极坐标下卡尔曼滤波算法的研究

A Kalman Filtering Algorithm in Polar Coordinates

针对在某些情况下直角坐标系中卡尔曼滤波算法运算量较大、模型建立比较困难等缺点 ,提出了极坐标下的卡尔曼滤波算法。该算法选用极坐标作为滤波坐标系 ,建立了目标运动模型和外推方程 ,给出了增益阵的一种新的计算方法。仿真结果表明 ,提出的滤波算法在数据率较高时 ,滤波精度略低于直角坐标下卡尔曼滤波算法 ,优于自适应 α- β滤波算法 ,但运算量明显低于直角坐标下卡尔曼滤波算法。

Kalman filtering algorithm for radar in orthogonal coordinates suffers from the following shortcomings: ① their computation overhead is too big; ② it is difficult to establish target model. We present a Kalman filtering algorithm in polar coordinates to overcome these shortcomings. We first get the target movement model (eqs.1 through 4). In such a model, all random disturbances that influence the acceleration of target are represented by a random acceleration w 1 in radial and w 2 in tangent. After a lengthy derivation, we get eq.(13) for computing the gain K R in radial and eq.(14) for computing the gain K θ in tangent. With these two equations, the computation overhead is greatly reduced. They can also overcome the influence of pseudo acceleration casued by polar coordinates. Simulation results (Figs.1 through 3) show that though the precision of new algorithm is a little worse than that of the standard Kalman filtering algorithm, it is much better than that of the adapted α-β filtering algorithm when the data rate is high. The computation overhead of this new algorithm is close to that of α-β filtering algorithm, and much less than that of the standard Kalman filtering algorithm.