The ESA starmapper is an optical-electronic instrument with an array of photo-sensitive slits, to "be strapped down to spinning spacecraft. Recorded times of passage of known stars over these slits, together with mathematical models for spacecraft dynamics and starmapper instrument, provide the basis for recursive estimation of the spacecraft attitude. The estimator is robust with respect to numerical errors as well as modelling errors. It is found advantageous to treat certain parameters as consider parameters. In the case of small nutation angles, attitude estimates can be obtained with an accuracy of about one arcminute. Degradation in accuracy occurs for larger nutation angles.