Underwater wireless optical sensor network (UWOSN) represents a vital technology for high-speed, low-latency underwater data transmission, supporting applications from environmental monitoring to underwater exploration. The performance of UWOSN critically depends on the accuracy of node localization. The underwater environment introduces distinct challenges, including node mobility due to ocean currents, severe signal attenuation, and energy constraints, which complicate precise localization. Although existing dynamic localization algorithms have advanced the field, they frequently struggle to address the unpredictability of node movement and environmental effects on signal propagation. This paper presents a novel dynamic localization algorithm based on optimal anchor node combination selection (DLOS) to address these challenges. The proposed DLOS algorithm combines advanced optimization techniques and machine learning to improve localization accuracy and success rate in dynamic underwater conditions.

The proposed DLOS algorithm incorporates four key innovations. First, it introduces a comprehensive fitness function to evaluate anchor node combinations by simultaneously considering three critical factors: position uncertainty, residual energy, and geometric coplanarity. This multi-criteria approach ensures the selection of anchor nodes that are both reliable and energy-efficient. Besides, the proposed DLOS algorithm employs an improved Lévy flight-based grey wolf optimizer (LGWO) to efficiently search for the optimal anchor combination. The LGWO is enhanced with a nonlinear distance control parameter and a good-point-set initialization method to improve convergence speed and avoid local optima. Additionally, the proposed DLOS algorithm incorporates a random forest-based dynamic ranging model to handle time-varying parameters such as trajectory angle and optical signal attenuation. This model is trained on extensive datasets to predict accurate distance measurements despite environmental fluctuations. To further enhance performance, by employing a hybrid localization approach that integrates time difference of arrival (TDOA) and received signal strength (RSS) ranging techniques, the proposed DLOS algorithm effectively mitigates localization errors induced by clock asynchrony. Based on the above key innovative methods, the proposed DLOS algorithm effectively increases localization accuracy and localization success rate in despite of node mobility.

The performance of the proposed localization algorithm DLOS is verified by simulations. In order to visually validate the performances of the proposed DLOS algorithm, the M-RSS algorithm, the LLSH algorithm, the RSS/KF algorithm, and the DLNS algorithm are selected as the compared algorithms. The proposed DLOS algorithm shows an obvious improvement in localization accuracy compared to the other four algorithms across varying numbers of anchor nodes (Fig. 7). Evidently, the DLOS algorithm leverages its optimal-anchor-combination selection mechanism for global search and rapid convergence, identifying the most suitable anchor combination. This significantly shortens localization time and reduces localization errors. As the ranging noise variance gradually increases from 0 to 1, the proposed DLOS algorithm outperforms the other four compared algorithms in RMSE (Fig. 8). In UOWSNs, both anomalous ranging values and amplified noise variance can affect the overall accuracy of position estimation. The DLNS and the DLOS algorithms consider the impact of noise on distance measurements. They utilize a random forest model to process each input data instance, ultimately yielding excellent distance values. Specifically, the localization accuracy of the DLOS algorithm, which incorporates the anchor node selection mechanism, significantly surpasses that of the DLNS algorithm. This is mainly because the anchor node selection mechanism can alleviate the generation of abnormal distance measurement. As the node communication radius varies, the proposed DLOS algorithm maintains lower RMSE compared to the other four algorithms (Fig. 9). This is attributed to the fact that the anchor node selection mechanism in the DLOS algorithm considers both remaining energy and node mobility, thereby reducing the impact of increased energy consumption caused by enlarging node communication radius on localization accuracy. The proposed DLOS algorithm exhibits the lowest RMSE with diverse attenuation coefficient compared to the other four algorithms (Fig. 10). This phenomenon mainly results from the fact that the mentioned algorithms all employ the RSS ranging technology, making their localization accuracy heavily depend on the extent of underwater signal path loss. As for the DLOS and DLNS algorithms, they use the variation of attenuation coefficient as input to the random forest model and train an effective model to predict the precise distance values between nodes. Additionally, the DLOS and DLNS algorithms integrate both RSS and TDOA ranging, alleviating the limitations of solely relying on RSS ranging, resulting in smoother error curves. The proposed DLOS algorithm outperforms the other four algorithms in localization success rate with different number of simulation times (Fig. 11). This can be attributed to the fact that the DLOS algorithm incorporates an optimal-anchor-combination selection mechanism based on an improved LGWO and employs the random forest model to reduce dynamic ranging errors. This enables the DLOS algorithm to maintain the highest localization success rate in the five algorithms.

This paper presents a dynamic localization algorithm based on optimal anchor combination selection, namely DLOS, for UOWSN. Through the implementation of a novel optimal anchor node combination strategy utilizing a comprehensive objective function and an improved LGWO, the proposed DLOS algorithm enhances localization accuracy and success rate. Furthermore, considering the stochastic mobility of underwater nodes and optical wave attenuation characteristics, a dynamic localization model based on random forest is incorporated to improve accuracy and success rate. The proposed DLOS algorithm also implements a hybrid localization strategy based on TDOA and RSS ranging approaches to minimize localization errors caused by clock asynchrony. Simulation results confirm that the proposed DLOS algorithm achieves superior performance in localization accuracy and success rate compared to the four reference algorithms.