With the continuous innovation and technological advancements, positioning-based services have gained increasing popularity among users. While the global positioning system (GPS) effectively caters to daily life needs, it encounters challenges, especially in complex indoor environments, due to susceptibility to multipath fading, leading to significant positioning errors [1]. Consequently, researchers have explored numerous indoor positioning methods, including ultrasonic, Wi-Fi, radio frequency identification, ZigBee Bluetooth, and ultra-wideband infrared, among others [[2], [3], [4], [5], [6]]. However, these approaches commonly exhibit high susceptibility to electromagnetic radiation interference, high deployment costs, and reduced positioning accuracy [7]. Conversely, visible light positioning (VLP) has emerged as a research focal point in the wireless localization field [8,9], offering advantages such as abundant bandwidth resources, cost-effectiveness, and immunity to electromagnetic interference.

Currently, the more traditional localization methods encompass angle of arrival (AOA), time of arrival (TOA), time difference of arrival (TDOA), and received signal strength (RSS) [[10], [11], [12], [13]]. Scholars have integrated these methods to enhance localization performance. Yang et al. introduced a 3D visible light indoor positioning system utilizing AOA and RSS, employing an LED array and tilted receivers to eliminate inter-cell interference. Experimental results demonstrate an average error distance of less than 3 cm [14]. In fingerprint localization, the objective is to establish the mapping relationship between RSS values and corresponding coordinates. Researchers leverage machine learning and deep learning algorithms [15], including convolutional neural networks (CNN), long short-term memory networks (LSTM), and gated recurrent unit networks (GRU) [[16], [17], [18]]. Concurrently, researchers combine various machine learning algorithms to further enhance localization accuracy. Hsu et al. proposed an RSS-based visible light positioning (VLP) system using CNN and data preprocessing to address under-illuminated regions. Results indicate that, at a 200 cm distance between the LED transmitter and receiver, the average localization error using only the CNN model is 10.19 cm, while the CNN with RSS preprocessing achieves an average localization error of 5.31 cm [19]. Wu et al. presented an RSS-based VLP system using sigmoid function data preprocessing (SFDP) method, applied to two regression-based machine learning algorithms: the second-order linear regression machine learning (LRML) algorithm and the kernel ridge regression machine learning (KRRML) algorithm. Experimental results show significantly improved positioning accuracy for LRML and KRRML algorithms using the SFDP method [20]. Chen et al. proposed an indoor high-precision 3D positioning system based on the improved immune particle swarm optimization (IIMPSO) algorithm. They optimized the field-of-view angle of the indoor receiver to minimize the effect of reflection selection and employed the kalman filtering algorithm to reduce external environmental influence. Finally, the IIMPSO algorithm optimized the search in space, improving positioning accuracy and convergence speed [21]. However, these schemes often use three or even nine LEDs, rendering them impractical in scenarios with sparse LED fixtures.

Some researchers have used a smaller number of LEDs to achieve the same high precision localization [22,23]. In the context of indoor visible light positioning, Hao et al. focused on sparse LED deployment, utilizing a single LED fixture. They achieved a remarkable indoor localization accuracy of 90% within 0.16 m by employing a smartphone as the receiver [24]. Liu et al. developed an indoor visible light localization system utilizing a single LED and a rotatable photodetector (PD). Their approach segmented the entire room into internal and four external zones using a random forest (RF) algorithm. The interior region was directly localized with a rotatable PD, while the exterior region leveraged an extreme learning machine (ELM) and density-based spatial clustering of applications with noise (DBSCAN) to enhance accuracy near interior walls and corners. Simulation results indicated a notable reduction in the average localization error of the exterior region to 1.43 cm with the proposed rotary localizer and hybrid algorithm, resulting in an overall room accuracy of 1.74 cm [25]. Cheng et al. proposed a visible light positioning system based on individual LED communication and an optical camera. This system utilized geometrical features of LED projection and the intersection line on a flat surface to address receiver tilt, achieving high localization accuracy for tilt angles ranging from ±45° to ±40° [26].

Moreover, researchers have empirically demonstrated that strategically adjusting the tilt angle of the receiver can substantially augment the channel capacity, thereby enhancing the visible light positioning (VLP) system's overall performance [27]. Yu et al. proposed a visible light positioning system employing a single LED and a novel receiver configuration. This receiver comprises a horizontal photodetector and two tilted PDs, with a detailed analysis of the impact of tilt and azimuth angles on positioning error. Experimental findings indicate that optimal accuracy is achieved with a tilt angle of 20° and an azimuth angle within the range of 30°–90° [28]. Building upon this foundation, Qin et al. utilized three tilted photodetectors and one horizontal PD in their receiver design. Their investigation delved into the effects of PD tilt angles, azimuth angles, and distances between horizontal and tilted PDs on localization accuracy. Simulation results reveal that, within a 1 m × 1 m × 1.5 m positioning area, the best accuracy is attained with a tilt angle (α) of 25°, azimuthal difference (θ) of 90°, placement angles (ω1, ω2, ω3) of 0°, 90°, and 180° respectively, and a 1 cm distance between the center of the horizontal PD and the center of the tilted PDs [29]. Han et al. employed a receiver comprising one horizontal PD and four tilted PDs. Simulation outcomes demonstrate high localization accuracy when the tilt angle of the PDs does not exceed 30° [30]. Importantly, this structured receiver type offers a distinct advantage by effectively diversifying data features, facilitating enhanced learning and understanding of signal changes in the environment by the network. This comprehensive capture of signal characteristics from different receivers enhances the network's sensitivity to various locations, leading to significantly improved localization performance.

Hence, we have constructed a visible light positioning system utilizing a single LED and multiple tilted photodetectors. Additionally, we propose a novel visible light positioning algorithm based on a deep residual shrinkage network (DRSN). This network enhances both performance and efficiency through the incorporation of a residual structure, facilitating multiple levels of abstract representation. The integration of a soft threshold function not only aids the network in processing anomalous and noisy data but also diminishes redundant information within the model, enhancing the network's adaptability to disturbances or noises. Concurrently, the introduction of squeeze and excitation empowers the network to allocate more attention to crucial channel features, thereby elevating the characterization ability of these features.

We emphasize the following contributions:

Our investigation unveils the utilization of fingerprint identification and deep residual shrinkage network algorithms in multiple photodetector-based VLP systems for precise localization, marking the pioneering nature of this work.

We perform distinct examinations to assess the localization accuracy of the deep residual shrinkage network under varying heights and different datasets. This detailed scrutiny serves to validate and strengthen the algorithm's generalization capabilities.

We conduct a comparative analysis of the DRSN against prevalent algorithms. Our experimental findings indicate the superior performance of DRSN over the other three algorithms within the specified settings.

The rest of the paper is organized as follows: first in Section 2, we describe the components of the indoor VLP localization system model. Then in Section 3 the localization principles are described. Then the simulation and experimental results are analyzed in Section 4. Finally in Section 5, conclusions are provided for this study.