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基于DRSS模型的相对误差估计及凸优化混合定位方法研究
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Abstract:
基于接收信号强度差(Difference of Received Signal Strength, DRSS)的定位模型具有节省能量、带宽和时间的优点，并且在定位过程中隐藏了发射机的传输方式，非常有益于机密监视或军事应用。然而DRSS模型具有较高的非凸性，在定位求解时比较困难，本文提出了一种改进的定位方法——相对误差及凸优化混合定位方法。首先借助相对误差方法构建最小化问题，然后借助半正定规划和二阶锥规划对模型进行近似求解。为了验证所提方法的有效性，引入均方根误差(Root Mean Square Error, RMSE)作为估计方法精度的评判标准，通过对比本文所提方法以及现有四种方法(A-BLUE、U-BLUE、LARE-SDP、SOCP)的RMSE，研究结果发现本文提出方法的RMSE值最低，并且更加贴近理论误差的CRLB下界。
The positioning model based on Difference of Received Signal Strength (DRSS) has the advantages of saving energy, bandwidth, and time, and hides the transmission mode of the transmitter during the positioning process, which is very beneficial for confidential monitoring or military applications. However, the DRSS model has high nonconvexity and is difficult to solve in localization. This paper proposes an improved localization method—a hybrid localization method of relative error and convex optimization. Firstly, the minimization problem is constructed using the relative error method, and then the model is approximately solved using semi positive definite programming and second-order cone programming. In order to verify the effectiveness of the proposed method, Root Mean Square Error (RMSE) was introduced as the evaluation criterion for the accuracy of the estimation method. By comparing the RMSE of the proposed method with four existing methods (A-BLUE, U-BLUE, LARE-SDP, SOCP), the research results showed that the RMSE value of the proposed method was the lowest and closer to the CRLB lower bound of the theoretical error.
| [1] | 杨铮, 吴陈沐, 刘云浩. 位置计算: 无线网络定位与可定位性[M]. 北京: 清华大学出版社, 2014. |
| [2] | Sand, S., Dammann, A. and Mensing, C. (2014) Positioning in Wireless Communications Systems. Wiley, Hoboken. https://doi.org/10.1002/9781118694114 |
| [3] | Rappaport. T.S. (2002) Wireless Communications: Principles and Practice. Prentice-Hall, Chichester. |
| [4] | 梁久祯, 陈璟. 无线传感与定位新技术[M]. 北京: 科学出版社, 2017. |
| [5] | Beck, A., Stoica, P. and Li, J. (2008) Exact and Approximate Solutions of Source Localization Problems. IEEE Transactions on Signal Processing, 56, 1770-1778. https://doi.org/10.1109/tsp.2007.909342 |
| [6] | Wang, G., Chen, H., Li, Y. and Ansari, N. (2014) NLOS Error Mitigation for TOA-Based Localization via Convex Relaxation. IEEE Transactions on Wireless Communications, 13, 4119-4131. https://doi.org/10.1109/twc.2014.2314640 |
| [7] | Zhang, S., Gao, S., Wang, G. and Li, Y. (2015) Robust NLOS Error Mitigation Method for TOA-Based Localization via Second-Order Cone Relaxation. IEEE Communications Letters, 19, 2210-2213. https://doi.org/10.1109/lcomm.2015.2482979 |
| [8] | Gao, S., Zhang, F. and Wang, G. (2017) NLOS Error Mitigation for TOA-Based Source Localization with Unknown Transmission Time. IEEE Sensors Journal, 17, 3605-3606. https://doi.org/10.1109/jsen.2017.2698073 |
| [9] | Park, C. and Chang, J. (2016) Closed-Form Two-Step Weighted-Least-Squares-Based Time-of-Arrival Source Localisation Using Invariance Property of Maximum Likelihood Estimator in Multiple-Sample Environment. IET Communications, 10, 1206-1213. https://doi.org/10.1049/iet-com.2015.0952 |
| [10] | Kowalczyk, K., Habets, E.A.P., Kellermann, W. and Naylor, P.A. (2013) Blind System Identification Using Sparse Learning for TDOA Estimation of Room Reflections. IEEE Signal Processing Letters, 20, 653-656. https://doi.org/10.1109/lsp.2013.2261059 |
| [11] | Nesta, F. and Omologo, M. (2012) Generalized State Coherence Transform for Multidimensional TDOA Estimation of Multiple Sources. IEEE Transactions on Audio, Speech, and Language Processing, 20, 246-260. https://doi.org/10.1109/tasl.2011.2160168 |
| [12] | Xu, S. and Dogancay, K. (2017) Optimal Sensor Placement for 3-D Angle-of-Arrival Target Localization. IEEE Transactions on Aerospace and Electronic Systems, 53, 1196-1211. https://doi.org/10.1109/taes.2017.2667999 |
| [13] | Xu, S. and Dogancay, K. (2015). Optimal Sensor Deployment for 3D AOA Target Localization. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, 19-24 April 2015, 2544-2548. https://doi.org/10.1109/icassp.2015.7178430 |
| [14] | Yin, F. and Gunnarsson, F. (2017) Distributed Recursive Gaussian Processes for RSS Map Applied to Target Tracking. IEEE Journal of Selected Topics in Signal Processing, 11, 492-503. https://doi.org/10.1109/jstsp.2017.2678105 |
| [15] | Li, X.R. (2007) Collaborative Localization with Received-Signal Strength in Wireless Sensor Networks. IEEE Transactions on Vehicular Technology, 56, 3807-3817. https://doi.org/10.1109/tvt.2007.904535 |
| [16] | Wang, G. and Yang, K. (2011) A New Approach to Sensor Node Localization Using RSS Measurements in Wireless Sensor Networks. IEEE Transactions on Wireless Communications, 10, 1389-1395. https://doi.org/10.1109/twc.2011.031611.101585 |
| [17] | Wang, G., Chen, H., Li, Y. and Jin, M. (2012) On Received-Signal-Strength Based Localization with Unknown Transmit Power and Path Loss Exponent. IEEE Wireless Communications Letters, 1, 536-539. https://doi.org/10.1109/wcl.2012.072012.120428 |
| [18] | Ouyang, R.W., Wong, A.K. and Lea, C.-T. (2010) Received Signal Strength-Based Wireless Localization via Semidefinite Programming: Noncooperative and Cooperative Schemes. IEEE Transactions on Vehicular Technology, 59, 1307-1318. https://doi.org/10.1109/tvt.2010.2040096 |
| [19] | Tomic, S., Beko, M., Dinis, R. and Lipovac, V. (2013) RSS-Based Localization in Wireless Sensor Networks Using SOCP Relaxation. 2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Darmstadt, 16-19 June 2013, 749-753. https://doi.org/10.1109/spawc.2013.6612150 |
| [20] | Tomic, S., Beko, M. and Dinis, R. (2015) RSS-Based Localization in Wireless Sensor Networks Using Convex Relaxation: Noncooperative and Cooperative Schemes. IEEE Transactions on Vehicular Technology, 64, 2037-2050. https://doi.org/10.1109/tvt.2014.2334397 |
| [21] | Vaghefi, R.M. and Buehrer, R.M. (2013) Received Signal Strength-Based Sensor Localization in Spatially Correlated Shadowing. 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, 26-31 May 2013, 4076-4080. https://doi.org/10.1109/icassp.2013.6638425 |
| [22] | Wang, B., Li, Y., Huang, H. and Zhang, C. (2008) Target Localization in Underwater Acoustic Sensor Networks. Proceedings of the Congress on Image and Signal Process, Vol. 1, 68-72. |
| [23] | Hosseini, M., Chizari, H., Soon, C.K. and Budiarto, R. (2010) RSS-Based Distance Measurement in Underwater Acoustic Sensor Networks: An Application of the Lambert W Function. 2010 4th International Conference on Signal Processing and Communication Systems, Gold Coast, 13-15 December 2010, 1-4. https://doi.org/10.1109/icspcs.2010.5709656 |
| [24] | Yan, Y., Wang, W., Shen, X., Yang, F. and Chen, Z. (2012) Efficient Convex Optimization Method for Underwater Passive Source Localization Based on RSS with WSN. IEEE ICUPC, Vol. 1, 171-174. |
| [25] | Xu, T., Hu, Y., Zhang, B. and Leus, G. (2016) RSS-Based Sensor Localization in Underwater Acoustic Sensor Networks. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, 20-25 March 2016, 3906-3910. https://doi.org/10.1109/icassp.2016.7472409 |
| [26] | Chang, S., Li, Y., He, Y. and Wang, H. (2018) Target Localization in Underwater Acoustic Sensor Networks Using RSS Measurements. Applied Sciences, 8, Article No. 225. https://doi.org/10.3390/app8020225 |
| [27] | Zhang, B., Wang, H., Xu, T., Zheng, L. and Yang, Q. (2016) Received Signal Strength-Based Underwater Acoustic Localization Considering Stratification Effect. OCEANS 2016, Shanghai, 10-13 April 2016, 1-8. https://doi.org/10.1109/oceansap.2016.7485561 |
| [28] | Lin, L., So, H.C. and Chan, Y.T. (2013) Accurate and Simple Source Localization Using Differential Received Signal Strength. Digital Signal Processing, 23, 736-743. https://doi.org/10.1016/j.dsp.2012.12.020 |
| [29] | Hu, Y. and Leus, G. (2017) Robust Differential Received Signal Strength-Based Localization. IEEE Transactions on Signal Processing, 65, 3261-3276. https://doi.org/10.1109/tsp.2017.2684741 |
| [30] | Wang, Z., Zhang, H., Lu, T. and Gulliver, T.A. (2019) Cooperative RSS-Based Localization in Wireless Sensor Networks Using Relative Error Estimation and Semidefinite Programming. IEEE Transactions on Vehicular Technology, 68, 483-497. https://doi.org/10.1109/tvt.2018.2880991 |
