A Joint Adjustment Method for Precise GNSS/Acoustic Underwater Positioning Based on Single-Differenced Observations

Global navigation satellite system/acoustic (GNSS/A) underwater positioning technique is widely used in the fields of marine scientific research and engineering applications. The conventional single-differenced (SD) positioning method generally treats the position of acoustic transducer obtained by GNSS positioning as known without error. However, error inevitably exists in the estimation of the transducer’s position determined by GNSS positioning, and the precision varies at different epochs. Ignoring the errors of acoustic transducer coordinates will lead to a worse estimation of the position of seafloor transponder. In this contribution, a joint adjustment method for precise GNSS/A underwater positioning is presented based on single-differenced observations. The positions of both transducer and transponder are treated as unknown parameters, and the positions of acoustic transducer are considered as virtual observations. The Helmert variance component estimation is used to adjust the weight ratio of two heterogeneous observations. To verify the performance of the proposed method, two field experiments were carried out. The lake experiment results show that the positioning accuracy with the proposed method can be improved by approximately 49% compared with the SD positioning method. The sea experiment results further demonstrate that the proposed method can perform much better than the SD positioning method, with the standard deviation values of coordinate components better than 0.06 m and the root mean square errors of the acoustic ranging residuals better than 0.02 m.