Public transit (PT) is a challenging service to provide, as it is often subsidized and planned to serve a varying demand via fixed supply network and timetable. One critical factor is the need of spatio-temporal demand data, but, increasing use of smart card (SC) fare collection systems has provided big data for free, and become a major PT data source and enabled deep analyses of PT-based mobility helps local authorities to manage PT operations. As SC data for bus PT systems mostly records transaction location with coordinates rather than the boarding stop (BS), there is a need to associate the coordinates with the boarding stop, which is the aim of this paper. To overcome with this issue, two different algorithms were developed as i) ground truth algorithm and ii) spatial temporal stop assignment algorithm supported by kinematic models which are the scope of this paper. As there was no shift or trip information in SC data, in the first algorithm, shift and trips were determined for each bus lines which were later used to assign transactions to BS. In the second algorithm, the speeds of vehicles were calculated using GPS data, and SC transactions were assigned to the stops spatially and temporally. One of the major problems faced during the BS determination was the precision/scattering of GPS points showing the location of transaction. Thus, the conditions of the assignment results were grouped as i) on stop and ii) en-route (while vehicle moving between stations) and iii) not assigned. For the application of these algorithms, one-month SC data of Konya City (Turkey) with 4.9 million boarding transactions was used as an example. The statistics on BS assignment by two algorithms were presented and their performance in terms of running times were compared. Besides the general limitations and problems in the assignment procedures were discussed in detail.