Segmented Exponential Stochastic Model for Underwater Acoustic Positioning Based on Travel Time

Objectives: High-precision underwater positioning requires accurate and realistic stochastic model. Currently, equal-weight stochastic model and stochastic model based on sound ray incidence angle are commonly used. However, the initial incidence angle is often unknown in underwater acoustic positioning, which limits the accuracy of stochastic models. Methods: To construct an accurate and realistic stochastic model, this research proposes a segmented exponential stochastic model that takes into account the travel time of sound ray propagation. We analyzed the effects of incidence angle perturbation, sound speed perturbation, and depth on sound ray propagation. Based on the response relationship between the variance of ranging perturbation and the travel time of sound ray propagation, we utilized a segmented exponential function to fit the variance of ranging perturbation, ultimately achieving the construction of the new stochastic model. Results: The model proposed is validated through simulation data and practical data. The results demonstrate that: 1) At the same depth, the weight matrix constructed based on different incidence angle perturbation exhibits excellent stability; 2) In the simulation data, the positioning precision of the model proposed improved by 0.169m, 0.107m and 0.024m compared to the equal-weight model, the incident angle exponent model and the incident angle cosine model, respectively. The positioning precision of the model proposed is comparable to that of the incident angle segmented cosine model and the incident angle segmented exponent model, but the model proposed retains more observational information. The proposed model has been further validated by practical data. Conclusions: The segmented exponential stochastic model proposed significantly improves positioning precision. This research provides new insights for the development of high-precision underwater positioning technology and has important application value in fields such as marine resource exploration, underwater target detection, and underwater navigation.