In recent years, with the rapid development of computer vision technology and the widespread application of deep learning algorithms, more possibilities emerge to further improve the stability and positioning accuracy of indoor positioning systems. Convolutional neural networks are very popular and effective computer vision architectures widely used. We research on an indoor positioning algorithm based on matrix factorization and deep neural networks. A dedicated dataset is constructed based on light emitting diode (LED) beacon image feature recognition, and a convolutional neural network classification model is designed. Through deep learning algorithms combined with matrix factorization for dimensionality reduction and noise reduction, accurate recognition of LED beacons is achieved, which effectively improves the recognition accuracy and positioning stability of the system model.

We combine the analysis of an indoor visual positioning system based on an LED array and conducts the following research: 1) We establish a convolutional neural network model for the indoor visual positioning system based on the LED array, construct an LED beacon dataset, analyze the fitting of the model’s training loss rate and validation loss rate, and evaluate the model’s generalization ability and recognition accuracy. 2) We propose a beacon recognition method based on matrix factorization and convolutional neural networks, which reduces the dimensionality and noise of input data through the matrix factorization algorithm, improves the accuracy of model beacon recognition, and enhances the positioning accuracy and stability of the system. Further, we quantify the parameter count (parameters) and floating-point operations (FLOPs) of the model and combine theoretical calculations with hardware measurement data to perform a complexity analysis, providing a theoretical basis for deploying resource-constrained mobile devices. 3) According to the indoor positioning scheme, we deploy LED beacons in actual scenarios to measure and analyze the beacon recognition accuracy and positioning accuracy of the positioning system before and after combining it with a convolutional neural network model based on the matrix factorization algorithm.

The actual testing environment in this article is a 7 m×5 m×3 m room, as shown in Fig. 3, and the relevant experimental parameters are listed in the table. The deployment spacing of the LED beacons is set to 2 m. We aim to improve the recognition accuracy of the beacons through deep neural network models, thereby enhancing the positioning accuracy of the system. Therefore, it is necessary to measure the recognition accuracy and positioning accuracy, which will be verified through the following two experiments. Experiment 1: to measure the recognition accuracy of the model for LED beacons, an LED beacon dataset is constructed. The number of datasets is shown in Table 2. To further enrich the complexity and diversity of the dataset and to simulate lighting changes, rainy and foggy weather, and dynamic interference, some example images are shown in Fig. 4. Based on the fixed size of the dataset, the model’s hierarchical parameter quantity and FLOPs quantity are calculated. The specific results are shown in Table 3. It can be seen that the total parameter quantity of the model is 1.55×10⁵, and the single sample inference calculation quantity is 2.8×10⁵ FLOPs. By training and learning on the dataset, both the training loss and validation loss rapidly decrease in the first three rounds of 20 training epochs, then stabilize, which indicates that the model has a good fit on the training data and good generalization ability on the validation set, as shown in Fig. 6, with recognition accuracy ranging from 99.33% to 100%. Figure 7 shows the analysis of the computational complexity of the model. The fully connected layer accounts for 92.4% of the total computational complexity, which indicates that this layer is the computational bottleneck of the model. In the future, it can be further optimized by replacing it with global average pooling. The trend of the computational complexity of the training and validation sets with respect to epochs shows that, due to the fixed dataset size, the computational complexity increases linearly, consistent with theoretical analysis. Experiment 2: to verify the positioning accuracy of fixed positions within the recognition range, positioning accuracy tests are conducted at different positions within the recognition range of a single LED beacon. The test results are shown in Fig. 8. The overall average positioning error is 6.12 cm, which is basically consistent with the theoretical positioning error of the algorithm. The positioning accuracy within the recognition range of the LED beacon is not affected. Further testing of the positioning accuracy is conducted by deploying the receiving end on the robot, which allows the robot to move at a constant speed in the experimental scene and collect positioning data. The number of successful positioning attempts is counted, and the deviation distance from the route is used as the positioning error. The cumulative distribution function (CDF) generated is shown in Fig. 9. After 1000 positioning attempts, the number of successful positioning attempts ranges from 956 to 985, with positioning errors below 6 cm exceeding 80%, and below 10 cm almost reaching 100%. Compared with the pre-application recognition method positioning system, the positioning accuracy has improved by 22.64%, which proves that the recognition method based on matrix factorization and the deep neural network model proposed in this paper has a certain effect on improving the positioning performance of indoor positioning systems.

We propose a deep neural network recognition algorithm based on matrix factorization optimization to address the problems of low beacon recognition accuracy and poor stability in LED array indoor positioning systems. By constructing a convolutional neural network (CNN) model based on non-negative matrix factorization (NMF), while retaining the spatial feature extraction ability of CNNs, and combining it with the sparse characteristics of LED beacons, NMF is used to achieve data dimensionality reduction and noise suppression. The experiment shows that the model achieves a recognition accuracy of 99.77% on the expanded multi-interference dataset, which is 8.50 percentage points higher than the comparison system. The average positioning error of this method is 6.12 cm, which is 22.64% better than the positioning accuracy of the comparison system. This method provides a new technical path for high-precision visible light positioning. The method proposed in this article has broad application potential. In smart home environments, it can achieve precise indoor positioning for automatic lighting control, energy management, and intelligent security systems. In industrial automation, this method can enhance robot navigation, asset tracking, and workspace safety by achieving real-time, high-precision positioning. In addition, in the field of healthcare, this method can be used for patient monitoring, elderly care, and indoor navigation in hospitals. Based on the research in this article, a potential future direction for research is enhancing the robustness of algorithms in dynamic and complex environments, which may require multi-sensor fusion of multi-source information. Additionally, exploring other machine learning or deep learning algorithms may further improve the accuracy and adaptability of recognition. At the same time, reducing algorithm complexity and achieving model lightweight, as well as testing algorithms in different real-world scenarios, are also crucial for their practical deployment. Overall, we lay a foundation for more reliable and secure LED-based indoor positioning systems, opening up new possibilities for advanced location-based services.