In most autonomous underwater vehicles (AUVs), the navigation system is based on an inertial navigation system (INS) aided by a Doppler velocity log (DVL). In several INSs, only the velocity vector, provided by the DVL, can be used as input for assistance, thus limiting the integration approach to a loosely coupled one. In situations of partial DVL measurements (such as failure to maintain bottom lock) the DVL cannot provide the AUV velocity vector, and as a result, the navigation solution is based only on the standalone INS solution and will drift in time. To circumvent that problem, the extended loosely coupled (ELC) approach was recently proposed. ELC combines the partial DVL measurements and additional information, such as the pervious navigation solution, to form a calculated velocity measurement to aid the INS. When doing so, the assumption made in the extended Kalman filter (EKF) derivation of zero correlated process and measurement noise covariance does not hold. In this paper, we elaborate the ELC approach by taking into account the cross-covariance matrix of the correlated process (INS) and measurement (Partial DVL) noises. At first, this covariance matrix is evaluated based on the specific assumption used in the ELC approach and then implemented in the EKF algorithm. Using a 6DOF AUV simulation, results show that the proposed methodology improves the performance of the ELC integration approach.