A practical example for the non-linear Bayesian filtering of model parameters

TL;DR

This paper provides a practical tutorial on non-linear Bayesian filtering of static parameters, demonstrating particle-based methods like SIS and SMC through a real-world example estimating Earth's gravitational acceleration using a pendulum.

Contribution

It offers a clear, tutorial-style explanation of particle filtering techniques with a practical Python implementation and real data example.

Findings

Particle filters enable adaptive estimation of static parameters.

Sequential Monte Carlo effectively updates estimates with new data.

The tutorial includes accessible code and data for practical understanding.

Abstract

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.