Matérn Kernel Adaptive Filtering With Nyström Approximation for Indoor Localization
Matérn Kernel Adaptive Filtering With Nyström Approximation for Indoor Localization
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DOI：
10.1109/tim.2023.3291800
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发表时间：
2023
影响因子：
5.6
通讯作者：
Wen Dong;Xifeng Li;Dongjie Bi;Yongle Xie
中科院分区：
文献类型：
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作者：
Wen Dong;Xifeng Li;Dongjie Bi;Yongle Xie
位置识别是物联网（IoT）中许多实时定位应用的最重要任务之一。然而，由于室内环境的高度复杂性，精确且鲁棒的室内定位总是受到很大影响。为了解决这个问题，一种新的核学习范式-核自适应滤波引起了人们的注意。核自适应滤波器（KAF）已经取得了巨大的成功，但其增长的网络结构，这导致了沉重的存储负担。为了平衡精度与神经网络的大小，稀疏化方法通常被引入到KAF中以产生稀疏的神经网络结构。与传统的稀疏方法不同，Nyström方法使用数据采样点的子集来生成固定大小的滤波结构，该结构可以有效地近似整个样本所覆盖的空间。在这项工作中，为了有效地对抗在室内环境中的大的异常，如脉冲噪声，Matérn核首次应用于KAF。在此基础上，提出了一种指数加权Matérn核递归最大相关熵（mKRMC）及其Nyström近似形式Nyström指数加权mKRMC（Nys-mKRMC），以在稀疏滤波器结构下获得期望的精度性能。此外，还给出了Nys-mKRMC算法的收敛性证明.最后，大量的实验结果表明，与现有的KAF算法和传统的机器学习方法相比，本文提出的mKRMC算法和Nys-mKRMC算法都具有较高的精度和较强的鲁棒性，且滤波器结构紧凑.
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.