一种针对恒模信号的运动单站直接定位算法
收稿日期: 2015-06-11
修回日期: 2015-12-19
网络出版日期: 2015-12-28
基金资助
国家自然科学基金(61201381)
A direct position determination algorithm for constant modulus signals with single moving observer
Received date: 2015-06-11
Revised date: 2015-12-19
Online published: 2015-12-28
Supported by
National Natural Science Foundation of China (61201381)
相比于常规的"测向+位置估计"两步定位模式,以Weiss等提出的目标直接位置确定(DPD)算法具有估计精度高、分辨能力强和无需数据关联等诸多优点。基于该类定位算法的基本理念,提出了一种利用单个运动天线阵列对恒模(即相位调制)信号的DPD算法。首先,依据最大似然(ML)准则以及恒模信号的恒包络特征,建立了相应的直接定位优化模型;接着,根据优化函数的代数特征提出了一种有效的多参量交替迭代算法,用以获得ML估计器的最优数值解;此外,推导了针对恒模信源的位置直接估计方差的克拉美罗界(CRB),从而为新算法的定位精度提供定量的理论下界。仿真实验表明:相比于已有的基于单个运动天线阵列的直接定位算法以及传统的两步定位算法,通过利用恒模信号的恒包络特征可以明显提高目标直接定位的估计精度。
关键词： 无源定位; 恒模信号; 最大似然估计器; 天线阵列; 克拉美罗界(CRB); 直接位置确定(DPD)
王鼎 , 张刚 , 沈彩耀 , 张杰 . 一种针对恒模信号的运动单站直接定位算法[J]. 航空学报, 2016 , 37(5) : 1622 -1633 . DOI: 10.7527/S1000-6893.2015.0347
Compared with the conventional two-step (including direction finding and position estimation) localization mode, the direct position determination (DPD) algorithm presented by Weiss et al have more advantages, such as higher estimation accuracy, strong resolution capability, no data association issue, etc. Based on the idea behind this novel localization mechanism, a new DPD algorithm for constant modulus (also called phase-modulated) signals with a moving antenna array is presented in this paper. First, the DPD optimization model is constructed based on maximum likelihood (ML) criterion as well as the constant modulus property of phase-modulated source. Then, an effective alternating iteration algorithm is devised according to the algebraic property of the cost function, which can provide the optimal numerical solution of the ML estimator. In addition, the Cramér-Rao bound (CRB) on the position estimation variance for constant modulus signals is also derived, which can be used as the theoretical lower bound for target position estimation. Simulation results demonstrate that compared to the existing DPD algorithm with single moving observer and the conventional two-step localization algorithm, the DPD estimation accuracy can be considerably improved if the constant modulus characteristic is incorporated into the localization algorithm.
[1] KUTLUYIL D. Bearings-only target localization using total least squares[J]. Signal Processing, 2005, 85(9):1695-1710.
[2] LU X N, HO K C. Taylor-series technique for source localization using AOAs in the presence of sensor location errors[C]//Proceedings of the 4th IEEE Workshop on Sensor Array and Multichannel Processing. Piscataway, NJ:IEEE Press, 2006:190-194.
[3] WANG D, ZHANG L, WU Y. The structured total least squares algorithm for passive location based on angle information[J]. Science Chain Information Science, 2009, 52(6):1043-1054.
[4] CHAN Y T, HO K C. A simple and efficient estimator by hyperbolic location[J]. IEEE Transactions on Signal Processing, 1994, 42(4):1905-1915.
[5] 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.
[6] YANG L, HO K C. An approximately efficient TDOA localization algorithm in closed-form for locating multiple disjoint sources with erroneous sensor positions[J]. IEEE Transactions on Signal Processing, 2009, 57(12):4598-4615.
[7] HO K C, LU X, KOVAVISARUCH L. Source localization using TDOA and FDOA measurements in the presence of receiver location errors:analysis and solution[J]. IEEE Transactions on Signal Processing, 2007, 55(2):684-696.
[8] SUN M, HO K C. An asymptotically efficient estimator for TDOA and FDOA positioning of multiple disjoint sources in the presence of sensor location uncertainties[J]. IEEE Transactions on Signal Processing, 2011, 59(7):3434-3440.
[9] 李金洲, 郭福成. 传感器位置误差条件下仅用到达频率差的无源定位性能分析[J]. 航空学报, 2011, 32(8):1497-1505. LI J Z, GUO F C. Performance analysis for passive source localization using merely FDOA measurements with erroneous receiver positions[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(8):1497-1505(in Chinese).
[10] WEISS A J. Direct geolocation of wideband emitters based on delay and Doppler[J]. IEEE Transactions on Signal Processing, 2011, 59(6):2513-2520.
[11] AMAR A, WEISS A J. Localization of narrowband radio emitters based on Doppler frequency shifts[J]. IEEE Transactions on Signal Processing, 2008, 56(11):5500-5508.
[12] WEISS A J. Direct position determination of narrowband radio frequency transmitters[J]. IEEE Signal Processing Letters, 2004, 11(5):513-516.
[13] AMAR A, WEISS A J. Advances in direct position determination[C]//Proceeding of 3rd IEEE Sensor Array Multichannel Signal Processing Workshop. Piscataway, NJ:IEEE Press, 2004:584-588.
[14] AMAR A, WEISS A J. Direct position determination of multiple radio signals[J]. EURASIP Journal on Applied Signal Processing, 2005, 1:37-49.
[15] AMAR A, WEISS A J. Direct position determination in the presence of model errors-known waveforms[J]. Digital Signal Processing, 2006, 16(1):52-83.
[16] HUANG L, LU Y L. Performance analysis of direct position determination for emitter source positioning[J]. American Journal of Signal Processing, 2012, 2(3):41-45.
[17] OISPUU M, NICKEL U. Direct detection and position determination of multiple sources with intermittent emission[J]. Signal Processing, 2010, 90(12):3056-3064.
[18] 张敏, 郭福成, 周一宇. 基于单个长基线干涉仪的运动单站直接定位[J]. 航空学报, 2013, 34(2):378-386. ZHANG M, GUO F C, ZHOU Y Y. A single moving observer direct position determination method using a long baseline interferometer[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(2):378-386(in Chinese).
[19] 张敏, 郭福成, 周一宇, 等. 运动单站干涉仪相位差直接定位方法[J]. 航空学报, 2013, 34(9):2185-2193. ZHANG M, GUO F C, ZHOU Y Y, et al. A single moving observer direct position determination method using interferometer phase difference[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(9):2185-2193(in Chinese).
[20] LESHEM A, VEEN A J. Direction-of-arrival estimation for constant modulus signals[J]. IEEE Transactions on Signal Processing, 1999, 47(11):3125-3129.
[21] STOICA P, BESSON O. Maximum likelihood DOA estimation for constant-modulus signal[J]. Electronic Letter, 2000, 36(9):849-851.
[22] VAN DER VEEN A, PAULRAJ A. An analytical constant modulus algorithm[J]. IEEE Transactions on Signal Processing, 1996, 44(5):1136-1155.
[23] WANG D. Calibration algorithm for multiplicative modeling errors using constant modulus auxiliary signals[J]. IET Signal Processing, 2015, 9(4):297-311.
[24] FRIEDLANDER B, WEISS A J. Direction finding in the presence of mutual coupling[J]. IEEE Transactions on Antennas and Propagation, 1991, 39(3):273-284.
[25] LIU Z M. Conditional Cramér-Rao lower bounds for DOA estimation and array calibration[J]. IEEE Signal Processing Letter, 2014, 24(3):361-364.
[26] 张贤达. 矩阵分析与应用[M]. 北京:清华大学出版社, 2004:328-340. ZHANG X D. Matrix analysis and applications[M]. Beijing:Tsinghua University Press, 2004:328-340(in Chinese).
[27] VIBERG M, OTTERSTEN B. Sensor array processing based on subspace fitting[J]. IEEE Transactions on Signal Processing, 1991, 39(5):1110-1121.
/
| 〈 |
|
〉 |
CJA