一类飞行轨迹重构估值器的参数灵敏度分析

Parameter Sensitivity Analysis of One Kind of Flight Path Reconstruction Estimator

各种参数的不确定性对非线性耦合微分方程组解的影响,可用富里埃系数法进行有效的分析。本文应用这种方法探讨推广的卡尔曼滤波器一类的飞行轨迹重构估值器对其本身各设计参数不确定性的灵敏度,效果也十分突出。分析结果表明,估值器初值的不确定性对估值结果影响最大,输入测量协方差阵不确定性的影响最小,初始滤波误差协方差阵及测量协方差阵的影响居中。文中还对这些设计参数阵与向量中具体元素的不确定性影响作了进一步的探究,以供分析、设计与调试飞行轨迹重构估值器时参考。

It is well known that the design parameters of the Kalman filter are initialstate vector y_0 initial filtering error covariance matrix P_0, input covariancematrix Q, and measurement covariance matrix R. Ref. [8](AD-A096393) is the only paper seen by the authors that exploresonly preliminarily some problems of sensitivity analysis connected with engine-ering design of random state estimator. Ref.[8] deals with the relatively simpleestimator of the steady state Kalman filter, and investigates only the sensitivityof such estimator to inaccuracies of parameters. In contrast to Ref. [8], this paper deals with the more complicated esti-mator of general Kalman filter for the nonlinear and time varying flight pathreconstruction. Unlike in Ref. [8], care must be taken to make good assump-tions of suitable initial state vector y_0 and inital filtering error covariance ma-trix P_0. This paper explores the parameter sensitivity of such estimator ofgeneral Kalman filter in ordr to examine the influences of uncertainties in y_0,P_0, Q and R on the estimated output of the filter. Parameter sensitivity canbe obtained with the help of Figs. 1 to 6. The results of the analysis show that y_0 of the estimator has the strongestinfluence on the estimated output, then come P_0 and R, but the influence ofQ is rather weak. The results of this paper are believed to be very helpful todesign and adjustment of the estimator of general Kalman filter. It is believed that the mathematical approach in this paper--this paper'sapproach involves principally the spectrum of Fourier coefficients--is muchbetter than that of Ref.[8].