New Max-Entropy Filter Tackles Hybrid Systems Without Solving Complex PDEs
Researchers extend MEM-KF to stochastic hybrid systems, capturing non-Gaussian uncertainty with moment propagation.
Stochastic hybrid systems, which blend continuous-time stochastic dynamics with discrete reset events (e.g., a bouncing ball hitting the ground), produce inherently non-Gaussian and often multimodal uncertainty. Traditional filtering approaches require propagating probability densities through hybrid Fokker-Planck equations, which is computationally expensive due to boundary-induced probability flux across guard sets. This complexity has limited real-time applications in robotics, control, and autonomous systems where sudden state changes occur.
Kaito Iwasaki, Tejaswi K. C., Anthony Bloch, Maani Ghaffari, and Taeyoung Lee propose a hybrid extension of the Max-Entropy Moment Kalman Filter (MEM-KF). Their key innovation is a moment propagation rule derived from Dynkin's formula with a jump-sum, where reset effects appear as a boundary-flux correction over the guard set. This yields tractable moment dynamics without solving the underlying hybrid PDE. The filter reconstructs beliefs using moment-constrained maximum-entropy distributions, capturing non-Gaussianity efficiently. In a stochastic bouncing-ball example, the method accurately models reset-induced uncertainty via corrected moment equations, offering a practical path for filtering in systems with intermittent events.
- Uses Dynkin's formula with a jump-sum to derive a moment propagation rule that accounts for discrete resets via boundary-flux correction over guard sets.
- Propagates a finite set of statistical moments instead of full densities, avoiding computationally expensive hybrid Fokker-Planck PDE solutions.
- Demonstrated on a stochastic bouncing-ball example, accurately capturing reset-induced non-Gaussianity while retaining the MEM-KF's optimization-based maximum-entropy representation.
Why It Matters
Enables efficient filtering for robotics and control systems with sudden state changes, like collisions or mode switching.