多站无源跟踪边缘化卡尔曼滤波算法

The marginalized Kalman filter algorithm for multi-plane passive tracking

多站无源跟踪量测方程非线性强,对跟踪算法的稳定性及精度提出了更高的要求。为实现稳定高精度跟踪,提出了新的基于边缘化卡尔曼滤波(MKF)的多机无源跟踪算法。该算法将非线性的量测方程表示为p阶Hermite多项式的加权和,将加权矩阵的先验分布建模为高斯过程,求得其后验分布后对其进行积分来消除加权矩阵的影响,最终可得对状态及其协方差矩阵估计的闭式解。以只测角跟踪为例对所提算法性能进行验证,仿真结果表明,相对于扩展卡尔曼滤波(EKF)算法、不敏卡尔曼滤波(UKF)算法及容积卡尔曼滤波(CKF)算法,所提算法具有更好的跟踪性能。

The measurement equation of multi-station passive tracking system is strongly nonlinear and thus more de-mands are required for the tracking algorithm. To realize robust and fast tracking, a novel passive tracking algorithm is pro-posed based on the marginalized Kalman filter. The proposed algorithm expresses the nonlinear measurement equation as a weighted sum of Hermite polynomials up to p order and then the prior distribution of the weight matrix is modeled as a Gaussian process. The influence of the weight matrix is removed by marginalizing it when its posterior distribution is availa- ble and then the close-form solution of the target state and its covariance can be got. The bearings-only tracking problem is taken as an example to verify the performance of the proposed algorithm. Simulation results indicate that compared to the extended Kalman filter （EKF） algorithm, the unscented Kalman filter （UKF） algorithm and the cubature Kalman filter （CKF）, the proposed algorithm has improved tracking performance.