鲁棒Kalman滤波及其在水下组合导航中的应用

Robust Kalman Filter and Its Application in Underwater Intergrated Navigation

关键词:  捷联式惯导系统  水下  非高斯  Huber  调节因子  自适应

Key words:  Strapdown inertial navigation system  Underwater  Non-Gaussian  Huber  Tuning factor  Adaptive

摘要:

在水下捷联惯导（SINS）/多普勒计程仪（DVL）组合导航系统中，当外部辅助信息受到野值等非高斯噪声污染时，选取调节因子γ为固定值将会降低基于Huber方法的鲁棒Kalman滤波（HRKF）算法的精度和鲁棒性。针对此问题，提出了一种基于马氏距离（MD）算法的调节因子自适应的鲁棒Kalman滤波（HRAKF）算法。首先利用MD算法对正常/异常的观测量进行辨识；进而建立γk递推关系式，并根据量测噪声特性对γ值进行实时调整；最后利用γk求取Huber权函数，并对量测噪声阵进行修正。选取8000s船载实测数据，分别利用Kalman滤波（KF）、HRKF及HRAKF算法进行水下组合导航半物理仿真试验。试验结果初步表明：在观测量受到野值或混合高斯分布噪声污染时，相较于KF和HRKF，HRAKF可实现更高精度、更加稳定的组合导航。

Abstract:

In the process of underwater integrated navigation of strapdown inertial navigation system (SINS), the accuracy and robustness of Huber-based robust filter (HRKF) will degrade when choosing the tuning factor as a fixed value in the non-Gaussian cases. To solve this problem, a Huber-based robust adaptive algorithm (HRAKF) with adaptive tuning factor based on Mahalanobis distance (MD) algorithm is proposed. The normal/abnormal measurements are firstly identified by using MD algorithm, and then adaptively estimate the tuning factor according to the characteristics of the measurement noise based on the relationship between γk and γk－1. Finally, the Huber weight function is obtained to modify the measurement noise covariance by using γk. The underwater integrated navigation experiment is carried out by the Kalman filter (KF) , HRKF and HRAKF based on 8000s ship test data, respectively. The experiment results demonstrate that the precision and robustness of HRAKF are higher than that of KF or HRKF under the conditions that the measurement is contaminated by outliers or thick-tailed non-Gaussian noise.