A surgical system for performing minimally invasive surgery through an aperture of a patient, the system comprising: a manipulator assembly including a surgical tool, the manipulator assembly having a plurality of joints and first degrees of freedom, the manipulator assembly being operable to position the surgical tool at the aperture of the patient; a tool position measuring device operable to measure a position of the surgical tool for each of second degrees of freedom of the surgical tool and to determine position measurements corresponding to the second degrees of freedom; and a controller operable to perform operations including: estimating a position of each joint of the plurality of joints, wherein estimating the position of each joint of the plurality of joints includes applying the position measurements to a kinematic model of the manipulator assembly, the kinematic model having third degrees of freedom, the third degrees of freedom including a corresponding degree of freedom for each of the first degrees of freedom and further including at least one specific degree of freedom that is missing from the first degrees of freedom, the application of the position measurements to the kinematic model including a forward-kinematic simulation of each of the third degrees of freedom, and the estimating of the position of each joint of the plurality of joints including a discarding of values for the at least one specific degree of freedom from a result of the forward-kinematic simulation; and controlling the manipulator assembly based on the estimated positions of the plurality of joints. a manipulator assembly including a surgical tool, the manipulator assembly having a plurality of joints and first degrees of freedom, the manipulator assembly being operable to position the surgical tool at the aperture of the patient; a tool position measuring device operable to measure a position of the surgical tool for each of second degrees of freedom of the surgical tool and to determine position measurements corresponding to the second degrees of freedom; and a controller operable to perform operations including: estimating a position of each joint of the plurality of joints, wherein estimating the position of each joint of the plurality of joints includes applying the position measurements to a kinematic model of the manipulator assembly, the kinematic model having third degrees of freedom, the third degrees of freedom including a corresponding degree of freedom for each of the first degrees of freedom and further including at least one specific degree of freedom that is missing from the first degrees of freedom, the application of the position measurements to the kinematic model including a forward-kinematic simulation of each of the third degrees of freedom, and the estimating of the position of each joint of the plurality of joints including a discarding of values for the at least one specific degree of freedom from a result of the forward-kinematic simulation; and controlling the manipulator assembly based on the estimated positions of the plurality of joints. estimating a position of each joint of the plurality of joints, wherein estimating the position of each joint of the plurality of joints includes applying the position measurements to a kinematic model of the manipulator assembly, the kinematic model having third degrees of freedom, the third degrees of freedom including a corresponding degree of freedom for each of the first degrees of freedom and further including at least one specific degree of freedom that is missing from the first degrees of freedom, the application of the position measurements to the kinematic model including a forward-kinematic simulation of each of the third degrees of freedom, and the estimating of the position of each joint of the plurality of joints including a discarding of values for the at least one specific degree of freedom from a result of the forward-kinematic simulation; and controlling the manipulator assembly based on the estimated positions of the plurality of joints.