卫星定位中的一种分步加权解算方法  

A Method of Multiple-Step Weighted Least-Square Estimate for Satellite Positioning

作　　者：何瑞珠[1,2] 刘成[1,2] 黄康[1] 

机构地区：[1]中国科学院国家天文台,北京100012 [2]中国科学院大学,北京100049

出　　处：《天文研究与技术》2015年第1期36-43,共8页Astronomical Research & Technology

基　　金：国家自然科学基金(61001109);中国科学院知识创新工程重要方向项目(KGCX2-EW-4071)资助

摘　　要：卫星定位中,当可视卫星数目多于4颗时常采用加权最小二乘(Web Login Server,WLS)算法,对各卫星解算权重进行重新评估而获得最优解。然而由于受到多重因素的影响,权矩阵W的构造与确定一直是各类加权算法中的重点和难点。从线性测量方程组出发,通过研究迭代解算过程中用户等效伪距测量误差对坐标位置误差的传递与放大规律,提出了一种新的加权最小二乘解算方法,及其权矩阵的具体构造与实现方法,从而对各未知数进行分步加权与分离解算。通过全球定位系统(Global Positioning System,GPS)实测实验,对方法的可行性和精度水平进行了分析与验证。结果表明,使用该分步加权方法进行定位,解算结果准确度更高、稳定性更好。The method of Weighted Least-Square estimate （WLS） is often used for satellite positioning to reevaluate the weights for various linkable satellites （of more than 4） in the fitting objective function for deriving optimal position solutions. However, because of a number of complex factors construction and determination of the important weight matrix W are difficult for all algorithms involving weighting for satellites. Starting from linear equations for optimal position solutions, we have studied the patterns of propagations of errors of equivalent pseudo ranges into coordinate errors of position solutions. The propagation patterns involve accumulation of errors in the iteration processes leading to solutions. We subsequently propose a new WLS method together with the approaches of construction and practical calculation of the weight matrix. What is mainly modified by the new method from the position-solving process of the original WLS method is as follows. In the new method arguments whose values are not known beforehand are solved in separate steps, with different steps having independent weight matrices. The new method effectively avoids the weight-matrix calculation that is used to minimize the global residual （residual-squared sum） of all the arguments. Instead, it minimizes the residual of each of the arguments separately. The best estimates of all coordinates constitute the optimal position solution for the location of a user. We have carried out a GPS measurement experiment to test feasibility and accurateness of the new method. The test results show that the new WLS method can appreciably improve the accuracy and stability of a position solution in satellite positioning.

关 键 词：卫星定位 线性方程组 权矩阵 加权最小二乘算法 

分 类 号：TN967.1[电子电信—信号与信息处理]