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arXiv 1807.03530eess.SP
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基于差分接收信号强度的鲁棒定位

Robust Differential Received Signal Strength-Based Localization

Yongchang Hu, Geert Leus

摘要:

基于信号强度测量的源定位由于其实用的简单性而变得非常流行。然而,严重的非线性和非凸性使得相关的优化问题在数学上难以求解,特别是当发射功率或路径损耗指数(PLE)未知时。此外,即使PLE是已知的,但没有完美地估计或锚位置信息是不准确的,所构建的数据模型将变得不确定,使问题再次难以解决。本文重点研究了在发射功率未知和PLE未知的情况下,基于差分接收信号强度(DRSS)的模型不确定性定位。首先提出并研究了一种新的白化模型,用于未知发射功率的基于DRSS的定位。当假设PLE是已知的,我们介绍了两个估计的基础上,一个先进的最佳线性无偏估计(A-BLUE)和拉格朗日估计(LE),然后我们提出了一个强大的半定规划(SDP)为基础的估计(RSDPE),它可以应付模型的不确定性(不完美的PLE和不准确的锚位置信息)。这三种估计器从不同的角度来看各有优势:A-BLUE算法复杂度最低; LE算法在小测量噪声下精度最高; RSDPE算法在大测量噪声下性能最好,对模型不确定性具有很好的鲁棒性。最后,我们提出了一个强大的基于SDP的块坐标下降估计(RSDP-BCDE)来处理一个完全未知的PLE和它的性能收敛到RSDPE使用一个完全已知的PLE。

英文摘要:

Source localization based on signal strength measurements has become very popular due to its practical simplicity. However, the severe nonlinearity and non-convexity make the related optimization problem mathematically difficult to solve, especially when the transmit power or the path-loss exponent (PLE) is unknown. Moreover, even if the PLE is known but not perfectly estimated or the anchor location information is not accurate, the constructed data model will become uncertain, making the problem again hard to solve. This paper particularly focuses on differential received signal strength (DRSS)-based localization with model uncertainties in case of unknown transmit power and PLE. A new whitened model for DRSS-based localization with unknown transmit powers is first presented and investigated. When assuming the PLE is known, we introduce two estimators based on an exact data model, an advanced best linear unbiased estimator (A-BLUE) and a Lagrangian estimator (LE), and then we present a robust semidefinite programming (SDP)-based estimator (RSDPE), which can cope with model uncertainties (imperfect PLE and inaccurate anchor location information). The three proposed estimators have their own advantages from different perspectives: the A-BLUE has the lowest complexity; the LE holds the best accuracy for a small measurement noise; and the RSDPE yields the best performance under a large measurement noise and possesses a very good robustness against model uncertainties. Finally, we propose a robust SDP-based block coordinate descent estimator (RSDP-BCDE) to deal with a completely unknown PLE and its performance converges to that of the RSDPE using a perfectly known PLE.

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