A new method for joint time delay and Doppler shift estimation based on the fractional lower-order cyclic cross ambiguity function (FCCA) and multi-cycle frequencies is proposed.The relationship among fractional lower-order cyclic correlation

second-order cyclic correlation and pth-order cyclic correlation is analyzed.By using fractional lower-order cyclic statistics and exploiting cyclostationarity property of more than one cycle frequency

the new algorithm share the signal selectivity and is highly tolerant to SαS noise and interfering signals.The performances of different methods in various environments are tested in simulations.Simulation results indicate that the proposed algorithm outperforms the methods which is based on the conventional cyclic cross ambiguity function (CCA) and pth-order cyclic cross ambiguity function (PCCA) respectively.