A Variable Step-size Mixed Modulated Lagrange Explicit Time Delay Estimation Algorithm

Time delay estimation of passive sonar plays a crucial role in target range and target azimuth. The accurate time delay estimation algorithm with non-integer sampling period, which is also called fractional time delay, has attracted much attention. To estimate the fractional time delay of bandlimited signals, the mixed modulated Lagrange explicit time delay estimator is put forward, and it acts well. It is a fixed step-size algorithm, which means it cannot procure fast convergence rate and simultaneously give out small steady-state error. In this paper, a variable step-size algorithm based on the iteration time is proposed for mixed modulated Lagrange explicit time delay estimator. Simulation results demonstrate that, for bandlimited BPSK signals, the proposed algorithm can yield faster convergence speed at early stage and smaller time delay estimation variance in its steady state than the fixed step-size one.