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In this paper, application potentiality and the difficulties of geometric positioning in Earth-centered Earth-fixed coordinate systems (ECEF) with airborne optical images are analyzed. A rigorous sensor model, which is based on initialization quaternion attitudes and refinement Euler bias angles, is presented. Compared to those models only with quaternion parameters, the proposed model can avoid the difficulties in the decorrelation of attitude parameters, in the refinement model for irregular changing attitudes, and in combined adjustment with attitude angles and other observed values. While comparable to those other models only in the Euler parameters, our model overcomes the problem of multiple solutions and possible singularity. The proposed model exploits existing mature methods found in traditional POS-supported bundle block adjustment to realize rigorous positioning in ECEF with airborne optical images. Tests using frame and three line sensor (TLS) images show that our model is effective and is not restricted by the range of image coverage. It can provide a reference for multiple image positioning including airborne optical images. [ABSTRACT FROM AUTHOR]