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The problem of estimating and tracking time delay between signals received at two spatially separated sensors is essential in varied fields. For example, in the sonar system, the information of time delay can be used to localize the radiating source. In real-time processing, an adaptive time delay estimation (TDE) method with desired performance and less computational time is preferred. In this short paper, a simple and efficient method is suggested for TDE. This is done by employing a direct formula coupled with the adaptive LMS TDE algorithm. The advantage of the presented method, in terms of the accuracy as well as execution time, over the conventional lookup table method and interpolation formula method is shown in both the stationary and nonstationary time delay environments. Moreover, the capability of estimating time delay in an environment with multipath propagations is investigated.

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In this paper, a general, linearly constrained (LC) recursive least squares (RLS) array-beamforming algorithm, based on an inverse QR decomposition, is developed for suppressing the moving jammers, efficiently. In fact, by using the inverse QR decomposition-recursive least squares (QRD-RLS) algorithm approach, the lease-squares (LS) weight vector can be computed without back substitution and is suitable to be implemented using the systolic array to achieve fast convergence and good numerical properties. The merits of this new constrained algorithm is verified by evaluating the performance, in terms of the learning curve, to investigate the convergence property and numerical efficiency, and the output signal to interference and noise ratio. We show that our proposed algorithm outperforms the conventional linearly constrained LMS (LCLMS) algorithm, and the one using the fast linear constrained RLS algorithm and its modified version.