飞行器轨迹的半参数估计方法

A semiparametric estimation method for aircraft trajectory

提出一种基于半参数建模的飞行器轨迹估计新方法,通过抑制不可参数建模的测量系统误差提高轨迹的估计精度。利用不等距节点B样条函数建立飞行器轨迹的参数模型,将轨迹参数模型代入测量模型中,并将测量模型中不可参数建模的系统误差表示为非参数,进而建立包含轨迹参数待估量和系统误差非参数待估量的半参数回归模型。采用轨迹参数估计和系统误差分离交替迭代的方式求解该半参数回归模型,利用非线性最小二乘法估计轨迹参数,通过小波分析从残差数据中分离系统误差。理论分析和仿真结果表明,半参数估计方法的轨迹估计精度优于忽略测量系统误差的参数估计方法。

A new estimation method of aircraft trajectory based on semiparametric modeling was proposed in this paper.This method improved the estimation accuracy of trajectory by mitigating the measurement systematic errors which could not be parameterized.The parametric model of aircraft trajectory was constructed by using the B-spline function with non-uniform knots,and this model was embedded into the measurement model.The systematic errors which could not be parameterized were expressed as non-parameters in the measurement model.Then,a semiparametric regression model was established containing two types of unknown variables to be estimated:the trajectory parameters and the non-parameters of systematic errors.Trajectory parameter estimation and systematic error separation were operated alternately and iteratively to solve this semiparametric regression model.The trajectory parameters were estimated by using nonlinear least square method,and the systematic errors were separated from residual data by wavelet analysis.Both theoretical analysis and simulation results showed that the trajectory estimation of semiparametric estimation method was more accurate than that of the parametric estimation method which ignored the systematic errors.