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The paper deals with optimisation of splittable resources aimed at the detection of a moving target, following a Markovian movement or a conditionally deterministic motion. Our work extends S.S. Brown's (1980) spatial optimisation method. By use of a generalised linear formalism, we developed a method for optimizing both spatially and temporally (modeling resource renew), with management of multiple resource types or multi-mode resources. Such optimisation also involves the fusion of several detection tools, in order to make them work together efficiently.