A TDOA-FDOA Passive Positioning Algorithm Based on the Semi-Definite Relaxation Technique
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摘要:
在运动目标的无源定位场景下，闭式算法在低噪声情况下可以到达克拉美罗下界(CRLB)，但是这些算法往往不能适应较大的测量噪声环境。针对目前闭式算法适应大噪声能力较差这一问题，该文联合到达时间差(TDOA)以及到达频率差(FDOA)，提出一种基于半定松弛(SDR)技术的无源定位算法。该算法首先构建传统闭式解的伪线性方程，其次利用随机鲁棒最小二乘(SRLS)的思想以及目标参数与额外变量之间的非线性关系，将无源定位问题转化为了具有2次等式约束的最小二乘问题；随后，将半定松弛技术应用到这一问题上，约束最小二乘问题松弛为半定规划(SDP)问题，最后，借助优化工具箱可以有效地对目标参数进行求解。该文所提出的算法不需要初始值先验条件，仿真实验表明了所提算法的有效性。
Abstract:In the passive location of moving target, the closed-form solution can reach Cramér-Rao Lower Bound (CRLB) under the low noise level, but these algorithms often can not adapt to the large measurement noise condition. For this problem, this paper proposes a passive positioning algorithm based on the Semi-Definite Relaxation (SDR) using Time Difference Of Arrival (TDOA) and Frequency Difference Of Arrival (FDOA). Firstly, this method constructs the pseudo-linear equation of the typical closed-form solution. Secondly, the idea of Stochastic Robust Least Squares (SRLS) and the nonlinear relationship between the target parameters and the additional variables are used to transform the localization problem into the least squares problem with quadratic equality. Using Semi-Definite Programming (SDP) technique, constrained least squares problem is then converted into the SDP problem, which is finally solved by the optimization toolbox. The proposed method does not require an initial priori information and simulations show the effectiveness of the proposed method.
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表 1 观测站的位置与速度
序号 位置(m) 速度(m/s) 1 300 100 150 30 –20 20 2 400 150 100 –30 10 20 3 300 500 200 10 –20 10 4 350 200 100 10 20 30 5 –100 –100 –100 –20 20 20 
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