基于B样条模型的参数化卡尔曼滤波器设计

以标准B样条函数为基础,建立了以位置、样条系数为状态变量的参数化卡尔曼滤波器,用于解决外测数据的实时滤波问题。按照时间更新跨节点与否,分2种情况给出了状态转移方程。在时间更新跨样条节点时,使用样条函数的一阶连续导数条件,估计新增样条节点系数,由此实现滤波器在跨节点处的平滑过渡。通过仿真数据对新方法进行验证,并与已有的2类典型滤波方法进行比较,结果表明,本方法的滤波精度与另一类直接基于弹道信号表示的样条递推滤波方法精度相当,且可表现出更优的收敛性。新方法具有样条参数化模型的相同优点,可对时域信号全时段建模,可利用先验信息设计弹道优选节点而实现滤波性能优化,缺点在于状态更新的策略较为复杂。

Design of a Parameterized Kalman Filter Based on B-Spline Model

A parameterized Kalman filter based on standard B-spline is developed to solve trajectory tracking measurement problem. The filter state variables include position and spline coefficients. Two state transition equations are given to model different system dynamics according to whether time update crosses the spline nodes or not. When the time update crosses the spline nodes, the filter achieves smooth transition by estimating the new spline node coefficient using the continuous first order derivative condition at the spline knots. Simulation data is used to evaluate the new algorithm and the performance of the new algorithm is compared with the existing two typical methods. The results show that the filter has equivalent performance to the recursive spline filter basing on direct trajectory signal representation and exhibits better convergence. The advantages of the new algorithm, which are the same as the spline model, include modeling the whole data uniformly and taking advantage of the optimized spline nodes from a priori design ballistics. Its disadvantage is that the state transition strategy is complicated.