A practical example for the non-linear Bayesian filtering of model parameters
Provides an educational example for practitioners learning particle filtering, but is incremental in nature.
This tutorial presents non-linear Bayesian filtering for static parameter estimation using particle filters, demonstrated by estimating Earth's gravitational acceleration from pendulum data with adaptive updating as new observations arrive.
In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential Importance Sampling (SIS) and Sequential Monte Carlo (SMC). Throughout the paper we illustrate the concepts and techniques with a practical example using real-world data. The task is to estimate the gravitational acceleration of the Earth $g$ by using observations collected from a simple pendulum. Importantly, the particle filters enable the adaptive updating of the estimate for $g$ as new observations become available. For tutorial purposes we provide the data set and a Python implementation of the particle filters.