用最大熵矩方法解决非线性非高斯系统的滤波难题
Max Entropy Moment Kalman Filter for Polynomial Systems with Arbitrary Noise
- 用矩约束最大熵分布表示任意概率分布
- 在过程和观测噪声中建模为最大熵分布，支持任意噪声类型
- 通过凸优化实现状态传播与估计，适合机器人定位等复杂任务
针对非线性非高斯系统的最优贝叶斯滤波设计极具挑战，主要难点在于：1）复杂信念的表示，2）非高斯噪声处理，3）过去状态的边缘化。为此，我们聚焦多项式系统，提出最大熵矩卡尔曼滤波器（MEM-KF）。为应对第1点，采用矩约束最大熵分布（MED）表示任意信念，给定足够多矩约束时可逼近任意分布。为应对第2点，将过程与观测模型中的噪声建模为MED。为应对第3点，通过传播矩并恢复为MED来避免符号积分，该方法通常不可行。MEM-KF中所有步骤（包括点估计提取）均可通过凸优化求解。我们在具有未知数据关联的机器人定位等挑战性任务中验证了MEM-KF的有效性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。