This article presents a model-based method for fusing data from multiple sensors with a hypothesis-test-based component for rejecting potentially faulty or otherwise malign data. Our framework is based on an extension of the classic particle filter algorithm for real-time state estimation of uncertain systems with nonlinear dynamics with partial and noisy observations. This extension, based on classical statistical theories, utilizes statistical tests against the system's observation model. We discuss the application of the two major statistical testing frameworks, Fisher significance testing and Neyman?Pearson hypothesis testing, to the Monte Carlo and sensor fusion settings. The Monte Carlo Neyman?Pearson test we develop is useful when one has a reliable model of faulty data, while the Fisher method is applicable when one does not have a model of faults, which may occur when dealing with third-party data, such as the Global Navigation Satellite System (GNSS) data of transportation system users. These statistical tests can be combined with a particle filter to obtain a Monte Carlo state estimation scheme that is robust to faulty or outlier data. We present a synthetic freeway-traffic state estimation problem where the filters are able to reject simulated faulty GNSS measurements. The fault-model-free Fisher filter underperforms the Neyman?Pearson filter when the latter has an accurate fault model but outperforms it when the assumed fault model is incorrect.

中文翻译：

---

潜在恶意第三方数据的稳健同化框架及其统计意义


本文提出了一种基于模型的方法，用于将来自多个传感器的数据与基于假设检验的组件融合，以拒绝潜在的错误或其他恶意数据。我们的框架基于经典粒子滤波算法的扩展，用于具有部分和噪声观测的非线性动力学不确定系统的实时状态估计。该扩展基于经典统计理论，利用针对系统观测模型的统计测试。我们讨论了两种主要统计测试框架（Fisher 显着性检验和 Neyman?Pearson 假设检验）在蒙特卡罗和传感器融合设置中的应用。我们开发的蒙特卡洛内曼皮尔逊检验在拥有可靠的错误数据模型时非常有用，而费舍尔方法则适用于没有错误模型的情况，这种情况在处理第三方数据时可能会发生，例如交通系统用户的全球导航卫星系统 (GNSS) 数据。这些统计测试可以与粒子滤波器相结合，以获得对错误或异常数据具有鲁棒性的蒙特卡洛状态估计方案。我们提出了一个综合高速公路交通状态估计问题，其中滤波器能够拒绝模拟的错误 GNSS 测量。当内曼·皮尔逊滤波器具有准确的故障模型时，无故障模型的 Fisher 滤波器的性能低于 Neyman?Pearson 滤波器，但当假设的故障模型不正确时，无故障模型的 Fisher 滤波器的性能优于 Neyman?Pearson 滤波器。