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In this paper, we study a frequency-modulated continuous-wave based radio-frequency identification system, which is composed of a reader with single transmitter and multiple receiving antennas as well as multiple active backscatter tags. In particular, our contribution is twofold in this paper. First, we construct a general architecture for achieving the functionality of wireless positioning based on the principle of the switched injection-locked oscillator (SILO). Unlike the previous SILO-based schemes, some limitations on the pulsed waveform generated by the tags are overcome. In addition, only one reader set up with multiple receiving antennas is used to precisely localize tags based on the delay and direction-of-arrival estimates. Second, the developed algorithms make use of a shift invariant property among the baseband signal snapshots of intra- and/or intermodulation intervals, i.e., snapshots in one modulation period and/or sets of snapshots in multiple modulation periods. A new joint singular value decomposition based ESPRIT algorithm is developed for determining the number of multiple active tags and their positions by implementing the matrix reconstruction and stacking techniques. The proposed method has its basic foundation on the processing of received data with global fusion scheme. In this way, this method can improve the performance of parameter estimates in terms of accuracy and resolution without suffering from the pair matching problem. System simulations and experimental validations are carried out to verify the proposed system architecture associated with the signal processing technique. [ABSTRACT FROM AUTHOR]