regularized Particle Filter ❌ - -
Multiple Model Filters
Interacting Multiple Model (IMM) ✅ bayesian_filters.kalman.IMMEstimator Docs
Multiple Model Adaptive Estimation (MMAE) ✅ bayesian_filters.kalman.MMAEFilterBank Docs
Smoothers
Rauch-Tung-Striebel (RTS) Smoother ✅ bayesian_filters.kalman.rts_smoother API
Fixed-Lag Smoother ✅ bayesian_filters.kalman.FixedLagSmoother API
Forward-Backward Smoother ❌ - -
Robust Filters
H-Infinity Filter ✅ bayesian_filters.hinfinity.HInfinityFilter Docs
Huber Filter ❌ - -
Other Estimation Methods
g-h Filter (Alpha-Beta Filter) ✅ bayesian_filters.gh Docs
Discrete Bayes Filter ✅ bayesian_filters.discrete_bayes Docs
Least Squares Filter ✅ bayesian_filters.leastsq Docs
Sigma Point Methods
Merwe Scaled Sigma Points ✅ bayesian_filters.kalman.MerweScaledSigmaPoints API
Julier Sigma Points ✅ bayesian_filters.kalman.JulierSigmaPoints API
Simplex Sigma Points ✅ bayesian_filters.kalman.SimplexSigmaPoints API

Legend: - ✅ Fully implemented and tested - ⚠️ Partially implemented (components available, full filter not assembled) - ❌ Not yet implemented

Future Roadmap

The following filters and methods are candidates for future implementation:

  1. Particle Filters: Full implementation of Sequential Importance Resampling (SIR) and Regularized Particle Filter
  2. Advanced Smoothers: Forward-Backward smoother for more complex scenarios
  3. Robust Filters: Huber filter for outlier rejection
  4. Adaptive Filters: Filters with online covariance estimation
  5. Constrained Filters: Filters that handle state and measurement constraints

Contributions are welcome! See our Contributing Guide for details on how to add new filter implementations.

Additional Resources

Contributing

Know of an important paper or resource that should be included? Please open an issue or submit a pull request!

This research compilation is maintained as part of the Bayesian Filters library. Last updated: 2025.