基于无源定位观测方程的一类伪线性加权最小二乘定位闭式解及其理论性能分析

Abstract

Utilizing a type of special measurement equation from the passive location problem, a novel theoretical analysis framework, which transforms nonlinear localization equations into pseudo-linear equalities and locates the source with a closed-form solution, is presented. An algebraic model is constructed for pseudo-linearizing the nonlinear localization equations, and the corresponding pseudo-linear weighted least-squares solution, namely Pwls-a, is provided under the assumption that system errors (i.e., observer position and velocity perturbations) are not present. Moreover, the estimation covariance matrix of solution Pwls-a is derived through a first-order perturbation analysis method, and its theoretical performance is proved to attain the corresponding Cramer-Rao bound (CRB). Furthermore, the statistical covariance matrix is also mathematically analyzed in a case in which system errors exist; the result shows that its asymptotical estimation variance cannot reach the relevant CRB in the presence of system errors. As a consequence, a pseudo-linear weighted least-squares solution, namely Pwls-b, is proposed to mitigate the effects of system errors, and its statistical performance is proved to be asymptotically equal to the CRB under the existence of system errors. In addition, the solution Pwls-b is extended into a scenario in which multiple targets are present. Finally, a location scenario with AOA/TDOA/GROA measurements is used as an example to describe the application of the pseudo-linearization method. Simulation experiments are conducted to show the effectiveness of the theoretical analysis and the advantages of the location solutions in this paper.