Intelligent Systems Research Institute, Sungkyunkwan University, Suwon, Gyeonggi-do 440-746, Korea.
Sensors (Basel). 2018 May 17;18(5):1610. doi: 10.3390/s18051610.
A general framework of data fusion is presented based on projecting the probability distribution of true states and measurements around the predicted states and actual measurements onto the constraint manifold. The constraint manifold represents the constraints to be satisfied among true states and measurements, which is defined in the extended space with all the redundant sources of data such as state predictions and measurements considered as independent variables. By the general framework, we mean that it is able to fuse any correlated data sources while directly incorporating constraints and identifying inconsistent data without any prior information. The proposed method, referred to here as the Covariance Projection (CP) method, provides an unbiased and optimal solution in the sense of minimum mean square error (MMSE), if the projection is based on the minimum weighted distance on the constraint manifold. The proposed method not only offers a generalization of the conventional formula for handling constraints and data inconsistency, but also provides a new insight into data fusion in terms of a geometric-algebraic point of view. Simulation results are provided to show the effectiveness of the proposed method in handling constraints and data inconsistency.
提出了一种基于将真实状态和测量的概率分布投影到预测状态和实际测量的约束流形上的一般数据融合框架。约束流形表示真实状态和测量之间需要满足的约束，它在扩展空间中定义，其中所有冗余的数据来源（如状态预测和测量）都被视为独立变量。我们所说的通用框架是指它能够融合任何相关的数据源，同时直接纳入约束条件并识别不一致的数据，而无需任何先验信息。这里提到的方法称为协方差投影（CP）方法，如果投影基于约束流形上的最小加权距离，则该方法在均方误差（MMSE）意义上提供无偏和最优的解决方案。该方法不仅提供了一种用于处理约束和数据不一致的传统公式的推广，而且还从几何代数的角度提供了数据融合的新视角。提供了仿真结果，以显示该方法在处理约束和数据不一致方面的有效性。
