In this paper, the kinematic model of a quadruped robot is derived. The model is equivalent to that of a parallel manipulator, in that each leg can be seen as a manipulator. However, the model is extended to consider that in one gait cycle some legs are in contact with the ground and others are not. In order to obtain the inverse kinematics model, this paper presents as contribution the use of the extended Kalman filter as optimizer in two different situations of the leg motion: unconstrained case, for the swing leg(s), and constrained case, for the leg(s) in contact with the ground. This method was evaluated for locomotion in plain and inclined surfaces. 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