An unbiased explicit adaptive gain and time-delay estimation algorithm

An unbiased explicit adaptive gain and time-delay estimation algorithm is presented. An earlier algorithm for explicit estimation of gain and time-delay proposed in is known to yield a biased estimate of the gain. By observing that the bias is due to the dependence of the power of the noise component of the error on the estimated gain, a normalization is introduced which ensures that the power of the noise component is not affected by the gain estimate. By using a stochastic averaging approach to analyze the convergence of the adaptive algorithm, it is shown that the modified algorithm is unbiased. Simulations are presented which confirm the theoretical analysis.