摘要
针对GPS快速定位中少数历元组成的法方程存在严重病态性的问题,研究了GPS单频整周模糊度快速解算的新方法:即首先采用改进SVD分解获得系数矩阵的精确奇异值,避免了较小奇异值抖动的影响;然后基于改进SVD分解结合法矩阵病态性特点,设计了一种改进Tikhonov正则化方法,合理构造了正则化矩阵,有效抑制法矩阵的病态性。算例表明:与LS估计-LAMBDA方法和Tikhonov正则化-LAMBDA方法相比,新方法能够有效降低法矩阵的条件数约3个数量级,仅解算4个历元数据,浮点解偏离真值的方差从41.89减小到1.04,可以快速获得准确、稳定的模糊度浮点解。模糊度固定性能结果进一步表明,新方法显著地提高模糊度搜索效率和成功率,解算成功率提高100%。
In view of the ill-condition of normal matrix which is formed by few epoch observations in GPS rapid positioning,a new ambiguity resolution method was proposed,in which the modified singular value decomposition(SVD) is designed to acquire the accurate singular values of coefficient matrix,which avoids the influence of small singular value disturbance. Then an improved Tikhonov regularization method is proposed,and a regularizer matrix is constructed based on the characteristics of ill-condition matrix and modified SVD. Experimental example shows that,compared with least squares estimation and Tikhonov regularization combining with LAMBDA algorithm,the improved method has reduced the condition number of normal matrix by about 3 orders of magnitude,and has reduced the variance of float ambiguity deviated from true value to 1.04 from the original 41.89. As a result,a more accurate and stable float solution can be quickly obtained only by the L1-frequency data of four epochs,while the success rate is improved to 100%.
出处
《中国惯性技术学报》
EI
CSCD
北大核心
2015年第5期624-630,共7页
Journal of Chinese Inertial Technology
基金
国家自然科学基金项目(61273049)
陕西省自然科学基金项目(2014JM8309)
关键词
改进Tikhonov正则化
整周模糊度
病态性
SVD分解
成功率
improved Tikhonov regularization
integer ambiguity
ill-condition
singular value decompo-sition
success rate