基于Bayesian估计理论的GPS导航算法  

Approach for GPS Navigation Basing on Bayesian Theorem

作　　者：周泽波[1] 沈云中[1,2] 

机构地区：[1]同济大学测量与国土信息工程系,上海200092 [2]现代工程测量国家测绘局重点实验室,上海200092

出　　处：《宇航学报》2009年第3期1073-1078,共6页Journal of Astronautics

基　　金：国家自然基金(40674003)

摘　　要：当观测信息冗余度小或出现异常时,仅依靠GPS单历元数据难以获得可靠的定位结果,需借助历史信息改善定位精度和可靠性。导出了Bayesian递推算法的一般形式,建立了基于移动窗口的牛顿向前插值模型与常速度、二次曲线最小二乘拟合模型的先验信息获取方式,引入了当前历元相关观测方程的抗差估计,并采用实测GPS动态数据计算分析,结果表明:抗差估计能有效抑制粗差对GPS定位结果的影响;拟合模型对误差具有平滑作用,其中二次曲线模型明显优于常速度模型,但两者均需实时计算拟合系数;而牛顿向前插值模型系数恒定,计算简单,显著提高了定位精度及可靠性。It is difficult to obtain the reliable positioning restflts when observations are influenced by abnormity or low redun- dancy. Historical information should be applied to improve the positioning precision and reliability. Basing on Bayesian theorem, a general recursive algorithm was developed. According to various prior information accessing, the Newton forward interpolation model, the constant velocity and quadratic curve fitting model were constructed in a chosen time window. Robust estimation for correlated observations was also introduced in the present epoch. In the end, a real-life example is tested, and the results show that robust estimation is effective to reduce the influence of outliers ; Fitting model can smooth errors, and quadratic curve is superior to constant velocity ; Nevertheless both of them need to compute the fitting coefficients ; however, the Newton forward interpolation model holds a constant coefficient and significantly enhances the precision and reliability.

关 键 词：全球定位系统 Bayesian估计 状态模型 导航 稳健估计 

分 类 号：V417.9[航空宇航科学与技术—航空宇航推进理论与工程]