The tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion. In this study, we examine whether a simplified linear model of these neurons can be used to esti- mate self-motion from the optic flow. We present a theory for the con- struction of an estimator consisting of a linear combination of optic flow vectors that incorporates prior knowledge both about the distance distri- bution of the environment, and about the noise and self-motion statistics of the sensor. The estimator is tested on a gantry carrying an omnidirec- tional vision sensor. The experiments show that the proposed approach leads to accurate and robust estimates of rotation rates, whereas transla- tion estimates turn out to be less reliable.