APPLICATION OF THE NEWTON METHOD TO IMPROVE THE ACCURACY OF TOA ESTIMATION WITH THE BEAMFORMING ALGORITHM AND THE MUSIC ALGORITHM

In this paper, a numerical method for improving the performance of the beamforming algorithm and the MUSIC algorithm for TOA (Time-of-Arrival) estimation is presented. It has been shown that the conventional beamforming algorithm and the MUSIC algorithm can be used for time delay estimation. Using the beamforming algorithm and the MUSIC algorithm for TOA estimation, the initial estimate for the TOA is obtained. To improve the accuracy of the TOA estimation, we apply the Newton iteration to the initial estimate. The initial estimates obtained from the beamforming algorithm and the MUSIC algorithm are updated to obtain the final estimates which are more accurate than the initial estimates in terms of the RMSE (Root Mean Square Error). To find the TOA which maximizes the beamforming spectrum or the MUSIC spectrum, we find the TOA at which the derivative of the beamforming spectrum with respect to the delay is zero. To find numerically the TOA at which the derivative of the beamforming spectrum or the MUSIC spectrum is zero, the Newton iteration is adopted. In numerical results, the validity of the proposed scheme is illustrated using various examples.