一种高斯型非线性迭代更新滤波器

针对高斯型非线性滤波器在大初始偏差条件下性能下降、甚至发散的问题，提出了一种新的非线性滤波算法，即迭代更新扩展卡尔曼滤波器（iterated update extended Kalman filter，IU-EKF）。首先，该算法在EKF框架下，将传统的一步量测更新在伪时间上分为多步进行，采用部分增益将当前量测信息逐步地引入量测更新过程实现对状态的后验估计；其次，由于多步量测更新过程引入了每一步的过程噪声，因此将量测噪声与每一步更新后的状态估计误差之间的互协方差代入误差协方差矩阵，再利用此误差协方差矩阵的迹对标准卡尔曼增益矩阵求导并令结果为零，以导出噪声相关条件下的最优卡尔曼增益矩阵表达式；最后，根据后验量测残差自适应地调整迭代更新次数，在保证一定滤波精度的前提下，降低了算法的计算量。以2维目标跟踪问题为例，在大初始偏差条件下，通过仿真实验将本文算法分别与EKF、IEKF、UKF、CKF算法进行对比，并针对不同迭代次数对滤波精度的影响进行对比分析。仿真结果表明：本文算法较EKF大幅提高了滤波估计精度，且在大初始偏差条件下，本文算法性能优于现有经典高斯假设滤波器。同时，当迭代次数按1、2、5、10、20递增时，本文算法的滤波精度也随之提升，但提升幅度逐渐减缓。

A Gaussian Nonlinear Iterated Update Filter

In order to solve the problem of performance degradation and divergence of the Gaussian nonlinear filter in the large initial deviation conditions,a new nonlinear filtering method called the iterated update extended Kalman filter (IU-EKF) was proposed.The new approach was carried out by introducing the current time measurement information gradually to the measurement update process with part of gain in pseudo-time. Meanwhile,since the multi-step measurement update process introduced the process noise at each step,the cross-covariance between the measurement noise and the posteriori state estimation error after each step was substituted into the covariance matrix,whose trace was then differentiated with respect to the standard Kalman gain and the result was set to zero.The optimal Kalman gain expression under correlated noise condition was derived then.At last,the number of iterations was adjusted adaptively according to the posteriori measurement residuals.In the premise of ensuring a certain filtering accuracy,the computational complexity of the algorithm was reduced.Taking the two-dimensional target tracking problem as an example,the algorithm was compared with EKF,IEKF,UKF and CKF respectively under the large initial deviation conditions.The influence of different iterations on the filtering accuracy was also compared and analyzed.The simulation results showed that the algorithm was more efficient than EKF,and the algorithm was superior to the classical Gaussian hypothesis filters under the conditions of large initial deviation.Furthermore,when the number of iterations was increased by 1,2,5,10,20,the filtering accuracy of the algorithm was improved,but the growth ratewas gradually slowed down.