无源定位观测方程的两类伪线性化方法及渐近最优闭式解

为避免无源定位中的迭代运算,该文针对两类特殊的无源定位(非线性)观测方程,分别提出将其进行伪线性化处理,从而实现目标位置闭式解算的理论分析框架.首先,在不限定具体物理观测量的前提下,归纳总结出两类将非线性观测方程转化为伪线性观测方程的数学模型,并推导出用于目标定位的加权线性最小二乘闭式解.接着,利用一阶误差分析方法定量分析两类闭式解的理论定位方差,并证明其参数估计性能均能够达到相应的克拉美罗界(在门限效应发生前),从而证明闭式解的渐近最优性.最后,文中以AOA/TOA联合定位和AOA/TDOA/FDOA联合定位为算例,分别阐述两类伪线性化无源定位方法的具体应用,并通过仿真实验验证文中理论分析的有效性.

Two Pseudo-Linearization Processing Methods and the Asymptotically Optimal Closed-Form Solutions for Passive Location

In order to avoid the iterative computations in passive location,two theoretical analysis frameworks used to solve two kinds of location equations are presented via converting the nonlinear measurement equations into the pseudo-linear equalities.First,two kinds of mathematical model for the pseudo-linearization of two nonlinear measurement equations are formulated,which are not limited to specific physical measurements,and then the corresponding weighted linear least squares (WLS) solutions are derived.Subsequently,the theoretical estimation variances of the two analytical solutions are derived through first-order perturbation analysis methodology,and their theoretical location performances are proved to be able to attain the corresponding Cramér-Rao bound (CRB) before the threshold effect occurs and,hence,the asymptotical optimality of the two pseudo-linearization location methods are verified.Finally,the AOA/TOA location and AOA/TDOA/FDOA location are taken as examples to describe the application of the two pseudo-linearization location methods,and the simulation experiments are conducted to corroborate the effectiveness of the theoretical analysis in this paper.