Bullet-proofing particle flow filters against stiffness

#particle #filters #Bayesian #algorithms

Bayesian particle flow has been used for deep learning, nonlinear filtering, weather forecasting, medical imaging and many other applications.  This algorithm is many orders of magnitude faster than standard particle filters, and it is embarrassingly parallelizable, unlike standard particle filters.  However, it can be extremely stiff and hence difficult to design.

We derive a new theory of Bayesian particle flow that bullet proofs the algorithm against stiffness.  This generalizes our recent work (Dai & Daum, IEEE AESS Transactions June 2023).  We also derive a very simple upper bound on the stiffness of our previous algorithm that shows that the stiffness is infinite if we do not measure all components of the state vector.  The new theory fixes this problem completely.

Many researchers have attempted to apply our previous particle flow algorithms, but sometimes they have gotten disappointing results owing to stiffness.  Such researchers might be experts in fancy estimation algorithms, but they are not experts in mitigating stiffness for Ito stochastic differential equations.  We solve this problem by bullet-proofing the particle flow algorithm itself against stiffness, rather than using stiff ODE solvers that require a large amount of computer run time, and which are not parallelizable.  We give a simple intuitive interpretation of the new algorithm.

This talk is for normal engineers who do not have Bayesian algorithms for breakfast.

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5:45pm - Webex link live

6-7pm - Presentation

7-7:15 - Questions and Discussion