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针对无源定位问题中的一类特殊观测方程,提出一种将其非线性观测方程进行伪线性处理,从而实现目标位置(闭式)解算的定位理论框架.首先,在不限定具体物理观测量的前提下,建立将非线性观测方程转化为伪线性观测方程的代数模型,并在没有系统误差(特指观测站位置状态扰动)的条件下,推导出伪线性加权最小二乘定位闭式解(称其为Pwls-a).接着,利用一阶误差分析方法定量证明该闭式解的统计方差可渐近逼近无系统误差时的克拉美罗界(Cram′er-Rao bound).随后,在系统误差存在条件下,定量推导闭式解Pwls-a的统计方差,并定量证明该方差无法渐近逼近系统误差存在条件下的克拉美罗界.对此,推导出另一种可抑制系统误差的伪线性加权最小二乘定位闭式解(称其为Pwls-b),并定量证明该闭式解的统计方差可渐近逼近系统误差存在条件下的克拉美罗界.此外,将闭式解Pwls-b推广应用于多目标联合定位的场景中最后,以协同AOA/TDOA/GROA信息的无源定位问题为算例,阐述伪线性无源定位理论框架的具体应用,并通过数值实验验证文中理论分析的有效性和定位方法的优越性.
Aiming at a kind of special observation equation in passive localization problem, this paper proposes a pseudo-linear processing of its nonlinear observation equation to realize the positioning theoretical framework of target position (closed) solution.Firstly, without limiting the physical observation We establish the algebraic model which transforms the nonlinear observation equation into pseudo-linear observation equation and deduces the pseudo-linear weighted least squares positioning closed-form under the condition of no systematic error (especially the disturbance of the position of the observing station) (Called Pwls-a) .Finally, the first-order error analysis method is used to quantitatively prove that the statistical variance of this closed-form solution can approach the Cram’er-Rao bound without systematic errors. , The statistical variance of the closed-form solution Pwls-a is quantitatively deduced under the condition of systematic error, and the variance is proved to be asymptotically approximate to the Cramer range in the presence of systematic errors. In this regard, (Which is called Pwls-b), the statistical variance of this closed-form solution can be asymptotically approximated to the caratmeline boundary in the presence of systematic errors.In addition, the Pseudo-Linear Weighted Least Squares positioning closed-form solution Closed Solution Pwls- Finally, the application of the pseudo-linear passive location theory framework is illustrated by using the passive location of AOA / TDOA / GROA information as an example. The theoretical analysis of the paper is validated by numerical experiments The effectiveness and positioning method of the superiority.