Approximate Closed-Form TDOA-Based Estimator for Acoustic Direction Finding via Constrained Optimization
Approximate Closed-Form TDOA-Based Estimator for Acoustic Direction Finding via Constrained Optimization
复制标题
基于近似闭式 TDOA 的估计器，用于通过约束优化进行声学测向
DOI：
10.1109/jsen.2018.2803150
复制
发表时间：
2018-04-15
影响因子：
4.3
通讯作者：
Lu, Songsheng
中科院分区：
文献类型：
--
作者：
Cui, Xunxue;Yu, Kegen;Lu, Songsheng
本文基于声传感器阵列的到达时间差(TDOA)测量，对三维空间中声发射体的方位和仰角进行了估计。基于TDOA的测向问题非常重要，因为在很多情况下，信号源只会发出瞬变信号，只有TDOA测量才能用来确定方向。线性最小二乘估值器提供了次优解，因为在非线性观测方程的线性化过程中存在非平凡的信息损失。为了避免信息损失，通常采用拉格朗日乘子法来实现约束优化，但计算复杂度较高。本文提出了一种约束最小二乘估计器来处理测向问题。该方法同时利用拉格朗日乘子和二次约束来形成代价函数。结果表明，所得估计器是近似闭合的，大大降低了计算复杂度，但在小噪声水平下对估计的贡献很小。推导出了用均方误差来评价该估计器理论精度的数学公式。仿真和现场实验结果表明，该估计器的性能优于传统的线性和非线性估计器。
This paper focuses on estimating the azimuth and elevation of a sound emitter in 3-D space based on time-difference-of-arrival (TDOA) measurements with an array of acoustic sensors. The TDOA-based direction finding problem is significant because in a range of scenarios the source only emits a transient signal and only TDOA measurements can be used to find the direction. The linear least squares estimator provides a suboptimal solution, since there is nontrivial information loss in the linearization of the nonlinear observation equation. To avoid the information loss, the Lagrange multiplier method is usually used to realize the constrained optimization, but the computational complexity is rather high. This paper proposes a constrained least squares estimator to deal with the direction finding problem. The proposed method makes use of both Lagrange multiplier and quadratic constraints to form the cost function. The resultant estimator is shown to be approximate closed-form so that the computational complexity is reduced greatly, but contributes little under a small noise level. Mathematical formula is derived to evaluate the theoretical accuracy of the proposed estimator in terms of mean square error. Both simulation and field experimental results demonstrate that the proposed estimator can outperform the traditional linear and nonlinear estimators.