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.
CITATION STYLE
Bulté, M., Latz, J., & Ullmann, E. (2020). A practical example for the non-linear bayesian filtering of model parameters. In Lecture Notes in Computational Science and Engineering (Vol. 137, pp. 241–272). Springer. https://doi.org/10.1007/978-3-030-48721-8_11
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