数学理论与应用 ›› 2020, Vol. 40 ›› Issue (3): 1-10.
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王志忠1,邹航1*,陈璎1
中南大学数学与统计学院 湖南长沙 410083
出版日期:
发布日期:
通讯作者:
基金资助:
国家自然科学基金重点项目No.41730105
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摘要:
本文将不确定性表示为状态约束,融入平差模型,建立基于状态参数不确定性的滤波模型。首先从无状态约束条件下的平差准则中推导出无约束滤波算法,该算法与卡尔曼滤波算法是一致的。然后扩展到不等式约束和椭球约束的平差准则,推导出基于状态约束的动态滤波算法。通过实例计算,对不同状态约束的动态滤波模型进行比较。结果表明基于状态不确定性的动态滤波算法要优于卡尔曼滤波算法,且简便高效,具有显示表达式。
关键词: 不确定性  , 动态滤波  , 状态约束  , 卡尔曼滤波  , 平差模型
不确定性  ,
Abstract:
Dynamic Filtering models were based on state constrained with uncertainty by regarding uncertainty as state constraint, incorporated into the adjustment models. The unconstrained filtering algorithm is proposed according to unconstrained adjustment model, which is equal to standard kalman filtering algorithm. The inequality state constrained filtering algorithm and ellipsoid state constrained filtering algorithm are provided as the solution of state constrained adjustment models. With simulation calculation, it is compared that the results of different dynamic filtering algorithms based on state constrained with uncertainty are compared. The results show that dynamic filtering algorithms based on state constrained with uncertainty are better than kalman filtering algorithm, obtained simplicity and effectivity.
Key words: Uncertainty , Dynamic Filtering Algorithm , State Constraints , Kalman Filtering , Adjustment Model
Uncertainty ,
王志忠, 邹航, 陈璎. 基于状态不确定性的动态滤波算法[J]. 数学理论与应用, 2020, 40(3): 1-10.
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https://mta.csu.edu.cn/CN/Y2020/V40/I3/1