Based on high speed moving target robust high-resolution direction of arrival (DOA) estimation problem under low signal-to-noise ratio and a small number of snapshots in the underwater acoustic vector signal processing framework, a novel spatial spectrum model combined with compressive sensing method is proposed. By studying the acoustic vector sensor structure, a generalized temporal filtering method based on sound pressure and particle velocity combined treatment is presented. According to the matrix spatial prefiltering theory, a new spatial filter with stopband constraint and mean square error min-max principle in passband is proposed which is used as vector sonar spatial prefiltering algorithm. Based on the methods above, a novel time-space domain jointly filtering high-resolution DOA estimation algorithm based on compressive sensing is proposed. The mathematical model, physical interpretation, and specific implement are explained in detail. Theoretical analysis and computer simulation results show that the new method has a lower dual-target distinguishing threshold and a higher estimation accuracy in solving the vector sonar high speed moving target robust DOA estimation problem under a small number of snapshots (single snapshot) condition. The higher robustness and better results of the proposed method are verified in the lake experiment.