Positioning algorithm based on space constraint of the PD array in VLP system

Due to factors such as indoor multipath effects and noise, the positioning signal becomes unstable, posing a challenge for visible light positioning systems relying on a single photodetector (PD) to achieve accurate position estimation. To enhance localization precision and ranging accuracy, a positioning algorithm based on spatial constraints of the PD array is introduced in this paper. By leveraging spatial information from the PD array and the channel state information (CSI) from multiple PDs, cross-matching among multiple PDs is performed to alleviate the limitation of unstable positioning information of a single PD during the positioning process. Moreover, the distances obtained through cross-matching are fused with those based on CSI, and the measured distance is iteratively updated to reduce the interference of reflection paths on ranging. This algorithm utilizes the spatial arrangement of the PD array to constrain positioning information received by multiple PDs, rather than relying on a single PD for positioning. This method can achieve joint optimization of positioning accuracy and ranging accuracy without requiring additional equipment or modifying the transceiver structure. Simulation results within a 4 m × 4 m × 3 m indoor space showcase the proposed method's effectiveness. The average positioning error has been reduced to 1.28 cm, and the root mean square error has been reduced to 1.51 cm. In comparison to the least squares (LS) algorithm based on CSI and the nonlinear LS algorithm based on CSI, the new approach reduces average localization errors by approximately 50.4% and 41.3%, respectively. Additionally, the algorithm attains a ranging accuracy of 3.86 cm, outperforming CSI-based distance estimation accuracy by 41.9%.