L₁-norm constraint kernel adaptive filtering framework for precise and robust indoor localization under the internet of things

The mixed noise such as Gaussian noise together with the abrupt noise widely exists in the indoor environment, which always leads to the problem of performance degradation of the positioning system under the Internet of Things (IoT). In this paper, a novel kernel function named generalized Student's t kernel (GSt) and a resulting sparse generalized Student's t kernel adaptive filter (SGStKAF) is proposed to attack this problem. The proposed SGStKAF utilizes the kernel mean p-power error criterion (KMPE) with the L₁-norm penalty. The proposed SGStKAF has three significant features. Firstly, the generalized Student's t kernel can suppress the abrupt noise effectively. Secondly, the L₁-norm penalty guarantees that the fixed-point sub-iteration is available so that the more precise solution can be obtained in a few iterations. At last, a sparse structure of neural networks for the implementation of the proposed method can also be obtained via the L₁ constraint. Three experiments and comparisons are carried out to prove the effectiveness of the proposed positioning framework in terms of accuracy and robustness in both the simulation situation and the real-world indoor environments.