Distributed sparsity-based non-linear regression with multiple kernels in wireless sensor networks

In this paper, we investigate the problem of non-linear time-varying regression in a wireless sensor network system. A field over an area is estimated using a number of fixed sensors distributed randomly in the region. Two regression schemes have been suggested: one for centralized regression and the other for distributed regression. The proposed method exploits the reweighted multiple kernel least squares as the data fidelity term. Moreover, using the idea that not all of the sensors affect the field value in a specific region point, we add the sparsity constraint on the weighting vector to obtain a better estimation of the field. Another TV-norm term is added to the total cost function to ensure the smoothness of the estimated field. The consensus-based term is adopted to develop a distributed estimation technique. In addition, the bandwidth of the kernels are defined to change adaptively over time using a least mean square (LMS) technique which enables the algorithm to track the time-variations of the under-lying field. The simulation results confirm the superiority of the proposed method over its counterparts in both synthetic and real data.