ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Novel Multiple Moving Observers TDOA Localization Algorithm Without Introducing Intermediate Variable
Received date: 2013-08-21
Revised date: 2014-02-18
Online published: 2014-02-28
Supported by
Aeronautical Science Foundation of China(20105584004)
The traditional time difference of arrival (TDOA) localization model needs an intermediate variable to obtain the linear equation, which requires a two-step solution procedure and is not suitable for multiple moving observers continuous localization. Therefore, a TDOA localization model without the intermediate variable is introduced and a constrained weighted least squares algorithm is proposed based on it. First, a weighted least squares problem is formed with respect to the model. Then, error items are deduced after substituting TDOAs in the observation matrix and the observation vector for the measured ones. Each column of error items is expressed as the product of a deterministic matrix and a random vector composed of TDOA measurement errors, based on which the quadratic constraint on the target state is formed. Finally, the estimated target state is obtained through generalized eigendecomposition and its analytic form is derived. Simulation results indicate that the proposed algorithm achieves the Cramer-Rao lower bound and has an asymptotically unbiased solution.
XU Zheng, QU Changwen, LUO Huizi. Novel Multiple Moving Observers TDOA Localization Algorithm Without Introducing Intermediate Variable[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(6): 1665-1672. DOI: 10.7527/S1000-6893.2013.0544
[1] Doanay K. UAV path planning for passive emitter localization[J]. IEEE Transactions on Aerospace and Electronic Systems, 2012, 48(2): 1150-1166.
[2] Kay S, Vankayalapati N. Improvement of TDOA position fixing using the likelihood curvature[J]. IEEE Transactions on Signal Processing, 2013, 61(8): 1910-1914.
[3] Chan Y T, Ho K C. A simple and efficient estimator for hyperbolic location[J]. IEEE Transactions on Signal Processing, 1994, 42(8): 1905-1915.
[4] Ho K C. Bias reduction for an explicit solution of source localization using TDOA[J]. IEEE Transactions on Signal Processing, 2012, 60(5): 2101-2114.
[5] Xu B, Qi W D, Wei L, et al. Turbo-TSWLS: enhanced two-step weighted least squares estimator for TDOA-based localisation[J]. Electronic Letters, 2012, 48(25): 1597-1598.
[6] Cheung K W, So H C, Ma W K, et al. A constrained least squares approach to mobile positioning: algorithms and optimality[J]. EURASIP Journal on Applied Signal Processing, 2006, 2006: 1-23.
[7] Li C, Liu C F, Liao G S, et al. Solution and analysis of constrained least square passive location algorithm[J]. Systems Engineering and Electronics, 2012, 34(2): 221-226. (in Chinese) 李淳, 刘聪锋, 廖桂生, 等. 约束最小二乘无源定位算法的求解与分析[J]. 系统工程与电子技术, 2012, 34(2): 221-226.
[8] Lin L X, So H C, Chan F K W, et al. A new constrained weighted least squares algorithm for TDOA-based localization[J]. Signal Processing, 2013, 93(11): 2872-2878.
[9] Yang K, An J P, Bu X Y, et al. Constrained total least-squares location algorithm using time-difference-of-arrival measurements[J]. IEEE Transactions on Vehicular Technology, 2010, 59(3): 1558-1562.
[10] Wang Z, Luo J A, Zhang X P. A novel location-penalized maximum likelihood estimator for bearing-only target localization[J]. IEEE Transactions on Signal Processing, 2012, 60(12): 6166-6181.
[11] Okello N, Fletcher F, Muicki F, et al. Comparison of recursive algorithms for emitter localisation using TDOA measurements from a pair of UAVs[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(3): 1723-1732.
[12] Wei X Q, Song S M. Improved cubature Kalman filter based attitude estimation avoiding singularity[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(3): 610-619. (in Chinese) 魏喜庆, 宋申民. 基于改进容积卡尔曼滤波的奇异避免姿态估计[J]. 航空学报, 2013, 34(3): 610-619.
[13] Doanay K, Hashemi-Sakhtsari A. Target tracking by time difference of arrival using recursive smoothing[J]. Signal Processing, 2005, 85(4): 667-679.
[14] Bakhoum E G. Closed-form solution of hyperbolic geolocation equations[J]. IEEE Transactions on Aerospace and Electronic Systems, 2006, 42(4): 1396-1403.
[15] Ho K C, Chan Y T. Geometric-polar tracking from bearings-only and Doppler-bearing measurements[J]. IEEE Transactions on Signal Processing, 2008, 56(11): 5540-5554.
[16] Ho K C. Bias reduction for an explicit solution of source localization using TDOA[J]. IEEE Transactions on Signal Processing, 2012, 60(5): 2101-2114.
[17] Ho K C, Chan Y T. An asymptotically unbiased estimator for bearings-only and Doppler-bearing target motion analysis[J]. IEEE Transactions on Signal Processing, 2006, 54(3): 809-822.
[18] Zhang X D. Matrix analysis and application[M]. Beijing: Tsinghua University Press, 2004: 262-266, 528-546. (in Chinese) 张贤达. 矩阵分析与应用[M]. 北京:清华大学出版社, 2004: 262-266, 528-546.
[19] Gu G X. A novel power-bearing approach and asymptotically optimum estimator for target motion analysis[J]. IEEE Transactions on Signal Processing, 2011, 59(3): 912-922.
/
| 〈 |
|
〉 |
CJA