Matérn Kernel Adaptive Filtering With Nyström Approximation for Indoor Localization

Position identification is one of the most important tasks for many real-time location-oriented applications in the Internet of Things (IoT). However, precise and robust indoor localization always suffers a lot from the high complexity of the indoor environment. In order to attack this problem, a new kernel learning paradigm named kernel adaptive filtering has come to our attention. Kernel adaptive filters (KAFs) have achieved great success except for their growing network structure, which leads to a heavy storage burden. To balance the accuracy with the size of neural networks, sparsification methods are usually initiated into the KAFs to produce a sparse structure of neural networks. Different from traditional sparse approaches, the Nyström method employs a subcollection of data sampling points to generate a fixed-size filtering structure, which can effectively approximate the space spanned by whole samples. In this work, in order to efficiently fight against the large abnormalities in the indoor environment such as impulsive noise, the Matérn kernel is applied to KAFs for the first time. Based on it, a so-called exponential weighted Matérn kernel recursive maximum correntropy (mKRMC) and its Nyström approximation version, Nyström exponential weighted mKRMC (Nys-mKRMC), are proposed to obtain the desired accuracy performance with a sparse filter structure. In addition, the convergence proof of the proposed Nys-mKRMC has also been given. Finally, extensive experimental results demonstrate that both the proposed mKRMC and Nys-mKRMC can provide high accuracy and strong robustness with the compact size of the filter structure compared with the state-of-the-art KAFs and traditional machine learning methods.