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The problem of target motion analysis (TMA) has been the subject of an important literature. However, present methods use data estimated by a short time analysis (azimuths, Dopplers, etc.). For far sources, the nonstationarities of the array processing outputs, induced by the sources motion, may be simply modeled. This model leads one to consider directly a spatio-temporal TMA. Then new (spatio-temporal) data can be estimated. These estimates correspond to a long time analysis. Further, note that they are estimated independently of the (classical) bearings. In this general framework, the concept of source trajectory replaces the classical instantaneous bearings. Corresponding TMA algorithms are then studied. Then the study of statistical performance is carefully studied.