无需中间变量的多运动站时差定位新算法
收稿日期: 2013-08-21
修回日期: 2014-02-18
网络出版日期: 2014-02-28
基金资助
航空科学基金（20105584004）
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)
传统时差 （TDOA）定位模型通过引入中间变量来得到线性方程，需要两步求解过程且该模型不适合多运动站连续定位。为此，引入无需中间变量的时差定位模型，并在此基础上提出了一种约束加权最小二乘定位算法。首先将基于该模型的时差定位问题转换为加权最小二乘问题，然后推导代入时差测量值后观测矩阵和观测向量的误差项，将其每一列表示为确定矩阵与随机时差测量噪声向量乘积的形式，并基于此推导了关于目标状态的二次约束方程，最终只需通过广义特征值分解来得到目标状态估计，并推导了该估计的解析表达式。仿真结果表明所提算法的连续定位性能逼近克拉美罗-限且所得定位解渐近无偏。
徐征 , 曲长文 , 骆卉子 . 无需中间变量的多运动站时差定位新算法[J]. 航空学报, 2014 , 35(6) : 1665 -1672 . DOI: 10.7527/S1000-6893.2013.0544
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.
[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.
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