任意ノイズを持つ多項式系のための最大エントロピー・モーメントカルマンフィルタ
Max Entropy Moment Kalman Filter for Polynomial Systems with Arbitrary Noise
多項式系を対象に、モーメント制約付き最大エントロピー分布で信念と非ガウスノイズを表現し、凸最適化でフィルタリングを行うMEM-KFを提案した。
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著者: Sangli Teng, Harry Zhang, David Jin, Ashkan Jasour, Ram Vasudevan, Maani Ghaffari, Luca Carlone
分類: cs.RO
原文アブストラクト
Designing optimal Bayes filters for nonlinear non-Gaussian systems is a challenging task. The main difficulties are: 1) representing complex beliefs, 2) handling non-Gaussian noise, and 3) marginalizing past states. To address these challenges, we focus on polynomial systems and propose the Max Entropy Moment Kalman Filter (MEM-KF). To address 1), we represent arbitrary beliefs by a Moment-Constrained Max-Entropy Distribution (MED). The MED can asymptotically approximate almost any distribution given an increasing number of moment constraints. To address 2), we model the noise in the process and observation model as MED. To address 3), we propagate the moments through the process model and recover the distribution as MED, thus avoiding symbolic integration, which is generally intractable. All the steps in MEM-KF, including the extraction of a point estimate, can be solved via convex optimization. We showcase the MEM-KF in challenging robotics tasks, such as localization with unknown data association.
