We propose a novel algorithm for motion estimation with k-space navigators. The algorithm operates on the complex k-space navigator signal. It uses a linear signal model, which describes how the navigator signal changes under rotation and translation of the imaged object. Rotation and translation are estimated simultaneously by means of linear least-squares parameter fitting using the linear model. We show that the algorithm achieves high accuracy and precision through a phantom experiment with a motionless phantom. Furthermore, we show the algorithms's applicability in-vivo during a volunteer experiment with and without intentional head motion.