Extended Object Tracking (EOT) is a useful technique for achieving situational awareness in autonomous vehicle systems. The EOT problem is to both estimate the kinematics and dimensions of an object based on high-resolution measurements. In the case of laser measurements or other types of measurements that correspond to points on the object's boundary, the true measurement model of the EOT problem is based on an implicit equation for the measurement coordinates. This intrinsic implicity is often not addressed directly in several EOT models found in the literature. In this paper, the EOT problem is reformulated as a least square minimization problem without compromising the original implicit measurement model by introducing an extra variable for each measurement. In addition, this new least squares formulation allows considering measurements and state variables for a whole time window, and not just a single time step. An EOT algorithm based on solving the derived least squares minimization problem is proposed and tested with simulated scenarios.