Long-range LBL underwater acoustic navigation considering Earth curvature and Doppler effect

•The accuracy of long-range LBL navigation is influenced by systematic errors.•A reversed acoustic ray tracking method is proposed for acoustic wave propagation.•An acoustic positioning model considering Doppler effect is constructed.•An observation equation of pressure gauge considering Earth curvature is presented.•Reasonable observation models may make up for the defects in geometry. The accuracy of underwater acoustic navigation is significantly influenced by geometry configuration and systematic errors coming from geophysical environment. Long baseline (LBL) systems exhibit superior positioning precision than other acoustic navigation systems, primarily attributable to the better Geometric Dilution of Precision (GDOP). However, the geometry configuration tends to degrade when the underwater vehicle is far away from the seafloor beacons. Factors such as acoustic ray bending error, Doppler effect and Earth curvature may seriously affect the navigation accuracy. To address these issues, we present a robust Kalman filter with systematic error compensation for long-range LBL systems. Firstly, a reversed acoustic ray tracking method is proposed for a unique phenomenon in acoustic wave propagation. Following that, we construct an acoustic positioning model with a time bias parameter, to weaken the impact of Doppler effect on acoustic ranging. This additional parameter was estimated with the state of the user vehicle in real time. At last, an observation equation of pressure gauge considering Earth curvature is presented for depth constraint. Long-range LBL experiments conducted in the South China Sea is employed to validate the performance of the proposed methods, taking the positioning results of inverted ultra-short baseline (iUSBL) system as reference. The results show that the proposed method outperform traditional method with a decrease of about 60 % in the three-dimensional root mean square (3DRMS) of navigation errors. With mentioned three improvements, the 3DRMS of the long-range LBL system with the longest distance of 20 km from the beacon center is less than 14 m. These findings can provide theoretical basis for other long-range LBL systems.