A kernel-approach for estimating the position of moving objects

Kernel regression is introduced as a method for solving ill-posed localization problems. To obtain a unique solution the missing data is augmented by the use of a kernel function that comprises the dynamic behavior of the studied system. The proposed approach is based on the minimization of a cost term which combines a least squares estimator and a regularizer in a reproducing kernel Hilbert space. The solution is represented by a finite number of parameters.While the method works for a large class of positive definite kernels we further point out the impact of the kernel design on the quality of the solution. The design of the preferred kernel function is physically motivated. The validity of the method is demonstrated by a real world problem where the available data origins from unsynchronized and singular range measurements to nodes of unknown position.