基于不完全测量数据的飞行器轨迹参数估计

Trajectory estimation for aircraft with incomplete measurements

提出基于稀疏优化的轨迹参数估计新方法,通过降低参数空间的维数改善模型的病态性。利用B样条函数实现轨迹参数的稀疏表示,根据轨迹参数与测量数据的关系建立估计轨迹参数的稀疏表示寻优模型,采用高斯牛顿法获得模型的解。寻优模型中待估参数的数量取决于样条节点数,利用样条函数的高阶导数在节点处的不连续性建立了选取样条节点的稀疏优化模型,采用凸优化方法求解该模型,实现样条节点数的最小化。仿真结果表明,稀疏优化方法能够大幅度提高不完全测量段落轨迹参数的估计精度。

A new estimation method based on sparse optimization was proposed. This method alleviated the ill-posedness by decreasing the dimension of parameter space. The sparse representation of the trajectory was achieved by using the B-spline function. An optimization model for trajectory estimation was constructed according to the relationship between the measurement data and the trajectory,and was solved by using the Gauss-Newton method. In this model,the number of the parameters to be estimated was determined by the number of the spline knots. A sparse optimization model for optimal knot selection was established by using the discontinuity of high order derivative of spline at the knots. This model was solved by using a convex optimization approach,and the number of knots was minimized. Simulation results showed that the sparse optimization method can dramatically improve the estimation accuracy of trajectory during the incomplete measured interval.