极坐标系中带多普勒量测的雷达目标跟踪

Radar Target Tracking with Doppler Measurements in Polar Coordinates

将仅仅考虑位置量测的二维去偏一致转换量测卡尔曼滤波算法进行推广,以解决包含多普勒量测且斜距误差和多普勒误差相关的雷达目标跟踪问题。首先用斜距和多普勒量测的乘积构造伪量测,以减小多普勒量测和目标运动状态之间的强非线性程度;然后用嵌套条件方法得到了转换量测误差前两阶矩的一致性估计;最后根据伪量测是目标运动状态二次函数的特性,用二阶EKF最优地实现了非线性跟踪滤波,其中为了进一步减小二阶EKF的近似误差,利用Cholesky分解实现了位置量测和伪量测的序贯处理。Monte-Carlo仿真结果表明采用新算法可以明显改善跟踪滤波器的性能。

The two-dimensional CMKF-D with only position measurements is extended to solve the radar target tracking problem with Doppler measurements, where the errors between range and Doppler measurements are correlated. Firstly, a pseudo measurement is constructed by the product of range and Doppler measurements to reduce the high nonlinearity of the Doppler measurements with respect to the state; then the consistent first two moments estimate of the converted measurement errors are derived by the nested conditioning method; finally, because the pseudo measurement is quadratic in the state, the second-order EKF is used to optimally implement the nonlinear tracking filtering, where the Cholesky factorization is used to decorrelate the converted position and pseudo measurement errors, and thus the position and pseudo measurements can be sequentially processed to reduce the approximation error in the second-order EKF. Monte-Carlo simulation results show that performance of the tracking filter is improved greatly.