This paper presents a simple linear operator that ac- curately estimates the position and parameters of ellipse features. Based on the dual conic model, the operator avoids the intermediate stage of precisely extracting indi- vidual edge points by exploiting directly the raw gradient information in the neighborhood of an ellipse?s boundary. Moreover, under the dual representation, the dual conic can easily be constrained to a dual ellipse when minimizing the algebraic distance. The new operator is assessed and com- pared to other estimation approaches in simulation as well as in real situation experiments and shows better accuracy than the best approaches, including those limited to the cen- ter position.