基于约束加权最小二乘的无源定位闭式解算方法

Closed-form solution for passive localization based on constrained weighted least squares

针对无源定位问题中可进行伪线性处理的观测方程,提出一种基于约束加权最小二乘的无源定位闭式解算的理论框架。首先,在不限定定位观测量情况下,建立基于约束加权最小二乘的定位模型,推导其无约束最优化形式;然后,只需通过广义特征值分解即可实现辐射源状态估计并给出其解析表达式,并在此基础上证明了该闭式解的全局最优性和减小定位偏差的特性;最后,将该理论框架应用于到达角(angle of arrival,AOA)/到达时间差(time difference of arrival,TDOA)联合定位场景,验证了其有效性。仿真结果表明,所提算法定位精度能够逼近克拉美-罗下限(Cramer-Rao low bound,CRLB),定位偏差明显小于加权最小二乘算法,尤其在连续定位时间较短,噪声强度较大等情况下,验证了所提理论框架的优越性。

For a type of measurement equations which can be transformed into pseudo-linear equalities im- mediately, a novel theoretical analysis framework is developed to position the source with a closed-form solution for passive location based on the constrained weighted least squares （CWLS）. Firstly, a localization model based on the CWLS is constructed and then the unconstrained optimization is derived. Secondly, the estimated target status is got through the generalized eigenvalue decomposition and its algebraic form is present, which can be utilized to prove that the estimation is the globally optimal solution and its characteristic of reducing location bias. Finally, a location scenario with angle of arrival/time difference of arrival （AOA/TDOA） measurements is used as an example to describe the application of the proposed theoretical framework. Simulation results indi- cate that this proposed algorithm can approximate the Cramer-Rao low bound （CRLB） performance and is much better than the weighted least squares （WLS） as for the estimation bias, especially when the observation time is short and the noise is loud. Simulations corroborate the advantages of the proposed theoretical analysis framework.