Indoor navigation systems are gaining traction due to their resistance to electromagnetic interference, abundant spectrum resources, and energy efficiency, underscoring the importance of indoor visible light positioning technology. Recent research focuses on using deep learning to enhance positioning accuracy, yet challenges remain in training costs, model efficiency, and performance in low Signal-to-Noise Ratio (SNR) scenarios. To address these issues, we propose a novel Long Short Term Memory network-Convolution Residual Network (LSTM-CRN) algorithm with a dataset construction method based on pilot extraction. Additionally, we introduce the Kolmogorov-Arnold Network (KAN) to improve accuracy under low SNR conditions. Extensive simulation results show that the network model trained on the dataset constructed by the pilot extraction method has higher localization efficiency and accuracy, especially compared with the network model trained directly using the received data to construct the dataset. The LSTM-KAN algorithm is trained on the dataset constructed by our method in this paper, and its average localization accuracy is verified to be 3.8 cm (SNR = 30). It also shows better localization accuracy, efficiency, and real-time performance than existing mainstream methods under different SNR conditions, proving that this method is the state-of-the-art in the system described in this article.

To fully exploit enormous data generated by intelligent devices in edge computing, edge federated learning (EFL) is envisioned as a promising solution. The distributed collaborative training in EFL deals with delay and privacy issues compared to traditional centralized model training. However, the existence of straggling devices, responding slow to servers, degrades model performance. We consider data heterogeneity from two aspects: high dimensional data generated at edge devices where the number of features is greater than that of observations and the heterogeneity caused by partial device participation. With large number of features, computation overhead on the devices increases, causing edge devices to become stragglers. And incorporation of partial training results causes gradients to be diverged which further exaggerates when more training is performed to reach local optima. In this paper, we introduce elastic optimization methods for stragglers due to data heterogeneity in edge federated learning. Specifically, we define the problem of stragglers in EFL. Then, we formulate an optimization problem to be solved at edge devices. We customize a benchmark algorithm, FedAvg, to obtain a new elastic optimization algorithm (FedEN) which is applied in local training of edge devices. FedEN mitigates stragglers by having a balance between lasso and ridge penalization thereby generating sparse model updates and enforcing parameters as close as to local optima. We have evaluated the proposed model on MNIST and CIFAR-10 datasets. Simulated experiments demonstrate that our approach improves run time training performance by achieving average accuracy with less communication rounds. The results confirm the improved performance of our approach over benchmark algorithms.