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现代定位系统中,传感器往往被安放在运动平台上,其位置无法精确得知,存在估计误差,将严重影响对目标的定位精度。针对这一问题,提出基于约束总体最小二乘(CTLS)的到达时差(TDOA)定位算法。首先通过引入中间变量,将非线性TDOA定位方程转化为伪线性方程,再利用CTLS技术,全面考虑伪线性方程所有系数中的噪声。在此基础上推导了定位方程的目标函数,再根据牛顿迭代方法,进行数值迭代,快速得到精确解。采用一阶小噪声扰动分析方法,对该算法的理论性能进行了分析,证明了算法的无偏性和逼近克拉美-罗下限(CRLB)。仿真实验表明,该算法克服了现有总体最小二乘(TLS)算法不能达到CRLB、两步加权最小二乘(two-step WLS)算法在较高噪声时性能发散的缺陷,在较高噪声时定位精度仍然能达到CRLB。
In modern positioning systems, the sensors are often placed on a moving platform, the position can not be accurately known, there is an estimation error, which will seriously affect the positioning accuracy of the target. To solve this problem, a time-difference-of-arrival (TDOA) localization algorithm based on constrained total least squares (CTLS) is proposed. First, by introducing intermediate variables, the nonlinear TDOA localization equation is transformed into a pseudo- linear equation, and then the CTLS technique is used to fully consider the noise in all the coefficients of the pseudo-linear equation. Based on this, the objective function of the positioning equation is deduced, and then the numerical iteration is performed according to the Newton iteration method to get the exact solution quickly. The first-order small-noise perturbation analysis method is used to analyze the theoretical performance of the algorithm. The unbiased algorithm and the approaching Cramer-Roche lower bound (CRLB) are proved. Simulation results show that the proposed algorithm overcomes the shortcomings that the existing total least square (TLS) algorithm can not achieve CRLB and the two-step WLS algorithm diverges at higher noise. At higher noise Positioning accuracy can still reach CRLB.