A method of space–time array processing is introduced that is based on the model-based approach. The signal and measurement systems are placed into state-space form, thereby allowing the unknown parameters of the model, such as signal bearings, to be estimated by an extended Kalman filter. A major advantage of the model-based approach is that there is no inherent limitation to the degree of sophistication of the models used, and therefore it can deal with other than plane-wave models, such as cylindrically or spherically spreading propagation models, as well as more sophisticated representations such as the normal mode and the parabolic equation propagation models. Since the processor treats the parameters of interest as unknown parameters to be estimated, there is no explicit beamformer structure, and therefore no accuracy limitations such as fixed beam bin sizes and predetermined number of preformed beams. After a theoretical exposition of the underlying theory, the performance of the processor is evaluated with synthesized data sets. The results indicate that the method is a highly effective approach that is capable of significantly outperforming conventional array processors.