Time delay estimation between signals, received at multiple spatially separated sensors has many important applications, such as locating sources and finding directions. Moreover, adaptive time delay estimation methods do not require a priori statistics about the source signals, and additionally, their computational complexities are suitable for real time processing.
Actually, fixed step-size algorithms for adaptive time delay estimation cannot simultaneously optimize the convergence speed and the delay variance. Besides, variable step-size algorithms based on noise power are quite sensitive to the noise disturbance.
WANG Leiou and his team from the Institute of Acoustics of the Chinese Academy of Sciences have recently proposed an iteration-based variable step-size algorithm for adaptive time delay estimation. This algorithm possesses fast convergence speed at early stages with small delay variance at steady state. Since its step size is controlled by the iteration time rather than the error signal, this algorithm is different from other variable step-size algorithms, and its performance is insensitive to the noise disturbance.
The research establishes the relationship between the iteration time and the step size. The step size decreases with the increase of the iteration number. The proposed method has a fast initial convergence speed due to its large step size. As the iteration number increases, the delay estimate will converge to its steady state and the step size will decrease gradually.
A threshold scheme is employed in order to make the proposed method has the tracking ability. Both the power of error signal and the error autocorrelation estimate need to be estimated,then the research summarizes the relationship between the steady state power of error signal and the error autocorrelation estimate at different signal-to-noise ratios.
Based on the value of the steady state power of error signal, a hard threshold scheme can be used to detect an abrupt change. If the square of power of error signal is larger than the threshold, it indicates that the step size reaches to its minimum value much earlier or an abrupt change occurs in the unknown systems. Afterwards, the step size of the proposed method needs to immediately increase to its maximum. Furthermore, the new method is a computationally efficient estimator, whose complexity is comparable to the simplest method.
Experiments are conducted to compare the performance of the traditional state-of-the-art to the proposed method. The source signals and noises are independent white Gaussian processes. To validate the effectiveness of the proposed method, the steady state mean square error is measured by 1000 independent Monte Carlo runs. Simulation results demonstrate that the proposed method provides better performance on the convergence speed and the delay variance for different environments with low computational cost.
WANG Leiou, WANG Donghui, ZHENG Feiyang, HAO Chengpeng. An Iteration-Based Variable Step-Size Algorithm for Joint Explicit Adaptation of Time Delay. IEEE Transactions on Circuits and Systems –II: Express Briefs (Vol. 64, No. 8, August 2017). DOI: 10.1109/TCSII.2016.2634592.
Institute of Acoustics, Chinese Academy of Sciences, 100190 Beijing, China