[Paper Review] Position USBL/DVL Sensor-based Navigation Filter in the presence of Unknown Ocean Currents

M. Luísa Morgado, Pedro Batista+2 more|arXiv (Cornell University)|Aug 26, 2010

Underwater Vehicles and Communication Systems9 references4 citations

TL;DR

This paper proposes a globally asymptotically stable (GAS) position navigation filter for AUVs using direct nonlinear USBL and DVL sensor readings, avoiding planar-wave approximations. By deriving a linear time-varying (LTV) system through state augmentation, it enables stable estimation of transponder position and unknown ocean current velocity, matching EKF performance while guaranteeing convergence to zero error.

ABSTRACT

This paper presents a novel approach to the design of globally asymptotically stable (GAS) position filters for Autonomous Underwater Vehicles (AUVs) based directly on the nonlinear sensor readings of an Ultra-short Baseline (USBL) and a Doppler Velocity Log (DVL). Central to the proposed solution is the derivation of a linear time-varying (LTV) system that fully captures the dynamics of the nonlinear system, allowing for the use of powerful linear system analysis and filtering design tools that yield GAS filter error dynamics. Simulation results reveal that the proposed filter is able to achieve the same level of performance of more traditional solutions, such as the Extended Kalman Filter (EKF), while providing, at the same time, GAS guarantees, which are absent for the EKF.

Motivation & Objective

• Address the lack of global asymptotic stability (GAS) in traditional AUV navigation filters like the EKF and planar-wave-based Kalman filters.
• Develop a navigation filter that directly uses nonlinear USBL range and RDOA measurements without approximations.
• Ensure stable convergence of position and current velocity estimation errors to zero despite unknown ocean currents and sensor noise.
• Enable accurate transponder position estimation for precision tasks like docking, even at close range.
• Extend prior work on single-range estimation to multi-receiver USBL arrays without motion excitation constraints.

Proposed method

• Formulate a nonlinear system model for AUV navigation using USBL range and RDOA measurements and DVL velocity readings.
• Derive a linear time-varying (LTV) system through state augmentation that exactly captures the nonlinear dynamics.
• Use the LTV model to design a Kalman filter with globally asymptotically stable error dynamics.
• Avoid linearization of range and RDOA measurements by embedding them directly in the filter structure.
• Incorporate unknown ocean current as an augmented state to estimate its bias on DVL readings.
• Use realistic sensor noise models for DVL (0.2% + 1 mm/s), rate gyros (0.05 deg/s), and USBL (1 m range, 6 mm RDOA accuracy).

Experimental results

Research questions

• RQ1 Can a navigation filter be designed that guarantees global asymptotic stability (GAS) for AUV position estimation using nonlinear USBL and DVL measurements?
• RQ2 Does avoiding the planar-wave approximation for USBL RDOA measurements lead to improved error convergence, especially at close range?
• RQ3 Can a linear time-varying (LTV) system be derived to fully represent the nonlinear dynamics of the USBL/DVL navigation problem?
• RQ4 How does the performance of the proposed LTV Kalman filter compare to the EKF and planar-wave-based Kalman filter in terms of steady-state error?
• RQ5 Is the proposed filter robust to realistic sensor noise and unknown ocean currents while maintaining GAS error dynamics?

Key findings

• The proposed LTV Kalman filter achieves steady-state position error RMS of 0.0880 m (x), 0.0837 m (y), and 0.1101 m (z), matching the performance of the EKF and KFPW.
• The EKF shows slightly lower x-axis error (0.0611 m) but lacks global asymptotic stability guarantees.
• The planar-wave-based Kalman filter (KFPW) has higher x-axis error (0.1122 m) and does not converge to zero error due to approximation-induced bias.
• All filters achieve similar steady-state performance, but only the proposed LTV filter guarantees global asymptotic stability.
• The initial convergence of the LTV filter is smooth and rapid, with position and current error converging to zero over time as shown in Figures 3 and 4.
• The filter maintains stable error dynamics without requiring persistent excitation or motion constraints, unlike prior single-range methods.