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About this paper
Kaito Iwasaki, Anthony Bloch, Taeyoung Lee, Maani Ghaffari
The Score Kalman Filter (SKF) introduces a Bayesian filtering method for nonlinear systems, representing belief distributions with polynomial maximum-entropy distributions. This approach enhances the scalability of moment-based filtering by replacing computationally intensive partition function evaluations with efficient linear algebraic operations, achieving lower root mean square error compared to Gaussian and particle filters in high-dimensional nonlinear benchmarks up to 20 states.
Key insights
- Score matching offers an efficient, partition-function-free method to parameterize complex polynomial exponential family distributions, making high-order moment filtering scalable to higher dimensions.
- Stein's identity provides a direct linear algebraic mechanism to close the moment hierarchy, enabling robust propagation of moments for nonlinear stochastic systems.
- The SKF formally generalizes the information-form Kalman filter, reducing to it when a second-order polynomial basis (Gaussian distribution) is used.
Summary by alphaXiv.
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