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This paper considers statistical detection theory for a system of two geographically distributed sensors. The performance of the two main fusion rules (OR and AND) is evaluated in the absence and presence of position errors in the observations, by means of receiver operating characteristics (ROC) curves. The analysis is restricted to three distributions that are representative of a Rician: Rayleigh, one-dominant-plus-Rayleigh (1D+R), and nonfluctuating signal amplitude. Rice's distribution is considered to be relevant for sonar and radar applications. In the absence of position errors, the performance is derived theoretically. It is shown that the best fusion rule depends on the assumed signal amplitude distribution and on the signal-to-noise ratio (SNR). Under operational conditions, position inaccuracies of the multiple observations are of main importance, raising association problems. In this case, the ROC curves are evaluated by means of simulations. It is found that position errors degrade detection performance by 3-6 dB if the AND fusion is used, whereas OR fusion is hardly affected.