# Particle Filtering methods

**URL:** <https://discourse.julialang.org/t/particle-filtering-methods/130828>\
**Category:** Modelling & Simulations\
**Tags:** question\
**Created:** [July 17, 2025, 9:20pm UTC](https://discourse.julialang.org/t/particle-filtering-methods/130828 "2025-07-17T21:20:10Z")\
**Posts on this page:** 1\
**Showing post:** 10

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**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [July 25, 2025, 6:07am UTC](https://discourse.julialang.org/t/particle-filtering-methods/130828/10 "2025-07-25T06:07:43Z")

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It depends on how large the uncertainty is in the initial distribution compared to the stationary distribution. If you push that example much further in time, it might converge. You can compute the stationary covariance matrix by solving a Riccati equation with the A jacobian, see [Influence of sample rate on performance · LowLevelParticleFilters Documentation](https://baggepinnen.github.io/LowLevelParticleFilters.jl/stable/sample_rate/) for some details or “Asymptotic form” in [Kalman filter - Wikipedia](https://en.wikipedia.org/wiki/Kalman_filter#Asymptotic_form)

```julia-auto
using MatrixEquations
A = Ajac(...)
C = Cjac(...)
R_stationary, _ = ared(A, C', R2, R1)

```

or something like that.

You are essentially plotting the evolution of the equation

X^+ = A X A^T - (A XB)(R\_2+B^T XB)^{-1}(B^T XA^T) + R\_1

where B = C^T, and you might not have plotted enough evolution of it for it to converge.

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