A stochastic model for precise GNSS/acoustic underwater positioning based on transmission loss of signal intensity

Abstract

Global navigation satellite system (GNSS)/acoustic (GNSS/A) underwater positioning technique is widely applied in the fields of marine scientific research and engineering applications. A more accurate and reliable stochastic model is required for precise GNSS/A underwater positioning. The transmission loss (TL) describes the decrease in acoustic intensity associated with a bubble curtain or other damping structure at a given frequency. It can characterize the noise level of acoustic ranging measurements in the presence of background noise in the ocean. This contribution proposes a stochastic model for precise GNSS/A underwater positioning based on the transmission loss of signal intensity. The transmission loss of signal intensity is obtained according to the acoustic ray-tracing method and then used in the proposed stochastic model to calculate the variance matrix of acoustic ranging measurements. To verify the performance of the proposed method, a lake experiment was carried out. The results show that the ray incidence angle stochastic model performs worse in seafloor transponder positioning if acoustic observations contain gross errors, especially when the observations with low incidence angles contain gross errors. The proposed method provides a stable positioning performance. The positioning accuracy with the proposed method is improved by approximately 30–83% over the equal-weighted stochastic model and 10–82% over the ray incidence angle stochastic model.

Appendix A

Ray incident angle stochastic model

To improve the precision of seafloor transponders based on GNSS/A underwater technique, a ray incident angle stochastic model involving four different forms (the general proportional form, the cosine form, the exponential form, and the piecewise cosine form) was proposed (Shuang et al. 2018). Both the simulation and field test show that the stochastic model performs better in the piecewise cosine form than those of the other three forms of the stochastic model. According to the acoustic ray incident angle at different epochs, the variance of acoustic ranging measurements is presented below:

$${\varvec{D}}_{\varepsilon } = \sigma_{0}^{2} {\varvec{P}}^{ - 1} = \left\{ {\begin{array}{*{20}l} {\frac{{k_{4} \sigma_{0}^{2} }}{{\cos^{2} \left( {\theta_{i} } \right)}}} \hfill & {\;\;\;\theta_{i} \le \theta_{0} } \hfill \\ {\frac{{k_{4} \sigma_{0}^{2} }}{{\cos^{4} \left( {\theta_{i} } \right)}}} \hfill & {\;\;\;\theta_{i} > \theta_{0} } \hfill \\ \end{array} } \right.$$

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where ${\theta }_{i}$ is the ray incident angle; ${\theta }_{0}$ is the preset incidence angle threshold; and ${k}_{4}$ is the scaling factor, generally set to 1.0. According to the previous research, it is reasonable to set the incidence angle threshold within 40°∼50° (Shuang et al. 2018). In this paper, the incidence angle threshold is set to 40° in the experimental analysis.