In this paper, a new adaptive constrained LMS time delay estimation (TDE) algorithm is devised. It is known that in the TDE problem, the time differences between relevant sensors can be modeled as a finite impulse response (FIR) filter whose weight coefficients are samples of a sinc function. Moreover, in case of non-integer TDE, the performance of estimation result is highly dependent upon the convergence rate of weight coefficients of the FIR filter. To speed up the convergence rate of the weight coefficients, in this paper, we propose a new constrained LMS TDE algorithm by making use of the constraint that the sum of the squares of the weight coefficients of the FIR filter equals unity. Here, we show that the constrained optimum solution is identical to the true weights solution which is the error free optimum solution. Also, to document the advantage of the proposed algorithm, the statistical analysis of the steady-state weight-error vector as well as the mean square error of the estimator, using the proposed algorithm, are derived. As confirmed by the theoretical and simulation results, the new proposed algorithm for non-integer TDE outperform the conventional LMS TDE algorithm.
