两阶段高维容积信息滤波及其在目标跟踪中的应用

Two-Stage High Degree Cubature Information Filter and Its Application in Target Tracking

非线性系统估计的过程是一个多传感器信息融合的过程,在集中处理量测数据的过程中,Kalman滤波具有很高的计算复杂度.尤其当系统模型中存在随机偏差时,扩维后计算量大幅增大,容易造成系统溢出和运行失败的问题.通过将两阶段容积Kalman滤波嵌入到扩展信息滤波框架的方式,提出了一种两阶段高维容积信息滤波算法.该算法初始化容易,计算量较小,直接利用协方差矩阵的逆与信息矩阵之间的等价关系参与滤波递推的过程,减少了对滤波增益阵的计算.在协方差矩阵的解算过程中,两阶段算法的协方差矩阵之间存在有耦合关系,因此在信息滤波中,两阶段信息矩阵之间也存在着某种耦合关系,算法中通过将非线性T变换和矩阵求逆应用于信息矩阵,得到了两阶段信息矩阵与协方差矩阵之间的耦合关系.通过纯方位跟踪系统的仿真实验,验证了两阶段高维容积信息滤波算法在精度上高于容积Kalman滤波算法,在运行时间上也短于容积Kalman滤波算法,证明了该算法的可用性.

The estimation process of nonlinear system is a process of multi-sensor information fusion.During the process of data processing,Kalman filter has high computational complexity.Especially when there are random deviations in the system model,the amount of calculation increases greatly after dimension expansion,which is easy to cause system overflow and operation failure.By embedded the two-stage Cubature Kalman filter into the extended information filtering framework,Two-stage High degree Cubature Information Filter(TSHCIF)is proposed.The algorithm is easy to initialization and small in computation.It takes advant age of the equivalence relation between the inverse of covariance matrix and information matrix to participate in the process of filter recurrence,and reduces the computation of filter gain matrix.In the solution of the covariance matrix,there is a coupling relationship in the covariance matrices of the two-stage algorithm.Therefore,there is a coupling relationship between the two stage information matrix.In the algorithm,the nonlinear T transformation and the inverse of the matrix should be applied to the information matrix.The coupling relationship between the two-stage information matrix and the covariance matrix is obtained.Through the simulation experiment of bearings only tracking system,it is verified that TSHCIF is superior to CKF in accuracy,and the running time is also shorter than CKF,which proves the availability of the algorithm.