An experimental evaluation of the proposed navigation system is presented in Section 5, where in particular, the performance of the navigation system both in the river trial and the sea trial is discussed. Finally, conclusions are drawn in Section 6.2.?Navigation Equations ModelThe Autonomous Underwater Vehicle discussed in the paper is equipped with a DVL and an INS consisting of three gyroscopes and three accelerometers. The INS calculates position, velocity and attitude using high frequency data from an Inertial Measurement Unit. Navigation propagation equations are introduced in this section. The estimated states include position, velocity, attitude, biases of the inertial sensors, and biases of DVL. The typical integrated navigation scheme for AUV is shown in Figure 1. INS/DVL integration is employed for autonomous navigation for most of the time in the missions. Once the GNSS signals are available, the current position can be reset.Figure 1.SINS/DVL integrated navigation.2.1. INS/DVL System EquationsThe local level frame North-Up-East (NUE) is chosen as the navigation frame n. b is the INS body frame; i is the Earth-centered inertial (ECI) orthogonal reference frame; e denotes the Earth-centered Earth-fixed (ECEF) orthogonal reference frame. The states of the system model include position Pn, velocity Vn, attitude parameters through the direction cosine matrix Cbn, gyro bias, ��;g accelerometer bias ��a and errors in DVL. The DVL measurement error is mainly caused by the scale factor error k and the misalignment error ��, both of which can be regarded as an constant during the mission. The system equations can then be presented as [25,26]:C�Bbn=Cbn(��nbb��),��nbb=��ibb?��g?Cnb(��ien+��enn)V�Ben=Cbn(fb?��a)?(2��ien+��enn)��Ven+glnP�Bn=Vn���Bg=0���Ba=0(1)where ��nbb is the angular rate of the navigation frame relative to the body frame; ��ibb is the angular rate of the inertial frame relative to the body frame; ��ien=[��iecosL,��iesinL,0] is the Earth’s rotation rate in the navigation frame; L is the geographic latitude; ��ie is the Earth’s rotation rate; ��enn is the angular rate of the navigation frame to the earth frame; fb is the accelerometer measurement; gln is the local level gravitational acceleration expressed in the n-frame.The scale factor error and the misalignments are assumed not to have a known time variation. Thus:�ŨB=0k�B=0(2)2.2. Observation EquationsThe velocity measurements d from DVL in the Doppler instrument frame d can be expressed as follows:V?d=Vd+��Vd+kVd(3)where Vd=[��xd,��yd,��zd]T is the true value of the velocity of DVL, k is the scale factor error, ��Vd presents the Gaussian white noise.Therefore, the observation equation can be expressed as:y=(1+k)CbdCnbVINSn(4)where Cdb is the misalignment matrix between INS and DVL. It is the skew matrix of the misalignments ��.3.?Parameter Calibration AlgorithmThe main advantage of the online calibration method proposed in [24] is that no external sensors are required.