This package's aim is to provide a versatile and efficient feedback particle filter implementation in Julia, with abstractions to flexibly construct, run, and analyze feedback particle filters for a variety of uni- and multivariate filtering problems with both diffusion and point process observations.

It provides implementations of the following algorithms:

• Kalman-Bucy filter KBF
• Feedback Particle Filter FPF
• Bootstrap Particle Filter (weighted) BPF
• Point-process Feedback Particle Filter ppFPF
• Ensemble Kushner-Stratonovich-Poisson Filter EKSPF

as well as

• Hidden state and observation models: diffusions, Poisson processes, etc.
• A variety of gain estimation methods: constant gain, semigroup, reproducing kernel Hilbert space, etc.
• Deterministic particle flow

If you have questions or comments, please open an issue!

This package is officially registered. To install it, use the built-in package manager:

pkg> add FeedbackParticleFilters

The package is currently tested on Julia 1.6-1.8, but should work on earlier versions too.

To load the package, use the command:

using FeedbackParticleFilters

Set up a basic one-dimensional linear-Gaussian continuous-time filtering problem:

using Distributions
state_model = ScalarDiffusionStateModel(x->-x, x->sqrt(2.), Normal())
obs_model   = ScalarDiffusionObservationModel(x->x)

filt_prob   = FilteringProblem(state_model, obs_model)

Once the filtering problem is defined, an appropriate filtering algorithm can be defined like this:

method = ConstantGainApproximation()
filter = FPF(filt_prob, method, 100)

The package comes with methods to automatically simulate a given system:

simulation = ContinuousTimeSimulation(filt_prob, filter, 10000, 0.01)
run!(simulation)

To learn more about how to use this package, please check out some tutorials or the documentation linked below.

There are various Jupyter notebooks that explore various key functions of the package:

1. Getting started
2. Gain estimation using the semigroup method
3. Harmonic oscillator example

In development...

This package was developed as part of academic research at Department of Physiology, University of Bern, Switzerland. The research was funded by the Swiss National Science Foundation.