Time-domain model identification based on reduced output data

System identification based on incomplete measurements has extensively been studied in recent years. In this paper, the difference between state space models identified based on single-output and multi-output data is studied. The purpose is to investigate the relation between a typical output signal and other input-output signals in observable systems. We investigate to what extent a multidimensional system can be modeled by exploiting single-output measurements. The subspace system identification framework is utilized to compare the time-domain models identified based on a single-output and multi-output data set. It is demonstrated that by manipulating some particular row space of measured outputs, it is possible to achieve predictions of unmeasured outputs. The notion is mathematically developed and verified by several numerical and experimental tests. The idea can be generalized for every time-domain identification technique and input type, specially in dealing with incomplete measurements. The consequence is useful for reducing the number of measuring instruments in experimental test of multi-dimensional systems.