Based on the multipath structure of shallow water ray acoustics, a new robust high-precision motion parameter estimation method using single hydrophone was proposed. Aiming at uniform linear motion target, colligating multipath delay difference and kinematic geometric relation, we have constructed a tridimensional multipath delay model. Then nonlinear time map can be obtained from motion parameters to delay difference, and the cepstrum expression of typical underwater acoustic channel can be studied. The delay difference is extracted from it, and the extraction strategy is put forward. Differential evolution algorithm is used to estimate motion parameters, and the robustness can be improved. Theoretical and simulation results show that the time resolution of cepstrum is not restricted by the bandwidth of signals, which depends mainly on the type of signals and the signal to noise ratio. The cepstrum of CW is not sensitive to Doppler effect. The precision of parameter estimation depends mainly on the accuracy of time delay estimation and the amount of information attached to the differential evolution algorithm. When the information includes recent data points, parameter estimation can be better. Pool test results further verify the correctness and validity of this method.