基于时频差的正交容积卡尔曼滤波跟踪算法

针对基于时频差测量的无源跟踪中面临的非线性估计问题, 提出一种正交容积卡尔曼滤波跟踪算法. 该算法在容积卡尔曼滤波算法的基础上, 通过引入特定正交矩阵改进容积采样方法, 在高维状态估计下减小因采样产生的误差, 在没有增加计算量的前提下, 有效提高收敛速度及跟踪精度. 仿真结果表明, 在基于到达时差和到达频差的联合无源跟踪问题中, 与扩展卡尔曼滤波及容积卡尔曼滤波算法相比, 本文所提算法在跟踪性能上有明显提升.

A tracking algorithm based on orthogonal cubature Kalman filter with TDOA and FDOA

In a passive target tracking system, the position and velocity of a target can be estimated based on time difference of arrival (TDOA) and frequency difference of arrival (FDOA) received by different stations. But TDOA and FDOA equations are nonlinear, which make the target tracking become a nonlinear estimation problem. To solve the nonlinear estimation problem, the most extensive research algorithms are those of extended Kalman filter (EKF), particle filter (PF), unscented Kalman filter (UKF), quadrature Kalman filter (QKF), and cubature Kalman filter (CKF). But the existing algorithms all come up with shortcoming in some way. EKF only retains the first order of the nonlinear function by Taylor series expansion, which will bring large error. PF has to face the degeneracy phenomenon and the problem of large computational complexity. The standard UKF is easy to become divergence in a high dimensional state estimation. QKF is sensitive to the dimension of state, and the calculation is of exponential growth with the growth of dimension. Although CKF can effectively improve the shortcomings, the discarded error is proportional to the state dimension, which may be large in high dimensional state. In view of the above problems, this paper presents an orthogonal cubature Kalman filter (OCKF) algorithm. This algorithm reduces the sampling error by introducing special orthogonal matrix to change the method of cubature sampling based on CKF. It eliminates the dimension impact on the sampling error. In the absence of additional computation, it effectively improves the tracking precision. Simulation results show that, based on the TDOA and FDOA, compared with the EKF and CKF algorithms, OCKF algorithm can improve the tracking performance significantly.