Multisensor Estimation Fusion Based on Kernel Mean Embedding

This work deals with the estimation fusion for distributed multisensor systems under the framework of local estimates being taken as probability density functions. The estimation fusion is formulated to an optimization problem that minimizes the sum of squared distances between the fused probability density and each local probability density. The maximum mean discrepancy, which is a distance between two probability density functions, is considered. It is defined by the kernel mean embeddings from the probability density function space to a reproducing kernel Hilbert space. For the quadratic, cubic and Gaussian kernels, either the analytical solutions are derived or the numerical methods are developed for solving the aforementioned optimization problem. Numerical experiments are provided to illustrate the performance of the proposed estimation fusion methods.