Recursive Bayesian Estimation

Recursive Bayesian Estimation

• Recursive Bayesian estimation (Bayes filter) is a general probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process model.
• The process relies heavily upon mathematical concepts and models that are theorized within a study of prior and posterior probabilities known as Bayesian statistics.

Sequential Bayesian filtering

• Sequential Bayesian filtering is the extension of the Bayesian estimation for the case when the observed value changes in time.
• It is a method to estimate the real value of an observed variable that evolves in time.
• The method is named:
  • filtering when estimating the current value given past and current observations,
  • smoothing when estimating past values given past and current observations, and
  • prediction when estimating a probable future value given past and current observations.

References

Bayesian Filtering Reference

• tittuvmathew/Bayesian_filtering_smoothing: MATLAB codes to perform Non-Linear Kalman filtering and smoothing using particle filters
• behnamasadi/Filters: This work contains implementation of Kalman Filter, Extended Kalman Filter and Particle Filter in python from scratch.
• xushangnjlh/Filter-SLAM: EKF(Entended Kalman Filter) and PF (Particle Filter) implementation by Python, with a GUI
• Jupyter Notebook Viewer
• rlabbe/Kalman-and-Bayesian-Filters-in-Python: Kalman Filter book using Jupyter Notebook. Focuses on building intuition and experience, not formal proofs. Includes Kalman filters,extended Kalman filters, unscented Kalman filters, particle filters, and more. All exercises include solutions. MIT
• Particle Filters: A Hands-On Tutorial - PMC
• jelfring/particle-filter-tutorial