Even sub-millimeter-size debris could cause a fatal damage on a spacecraft. However, such tiny debris cannot be followed up or tracked from the ground. Therefore, Kyushu University has initiated IDEA the project for In-situ Debris Environmental Awareness, which conducts in-situ measurement of sub-millimeter-size debris. One of the project’s objectives is to estimate the location of on-orbit satellite fragmentations from measurements. The previous study derived a constraint equation that applies for the orbital parameters of a broken-up object. The previous study also concluded that two or more measurement satellites are necessary to properly estimate a couple of orbital parameters of the broken-up object in certain special case. This study finds out that even a single measurement satellite can estimate the orbital parameters of the broken-up object. Furthermore, this study derives a new constraint equation that applies for the nodal regression rate of the broken-up object. Finally, this paper demonstrates an effective procedure for a single measurement satellite to estimate the location of on-orbit satellite fragmentations.