Objective  The velocity output of an electromagnetic log (EML) is actually a velocity relative to the water. The current velocity will affect the velocity output of an EML in marine applications. If a ring laser gyroscope inertial navigation system (RLG-INS) is integrated with an EML to construct an integrated navigation system, the current velocity will produce negative effects on the calculation of calibration parameters, which thus leads to a degraded navigation performance in the following navigation process. In order to reduce the current velocity's effect on the calibration of a RLG-INS/EML integrated navigation system and improve the calibration accuracy of the relevant parameters, a calibration method of considering the current velocity effect is introduced.

  Methods  Based on the integrated navigation principle, the current velocity can be augmented as an extra state in the calibration Kalman filter, while the GNSS position and velocity outputs are implemented as the Kalman filter's measurements to estimate these calibration parameters. The proposed method is beneficial in improving the calibration accuracy while estimating the current velocity concurrently. In such a case, the states estimated in the Kalman filter include attitude error, velocity error in eastern, northern and up directions, position error (longitude, latitude and height), gyroscope biases (three directions), accelerometer biases (three directions), installation error, scale factor error and current velocity in eastern and northern directions. Based on the calibration function, the effects of the current velocity on the EML scale factor and installation error are analyzed, which also reveals the coupling relationship among different calibration parameters. It is indicated that the attitude error related terms can be eliminated from the calibration equation especially when the attitude error is very large at the beginning of the navigation Kalman filter, which may cause a negative effect on the parameter estimation. An analysis of the current velocity's observability is also conducted, which is helpful in determining a proper calibration path to estimate the relevant states. Based on this observability analysis, a turn can help speed up the current velocity convergence. Therefore, it is suggested that some turns should be conducted during the calibration process.

  Results and Discussions   The proposed method is further examined through the simulation and experiment. In the simulation, due to the absence of the EML, the EML velocity output is generated by converting the GNSS velocity in the navigation frame to the EML frame based on a real ship trajectory (Fig.2), while some errors such as scale factor error and installation error are also added to the generated simulation data. The simulation result indicates that the calibration parameters' residues can be reduced to a very small quantity after three iterations (Fig.3-8), if there are several turns in the trajectory. In the experiment, an EML and an INS are mounted together in a ship. The total experiment period is about 9.4 h, while the first 2.4 h are utilized to calibrate these parameters (Fig.9). All the parameters can be well estimated after 3 iterations and several turns, which verifies the effectiveness of the proposed method (Fig.10-12). The whole experiment period is used to examine the correctness of the calibration parameters. Compared with the result without calibration, the navigation performance can be greatly improved with the proposed calibration method (Fig.13). The maximum position drift is much smaller than the case without calibration.

  Conclusion  The calibration of RLG-INS/EML integrated navigation system is very important in maintaining the navigation performance. Due to the effect of the current velocity, the calibration parameters will be polluted by this extra velocity. In this manuscript, a calibration method of considering the current velocity effect in proposed. The current velocity is augmented as an extra state in the calibration Kalman filter. The coupling relationship among different parameters is analyzed in theory, while a calibration strategy of improving the observability is also introduced. The simulation and experiment results verify the effectiveness of the proposed method. The proposed method can simplify the calibration process, which has potential in improving the calibration efficiency while maintaining the calibration accuracy.