This paper deals with the problem of grid map merging in multi-robot SLAM (simultaneous positioning and mapping) where the initial relative pose between robots is unknown. When robots encounter each other, it is easy to obtain a map transformation between robots for grid map merging if bilateral observation measurements are available between robots. However, since the bilateral observation measurements are obtained by encounters between robots, they may limit the availability of using multi-robot systems. To overcome the limitation, spectra-based map merging can be applied without any observation measurements between robots. However, it requires sufficient overlapping areas between indivisual maps of robots, which can also limit the availability of using multi-robot systems. In this paper, therefore, to overcome both limitations, an extension of spectra-based map merging using not bilateral but unilateral observation measurements. The proposed method was tested with datasets obtained from real experiments with mobile robots equipped with a sensor fusion system which can obtain unilateral observation measurements to other robots. Experimental results showed that the proposed map merging method works successfully without any bilateral observation measurements.