Navigation and uncertainty

Navigation for AUV is a major component that has been in continual development. It has been broken down to three types, these being dead reckoning and inertial navigation system (INS), acoustic navigation and geophysical navigation. These different models and methods can then be integrated in different ways to increase the robustness of navigation systems, similar to how multiple methods and measurements are integrated for increased redundancy for traditional  positioning. Given the dynamic nature of positioning for navigation, models are developed with computing algorithms to generate a prediction for the vessel’s position.

Dead reckoning is where with the knowledge of velocity and direction, the new position of the vessel can be deduced from its original position. This will require vessel speed sensors as well as water current velocity information and compass. Hence, ADCP, DVL and IMU are used as part of this method. Errors in this method are cumulative and significant drift can happen over a period of time.

Acoustic navigation are LBL and USBL systems where errors can mainly arise from the assumed beacon geometry and their positions and also from the assumed sound speed profiles which will affect the distance measurements derived from the pings received from the beacons.

Paull, Saeedi, Seto, Li 2014. USBL, LBL systems

Geophysical navigation is identifying features from the sensor data and matching to bottom features in an available initial map or model of the area. 3D forward scanning would be used for these sensors. Therefore, the challenge is in obtaining an accurate and valid initial map as well as having appropriate environmental features. This leads onto algorithms used to match parameters from sensor data and SLAM algorithms.

A combination of these are used for AUVs, some as additional aids. Dead reckoning and INS are more suited to short lines or survey paths with more turns as errors are cumulative relative to the body. Surfacing can give the vessel a fixed position to correct errors or when in deeper conditions LBL and USBL can provide aids. Vertical uncertainty can increase in depth as measurements depend on the climatology model for average temperature as well as a model for water density.

Integrating the different methods and their errors requires uncertainty modelling. Commonly, a Kalman filter is applied which is used for prediction states that was developed in 1960. This algorithm is applied using recursive equations on time updates and measurement updates to have covariances converge or be reduced to an appropriate tolerance. This applied in real-time will only use historical data. Post processing can be done for better results, mostly for vertical uncertainty. There are variations of the algorithm, such as the extended kalman filter, which is used in many SLAM systems. There are other techniques for state estimation including the particle filter which is a stochastic method with random sampling.

Welch,Bishop 1995. Operation of Kalman filter

The Centre for Coastal and Ocean Mapping with the University of New Hampshire has done AUV uncertainty modelling using NOAA vessels. Also, NTNU have published work on particle filters for robust navigation.

Further reading:
Welch, G., & Bishop, G. (1995). An introduction to the Kalman filter.

Leonard, J. J., Bennett, A. A., Smith, C. M., Jacob, H., & Feder, S. (1998). Autonomous Underwater Vehicle Navigation. In MIT Marine Robotics Laboratory Technical Memorandum.

J. S. Byrne and Schmidt, V. E., “Uncertainty Modeling for AUV Acquired Bathymetry”, U.S. Hydrographic Conference (US HYDRO). Gaylord Hotel, National Harbor, Maryland U.S.A., 2015.

Zhao, B., Skjetne, R., Blanke, M., & Dukan, F. (2014). Particle filter for fault diagnosis and robust navigation of underwater robot. IEEE Transactions on Control Systems Technology, 22(6), 2399-2407.

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