一种线性最小二乘法的声源目标精确定位方法

An accurate localization approach of acoustic source target with linear least square method

在分析了声音能量距离衰减模型的基础上,提出了一种声源发射能量未知下的声源目标位置精确定位计算方法。将声音能量定位模型转化为非约束线性最小二乘法估计问题,其定位结果直接用代数解表示。同时对非约束线性最小二乘法下的参数进一步优化,提出了约束线性最小二乘法以提高定位精度。对信标节点位置坐标存在高斯噪声下的定位计算方法进行了改进以减少定位误差。仿真验证了该定位计算方法的有效性,数值模拟了不同观测信号噪声和信标节点位置噪声对定位误差的影响。结果同时表明,约束线性最小二乘法比非约束线性最小二乘法的定位误差更小,更接近于定位误差的克拉美罗下界值。

Based on the analysis of the decay model depicted by acoustic energy and distance, an accurate localization approach of source target with unknown acoustic emission energy is proposed. When the localization model of acoustic energy is transformed as the estimation problem of unconstrained linear least square （ULLS） method, the accurate localization results are directly represented as algebraic solutions. The parameters of ULLS method are further optimized, then the constrained linear least square （CLLS） method is put forward to improve the localization accuracy. To decrease the localization error the localization computation method is improved when the beacon positions contain Gaussian noises. The simulations demonstrate the validity of the localization computation method and numerically simulate the impacts of observation signal noises and beacon position noises on localization error. The results also show that the localization error of CLLS method is less than that of ULLS method and more closely to the Cramer-Rao low bound （CRLB） of localization error.