Disturbance analysis of underwater positioning acoustic ray and design of piecewise exponential weight function

The sound velocity error is an important error source of underwater positioning, which mainly includes the uncertainty of sound velocity measurement and the sound velocity error caused by the temporal-spatial variation of the sound speed field. Based on the constant gradient sound ray tracking model, we derive a mathematical model for the sound ray disturbance analysis about the incident angle, sound velocity gradient and water depth. The results show that, for the same water depth and sound velocity error, the greater the incident angle is, the greater the impact of incident angle perturbation on the sound ray, and the greater the impact of sound ray bending will be. According to the derived function response relation between incident angle disturbance and acoustic ray disturbance, a piecewise exponential function stochastic model of underwater positioning based on incident angle correlation is established. The positioning results of the piecewise-exponential function random model are compared with the equal weight model. The piecewise-cosine weighting model is also validated, but the random model in this article will retain more observation information