对角加载最小二乘法的时间延迟估计
Diagonal loading least squares time delay estimation
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摘要: 最小二乘法是一种经典而有效的时间延迟估计算法,但由于最小二乘法矩阵求逆不稳定,在低信噪比情况下将失效。本文提出了对角加载最小二乘法(DL-LS),对求逆的矩阵加上一个正定阵,可以解决矩阵求逆不稳定的问题。并从正则化的角度分析了固定加载量的缺点一提高对低信噪比容忍性的同时降低了准确性,从而进一步提出了二次加载来解决这个问题。利用第一次估计的信道响应的倒数作为加载量,使得在回波到达的时刻加载量尽量小,其他时刻有一定加载量。最后,数值仿真和水池实验验证了对角加载对最小二乘法的改进效果。Abstract: Least squares (LS) time delay estimation is a classical and effective method. However, the performance is degraded severely in the scenario of low ratio of signal-noise, by reason of the instability of matrix inversing. In order to solve the problem, diagonal loading least squares (DL-LS) is proposed, by adding a positive definite matrix to the inverse matrix. Furthermore, the shortcoming of fixed diagonal loading is analyzed from the point of regularization that when the tolerance in low ratio of signal-noise is increased, veracity is decreased. This problem is resolved by reloading. The primary estimation's reciprocal is introduced as diagonal loading and it leads to small diagonal loading at the time of arrival and larger loading at other time. Simulation and pool experiment prove the algorithm has better performance.