Gaussian Process Regression for Improved Underwater Navigation

TL;DR

The paper tackles the difficulty of underwater navigation where GNSS is unavailable and INS drift accumulates errors. It introduces a data-driven multi-output Gaussian process regression (MOGPR) to replace the LS-based DVL velocity estimator, providing both velocity means and covariance for adaptive EKF fusion. Evaluated on real AUV sea-trial data, MOGPR yields around 20% reductions in velocity RMSE and notable improvements in orientation estimates, while enabling an adaptive EKF through uncertainty-aware updates. The study demonstrates the practical value of uncertainty-aware learning for robust navigation in dynamic underwater environments, while also noting computational and data requirements as limitations.

Abstract

Accurate underwater navigation is a challenging task due to the absence of global navigation satellite system signals and the reliance on inertial navigation systems that suffer from drift over time. Doppler velocity logs (DVLs) are typically used to mitigate this drift through velocity measurements, which are commonly estimated using a parameter estimation approach such as least squares (LS). However, LS works under the assumption of ideal conditions and does not account for sensor biases, leading to suboptimal performance. This paper proposes a data-driven alternative based on multi-output Gaussian process regression (MOGPR) to improve DVL velocity estimation. MOGPR provides velocity estimates and associated measurement covariances, enabling an adaptive integration within an error-state Extended Kalman Filter (EKF). We evaluate our proposed approach using real-world AUV data and compare it against LS and a state-of-the-art deep learning model, BeamsNet. Results demonstrate that MOGPR reduces velocity estimation errors by approximately 20% while simultaneously enhancing overall navigation accuracy, particularly in the orientation states. Additionally, the incorporation of uncertainty estimates from MOGPR enables an adaptive EKF framework, improving navigation robustness in dynamic underwater environments.

Figures (5)

• Figure 1: Illustration of a DVL mounted on an AUV, transmitting four acoustic beams to the seabed.
• Figure 2: The block diagram of the proposed approach begins with (a), where the training data is fed into each of the ARD kernels, which are then combined. The hyperparameters within the kernels are optimized by minimizing the negative log-likelihood. Once the optimized parameter vector is obtained, the process moves to (b), where a test point is incorporated to generate the velocity prediction along with its associated covariance. These values are then used within the EKF for state estimation.
• Figure 3: The two, out of the thirteen trajectories taken from cohen2024kit, that were used for testing are trajectory number 12 (a) and trajectory number 13 (b).
• Figure 4: The velocity RMSE for each of the compared approaches as a function of the added bias value is presented. In (a), the results for trajectory 12 are shown, while in (b), the corresponding results for trajectory 13 are displayed.
• Figure 5: The standard deviation values for each of the compared approaches are presented as a function of time. For LS, it is 0.02 [m/s], as specified by the sensor manufacturer. For BeamsNet, the value was determined through trial and error, while for MOGPR, it was derived from its equations. In (a), the results for trajectory 12 are presented across all axes, and in (b), the corresponding results for trajectory 13 are shown.