A process for determining an attitude measurement of a spacecraft is provided. The process employs a Horizon-Crossing Indicator (HCI) sensor 108. The process uses three time tagged crossings of the earth circle 104 to provide sufficient HCI data to determine the earth center 106. Since these observations may be infrequent, the relative attitude of the spacecraft 100 changes for each observation time. Therefore, once the integrated angular rate data, and thus the attitude relative to some reference, for the first, second and third horizon crossings is obtained, the sensor bore-sight data for each of these observations is transformed back to a known reference time. In one example, the integrated angular rate data from the third and second horizon crossings is transformed back to first horizon crossing time T1. Then, existing techniques can be applied to compute the transformation from the axes of the satellite 100 at the reference time T1 to some other axes at that time, resulting in an attitude estimate for the satellite 100.