For underwater acoustic systems, new space-time signal processing (STSP) algorithms have been developed and researched. They realize the maximum likelihood STSP in complex conditions. These algorithms take into consideration a complicated antenna's motion in space, the particularities of the additive noise, and the properties of the medium together. It was assumed that the antenna moved in three dimensions with variable velocity and angle rotations, the noise was multicomponent Gaussian space-time correlated, and the medium was inhomogeneous. The algorithms were obtained for two types of signals: partially coherent and stochastic ones. The signal-to-noise ratio was calculated and compared for different systems and work conditions. Optimum, some near optimum, and nonoptimum STSP systems were studied. As a result of research it was found that ignoring the fact of the antenna's motion and the local noise component, often led to a significant loss in noise immunity of STSP systems. In some cases, a complicated antenna's motion plays a positive role and assists in the rising of noise immunity. This effect may be used in different systems, in particular, in the systems with towed arrays for alienating ambiguity in estimation of signal direction.