### 异常值和未知观测噪声鲁棒的非线性滤波器

1. 1. 复旦大学 智慧网络系统研究中心, 上海 200433;
2. 复旦大学 电子工程系, 上海 200433;
3. 上海市空间智能控制技术重点实验室, 上海 201101
• 收稿日期:2020-08-27 修回日期:2020-09-28 发布日期:2020-10-30
• 通讯作者: 李旦 E-mail:lidan@fudan.edu.cn
• 基金资助:
国家自然科学基金（11827808，11974082）：上海市2019年度"科技创新行动计划"社会发展科技领域（19DZ1205805）

### Nonlinear filter robust to outlier and unknown observation noise

FANG Anran1,2, LI Dan1,2,3, ZHANG Jianqiu1,2

1. 1. The Research Center of Smart Networks and Systems, Fudan University, Shanghai 200433, China;
2. Department of Electronic Engineering, Fudan University, Shanghai 200433, China;
3. Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai 201101, China
• Received:2020-08-27 Revised:2020-09-28 Published:2020-10-30
• Supported by:
National Natural Science Foundation of China (11827808, 11974082); Shanghai 2019 Science and Technology Innovation Action Plan Social Development Technology Field(19DZ1205805)

Abstract: An outlier-robust posterior linearization filter is presented to address the filtering problem of nonlinear systems with observation outliers. Analysis shows that a new optimization criterion function can be constructed when the l2 norm of the observation errors in a maximum posterior criterion in filter derivation is replaced by the Huber loss function. Since the Huber loss function has the properties of both l1 and l2 norms, the filter derived from the new criterion presented in this paper not only has a low fitting error as the l2 norm does, but is robust to outliers as the l1 norm. When the distribution of the observation noise is unknown, a boxplot method is introduced to detect the outliers in the observations and estimate the statistical distribution parameters of the observation noise. Thus, an outlier and unknown observation noise-robust posterior linearization filter is further proposed. Simulation verifies the analytical results and further shows that the performance of the proposed algorithms surpasses that of the nonlinear filtering algorithms reported in the literature.