视线坐标系下的解耦无偏转换测量Kalman滤波算法

由于无偏转换测量Kalman滤波算法(unbiased converted measurement Kalman filter,UCKMF)的转换测量噪声协方差矩阵是非对角矩阵,所以无法直接给出该算法的解耦算法。针对此问题通过从参考坐标系(reference coordinate system,RCS)到视线坐标系(line-of-sight coordinate system,LCS)的坐标变换,在视线坐标系下得到了对角形式的转换测量噪声协方差矩阵,实现了转换测量噪声在三个坐标方向上的去相关化,并进一步在三维空间中推导了解耦的UCMKF滤波算法。在算法中,采用递推公式对参考坐标系与视线坐标系的坐标变换矩阵进行估计,并通过一个补偿矩阵提高了估值精度。仿真结果表明,对于匀速运动的目标,解耦UCMKF算法与耦合UCMKF算法的跟踪性能非常接近,但计算量大大降低,因此比较适合在多目标跟踪中应用。

Decoupled unbiased converted measurement Kalman filter in LOS coordinate system

The decoupled algorithm for unbiased converted measurement Kalman filter(UCKMF) cannot be directly obtained because its covariance matrix of converted-measurement noises is not diagonal.The diagonal covariance matrix of converted-measurement noises is gained and the decorrelation of converted-measurement noises between the three coordinate dimensions is implemented by the conversion from the reference coordinate system(RCS) to the line-of-sight(LOS) coordinate system(LCS),and the decoupled UCMKF algorithm is deduced in 3-D space.In this algorithm,the coordinate transformation matrix between the RCS and the LCS is estimated by a propagative equation,and the estimated accuracy is improved by a compensation matrix.For the constant-velocity target,the simulation results show that the decoupled UCMKF can get exactly same performance as the UCMKF,but the amount of computation is greatly reduced,so this algorithm is comparatively applicable to the multi-target tracking.