Diagonal loading least squares time delay estimation

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.