一种约束鲁棒加权最小二乘静默定位算法

A Constrained Robust Weighted Least Squares Silent Positioning Algorithm

水下静默定位算法是一种具有高度隐蔽性的被动定位算法,仅通过接收来自参考节点的定位信号,目标节点即可完成对自身的定位,且各节点间无须保持时钟同步。针对传统水下静默定位算法定位精度低和对测量噪声鲁棒性较差的问题,本文提出一种结合卡尔曼滤波的约束稳健加权最小二乘算法。该算法首先将目标节点和参考节点之间的距离作为辅助变量,将静默定位问题转换为二次规划问题,并利用辅助变量与目标节点坐标之间隐含的相关性对方程加以约束。其次,为减小测距误差的影响,利用IGG3权函数对观测数据进行稳健加权处理,通过迭代平差法,不断降低噪声较大观测数据的所占权值,从而减小了观测信息中的噪声对定位精度的影响。然后,通过引入拉格朗日乘子法和广义奇异值分解对目标函数进行求解,得到目标节点位置的解析表达式。最后,为充分利用观测量,在水下目标节点的动态定位中估计出位置后,利用状态变量的连续性,对其进行卡尔曼滤波以进一步提高定位精度。仿真及海试结果表明,在水下测量噪声较大的情况下,相比于经典最小二乘算法,本文所提出的约束稳健加权最小二乘算法定位精度更高且该算法对测距误差具有更好的鲁棒性。

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 al-gorithm.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 measure-ment errors,we use IGG3 weighting function to deal with the observations with robust weighting.Through iterative proce-dure,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.Fi-nally,in order to make full use of the observations,after the position of underwater target node is estimated in Dynamic po-sitioning,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 position-ing accuracy and better robustness to measurement errors.