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When the size of targets is comparable to the range resolution of monopulse radars, these targets should be considered as extended rather than point targets. If several closely-spaced targets fall within the same radar beam and between adjacent matched filter samples in range, the full monopulse information from all of these samples can and should be used to resolve these targets, i.e., estimate the number of targets and their respective angles-of-arrival and ranges. To detect and localize multiple unresolved extended targets, we establish a model for monopulse radar returns from extended objects, and present a maximum likelihood estimator (MLE) to localize the targets. Rissanen's minimum description length (MDL) criterion will be used to decide the number of existing extended objects. We also derive the upper limit on the number of targets and their scattering centers that can be resolved, and we provide necessary conditions for these targets to be uniquely identified. We compare the new extended target monopulse processing scheme with previously developed point-target monopulse techniques in the simulations.