基于高斯置信传播的分布式卡尔曼滤波器
Distributed Kalman Filter via Gaussian Belief Propagation
摘要：
最近的结果表明，如何分布式和有效地计算线性MMSE的多用户检测问题，使用高斯BP算法。在目前的工作中，我们扩展了这种结构，并表明，操作该算法两次匹配的输入，有几个有趣的解释。首先，我们证明了等价于计算一个迭代的卡尔曼滤波器。其次，我们证明了卡尔曼滤波器是高斯信息瓶颈算法的一个特例，当权参数$β= 1$。第三，我们讨论了仿射尺度邻近点法的关系，并指出它是卡尔曼滤波器的一个特例。除了这种链接估计，压缩/聚类和优化的理论兴趣，我们允许一个单一的分布式实现这些算法，这是一个非常实用和重要的任务，在传感器和移动ad-hoc网络。许多问题领域的应用包括通信网络中的协作信号处理和分布式资源分配。
英文摘要：
Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter $β= 1$. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of resources in a communication network.
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