A Constrained Robust Weighted Least Squares Silent Positioning Algorithm

‍ ‍Underwater silent positioning is a passive positioning algorithm with highly concealment， the target node can complete its own positioning only by receiving the signal from the reference node without keeping the clock synchronization among the nodes. This paper proposes a constrained robust weighted least squares algorithm combined with Kalman filter to solve the problem of low accuracy and sensitivity to measurement noise in conventional underwater silent positioning algorithm. Firstly， the algorithm takes the distance between the target node and the reference node as an auxiliary variable， transforms the silent localization problem into a Quadratic programming problem， and uses the implicit correlation between the auxiliary variable and the target node to constrain the equation. Secondly， in order to reduce the impact of measurement errors， we use IGG3 weighting function to deal with the observations with robust weighting. Through iterative procedure， the weight of observations with significant noise can be reduced continuously， which reduced the impact of noise in observations on positioning accuracy. Then， the objective function is solved by introducing Lagrange multiplier method and generalized singular value decomposition， and we can obtain the analytic expression of the target node position. Finally， in order to make full use of the observations， after the position of underwater target node is estimated in Dynamic positioning， we use Kalman filter to further improve the positioning accuracy by utilizing the continuity of state variables. The simulation and sea trial results show that in the case of high underwater measurement noise， compared to the classical least squares algorithm， the constrained robust weighted least squares algorithm proposed in this paper has higher positioning accuracy and better robustness to measurement errors.