The wavelet based wideband cross ambiguity function can be used for joint time delay and Doppler stretch estimation.But it cannot suppress the effect due to correlated Gaussian noises.A definition of fourth-order wavelant is given by combining the wavelet and the higher-order cumulant.And a higher-order wavelant based wideband cross ambiguity function algorithm is presented based on the definition.This method can overcome the fault of the traditional algorithm and can be used in unknown correlated Gaussian noise environment.The simulation results are presented to demonstrate the effectiveness of this novel approach.