This letter investigates the localization problem with distance-dependent noise and sensor location uncertainty. The formulated localization problem is very challenging and non-convex due to the coupled distance-dependent noise variance and the location uncertainty, as well as the nonlinearity in the distance function. A low complexity two-step algorithm that incorporates maximum likelihood and Gaussian message passing (ML-GMP) algorithms is proposed to estimate the target location. It first transforms the distance-dependent noise into distance-independent one by introducing the distance as an intermediate parameter and adopting ML criterion for estimation. A low complex GMP algorithm is then followed to deal with the sensor location uncertainties and estimate the target location. Convergence of the proposed algorithm is proved, and simulation results show the proposed ML-GMP algorithm can approach the Bayesian Cramer-Rao bound (BCRB) and outperforms the other existing algorithms.

中文翻译：

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具有距离相关噪声和传感器位置不确定性的稳健定位

这封信研究了具有距离相关噪声和传感器位置不确定性的定位问题。由于耦合的距离相关噪声方差和位置不确定性以及距离函数的非线性，公式化的定位问题非常具有挑战性和非凸性。提出了一种结合最大似然和高斯消息传递（ML-GMP）算法的低复杂度两步算法来估计目标位置。它首先通过引入距离作为中间参数并采用ML准则进行估计，将依赖于距离的噪声转化为与距离无关的噪声。然后遵循低复杂度的 GMP 算法来处理传感器位置的不确定性并估计目标位置。证明了所提算法的收敛性，