传感器位置误差条件下的约束总体最小二乘时差定位算法

Constrained Total Least-squares for Source Location Using TDOA Measurements in the Presence of Sensor Position Errors

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。

Modern location system often uses dynamic mobile platforms as receivers. The sensors＇ position may not be known exactly when using dynamic mobile platforms as receivers, and a slight error in sensor positions can lead to a big er- ror in source localization estimation. In this paper, by utilizing the time difference of arrival （TDOA） measurements of a sig- nal received at a number of sensors, a constrained total least-squares （CTLS） algorithms for estimating the position of a source with sensor position errors is proposed. By introducing an intermediate variable, the nonlinear TDOA location prob- lem has been mathematically reformulated as a pseudo linear equations. And the CTLS method, as a natural extension of least-squares （LS） when noise occurs in all data and the noise components of the equations~ coefficients are linearly de- pendent, is more appropriate than LS method for the above problem. On the basis of Newton＇s method, a numerical itera- tive solution can be obtained allowing real-time implementation. After the perturbation analysis, the bias and covariance of the proposed CTLS algorithm are also derived, indicating that the proposed CTLS algorithm is an unbiased estimator, and it could achieve the CRLB when the TDOA measurement noise and the sensor position errors are sufficiently small. Simulation results show that the proposed estimator achieves remarkably better performance than the total least-squares （TLS） and two-step weighted least squares （WLS） approach, which makes it possible that the Cram^r-Rao lower bound （CRLB） is reached at a sufficiently high noise level before the threshold effect occurs.