采用卡方检验和牛顿插值的抗差卡尔曼滤波新算法

A New Robust Kalman Filter Algorithm Based on Chi-Square Test and Newton Interpolation

针对组合导航中卫星信号受到干扰导致误差增大的问题,提出一种基于卡方检验和牛顿插值的抗差卡尔曼滤波新算法。该算法以故障观测值的残差不再服从均值为零的高斯分布为理论依据,以仿真实验为基础,通过设计满足显著性水平要求的卡方检验阈值选取方法,提高卡方检验对故障观测值的定位精度;在此基础上,利用过去时刻的观测值构造牛顿插值多项式并进行外延,得到新的当前时刻的观测值,并通过引入改善因子改进观测噪声,使观测噪声更加接近正常值,最终提高导航精度。实验结果表明:该算法相比于一般滤波算法位置误差减小约75%,速度误差减小约80%,该算法能够有效抑制观测值故障带来的影响,提高了组合导航系统的可靠性。

Aimed at the problem that the satellite signals in integrated navigation have an effect on error,a new robust Kalman filter algorithm based on chi-square on test and Newton interpolation is proposed.The algorithm is to improve the positioning accuracy of chi-square test to the fault measurement value by taking the residual error of the measurement value disobeyed the Gaussian distribution with the mean value being zero as a theoretical basis and the simulation experiment as a basis through designing a method to select the threshold of chi-square test to meet the significance level requirement.On the basis mentioned above,the Newtonian interpolation polynomial is constructed by using the observed values at the past time and donated to get the new measured values at the current time,and measurement noise is improved by introducing improvement factor,making measurement noise more close to normal value,and finally improving navigation accuracy.The experimental results show that the algorithm proposed in this paper reduces the position error by about 75%and the speed error by about 80%,compared with the general filtering algorithm,and can also effectively suppress the influence of observed faults and improve the reliability of integrated navigation system.