基于最大熵准则的GNSS/SINS组合导航滤波算法

GNSS/SINS Integrated Navigation Filtering AlgorithmBased on Maximum Entropy Criterion

在高斯假设下,GNSS/SINS组合导航系统的常规卡尔曼滤波器(KF)在最小均方误差(MMSE)准则下是最优的。然而,当测量噪声受到重尾脉冲噪声干扰时,KF的滤波性能会严重下降。为解决该问题,提出组合导航系统的最大熵卡尔曼滤波器(MCKF)。首先,建立MCKF的状态方程及测量方程;然后,利用相对熵的原理,建立基于最大熵准则的卡尔曼滤波器,并设计其滤波迭代流程;最后,在混合高斯噪声及重尾脉冲噪声环境下,分别对GNSS/SINS组合导航系统进行仿真实验。仿真实验结果表明,在混合高斯噪声干扰下,KF的性能优于MCKF;在重尾脉冲噪声干扰下,MCKF的滤波性能明显优于KF,且核带宽趋于无穷时,MCKF等价于KF。

The traditional Kalman filter(KF)of GNSS/SINS integrated navigation system is optimal under the minimum mean square error(MMSE)criterion and under the Gaussian hypothesis.However,when the measurement noise is disturbed by heavy tail pulse noise,the filtering performance of KF is seriously degraded.To solve this problem,we propose a maximum entropy Kalman filter(MCKF)for integrated navigation system.First,we establish the state equation and measurement equation of MCKF.Then,using the principle of maximum entropy,we establish a Kalman filter based on the maximum entropy criterion,and design its filter iteration flow.Finally,we simulate the GNSS/SINS integrated navigation system in the environment of mixed Gaussian noise and heavy tail pulse noise,respectively.The simulation results show that KF performs better than MCKF under mixed Gaussian noise interference,MCKF has better filtering performance than KF under the interference of heavy tail pulse noise,and MCKF is equivalent to KF when the kernel bandwidth tends to infinity.