约简二次扩展平方根容积卡尔曼滤波及其应用
收稿日期: 2013-11-06
修回日期: 2014-02-26
网络出版日期: 2014-03-05
基金资助
国家“863”计划（2010AA7010213）
Reducted Twice Augmented Square-root Cubature Kalman Filter and Its Application
Received date: 2013-11-06
Revised date: 2014-02-26
Online published: 2014-03-05
Supported by
National High-tech Research and Development Program of China (2010AA7010213)
对于具有复杂加性噪声特点的非线性动态系统，往往很难直接运用传统非扩展容积卡尔曼滤波（CKF）方法对其状态进行有效估计。针对这一问题，通过非扩展和扩展Cubature变换精度的对比分析，结合扩展Cubature点集的约简特性，提出了一种约简二次扩展平方根容积卡尔曼滤波（RTA-SRCKF）方法。该方法采用二次扩展策略，在时间更新环节将过程噪声进行扩展，在量测更新环节将量测噪声进行扩展，有效缩减了采样点，降低了算法复杂度，具有很好的实时性，且在未损失滤波精度的前提下算法计算量明显降低，适用于具有复杂加性噪声特点的非线性动态系统状态估计。捷联惯性导航系统（SINS）大失准角初始对准仿真结果验证了理论分析结论，方位对准精度接近理论极限对准精度。
赵曦晶 , 汪立新 , 何志昆 , 张博 . 约简二次扩展平方根容积卡尔曼滤波及其应用[J]. 航空学报, 2014 , 35(8) : 2286 -2298 . DOI: 10.7527/S1000-6893.2014.0002
The traditional nonaugmented cubature Kalman filter (CKF) fails to estimate the status of a nonlinear dynamic system because of its complex additive noises. By analyzing the accuracy of the nonaugmented and augmented cubature transformation, a reduction algorithm of twice augmented square-root CKF (RTA-SRCKF) is proposed based on the reduction of the augmented cubature points. The novel filter, by twice augmenting the process noise and the measurement noise respectively in the time-update and the measurement-update step, is suitable for estimating the states of the nonlinear dynamic system with complex additive noises. Without any loss of estimation accuracy, its complexity is simplified, the computational cost is reduced and real-time performance is also improved since its number of sampling points is greatly reduced. The theoretical analysis result is verified by the initial alignment simulation of the strapdown inertial navigation system (SINS) with large misalignment angles and the estimation accuracy of the azimuth misalignment angle is close to its limit precision in theory.
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