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Convolutional Bayesian Filtering
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AI
DOI：10.1109/tac.2026.3710442.png)
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Abstract
En 中文
Bayesian filtering serves as a mainstream framework for state estimation in dynamical systems, yet its accuracy depends on the assumption that the underlying mathematical model perfectly matches the real system. In practice, unmodeled dynamics, disturbances, and structural simplifications often cause significant model mismatch, which conventional filters cannot explicitly handle. To address this limitation, we reformulate the probabilistic foundation of Bayesian filtering by relaxing the exact conditioning assumption in transition and measurement models, both of which are defined through conditional probabilities. By introducing an additional conditioning event that tolerates bounded discrepancies between the virtual and real variables, we reformulate conditional probability into an integral form analogous to convolution, leading to the concept of convolutional conditional probability. Building on this idea, we develop a generalized filtering framework termed convolutional Bayesian filtering (ConvBF), which modifies both prediction and update steps to explicitly accommodate model mismatch and offers flexible robustness through the choice of distance metrics. For systems with Gaussian noises and Euclidean distance metrics, ConvBF yields a family of robust Kalman filters through modified noise covariance matrices. For general systems with cross-entropy distance, we further propose an efficient exponential density rescaling approach that approximates convolutional effects by rescaling probability densities into fractional powers. Finally, the effectiveness of ConvBF is demonstrated by reformulating classical filtering algorithms, including the Kalman filter, extended Kalman filter, and unscented Kalman filter, into their convolutional counterparts.
Keywords:
Bayesian filtering
conditional probability
convolution
model mismatch
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7
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1.3W
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7.1W
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