Leveraging Past DVL Velocity Measurements for Acceleration-Aided AUV Navigation

Autonomous underwater vehicles (AUVs) rely on fusing Inertial Navigation System (INS) data with Doppler Velocity Log (DVL) measurements to maintain accurate navigation solutions, and this paper proposes enhancing this fusion by incorporating DVL-based acceleration measurements derived from past velocity data. This method is significant because it aims to increase system accuracy and improve convergence speed, especially in situations where DVL beam availability is partial or incomplete.

The gist

The proposed method calculates the AUV acceleration vector based on past DVL measurements and uses it as an additional update to increase the system’s accuracy, which exhibits rapid convergence and significantly improves overall performance compared to baseline INS/DVL fusion approaches.

How it works: DVL Velocity Vector Extraction

The process begins with extracting the DVL velocity vector from beam velocity measurements. The relationship between received frequency and transmitted frequency is defined by Equation (1):

fr = f t / (1 ± vbeam / c)

Under the assumption that the AUV’s speed is less than the speed of sound, this simplifies to approximating the frequency shift as:

∆f ≈ 2f t vbeam / c (Equation 2)

The beam velocity can then be defined as:

vbeam ≈ c squared f t ∆f (Equation 3)

The direction of each beam in the DVL’s body frame is geometrically determined by the yaw angle ψ˙ı and a fixed pitch angle α, expressed by Equation (4). The relation between the DVL velocity in the body frame, v b/b, and these beam velocity measurements (y) is modeled using a transformation matrix H:

vbeam = Hv b/b (Equation 6)

The estimated DVL velocity vector, denoted as v̂ b/b, is obtained using a least squares (LS) estimator:

v̂ b/b = (HTH)−1 HTy (Equation 8). This estimator performs two main operations: filtering the bias and noise, and transforming the beam velocity measurements to estimate the DVL velocity.

How it works: DVL Acceleration Vector Extraction

To address situations of DVL outages, the paper leverages an approximation method based on a Taylor series proposed by Klein and Lipman [16]. The velocity vector v T(t) at time t is obtained through a polynomial approximation of the form:

v T(t) = v T0 + ˙v T0(t − t0) + 1/2 ¨v T0(t − t0) squared + · · · (Equation 11)

The explicit solution for the velocity vector derivatives, V, is derived by substituting the polynomial approximation and an extrapolation function r into the coefficient matrix equation:

V = S [Pm−1 i=0 V T P h,i tiV T h,i... Pm−1 i=0 1/(m−1)!tm−1V T h,i] (Equation 18)

This explicit form is used to calculate the DVL-based acceleration vector (a˜d), which is then introduced into the navigation filter as an external measurement. The derived acceleration update measurement model for the filter residual is given by:

δz = a˜b − R bd · a˜d (Equation 40)

How it works: INS/DVL Fusion and Error State Estimation

The INS equations of motion are expressed in the north-eastdown (NED) coordinates, forming the nonlinear system dynamics of the filter. A 12 error-state vector δx ∈ R12 is defined to capture velocity errors, misalignment errors, and sensor bias residual errors:

δx = [δvn ϕ n ba bg T] (Equation 26)

The linearized error state dynamic model for the INS is given by:

δx˙ = Fδx + Gw (Equation 27)

The Kalman filter operates in two phases: Prediction and Update. The baseline INS/DVL fusion uses only DVL velocity measurements, where the measurement residual is defined as δz = vˆ n − v˜ n DVL (Equation 36).

As a fastidious researcher, I have analyzed the provided paper, INS/DVL Fusion with DVL Based Acceleration Measurements, and identified specific, high-impact improvements that can be implemented in AI systems for Autonomous Underwater Vehicles (AUVs) and related navigation platforms.

Here are the specific improvements and what the improved AI system can do:

1. 】Implementation of a DVL-Based Acceleration Prediction Module within an Error-State Extended Kalman Filter (ES-EKF):

2. 】The core improvement is integrating an analytical acceleration model derived from past DVL velocity measurements (Equations 21–23) directly into the measurement update step of the navigation filter. This transforms the filter from a standard INS/DVL fusion system into an INS/DVL Fusion with DVL-Based Acceleration Measurements system.

3. 】The proposed AI can now estimate and correct accelerometer errors (bias) by leveraging past velocity data, even during periods of partial or complete DVL beam outages. This directly addresses the primary weakness of standard INS/DVL fusion—the drift caused by unmodeled sensor errors.

4. 】Enhanced Robustness to Sensor Outages:

5. 】The system gains a significant advantage in partial or incomplete beam availability. When DVL beams are unavailable (e.g., during extreme maneuvers or passing over trenches), the AI can still provide an estimate of the acceleration vector, allowing the navigation solution to remain bounded and accurate, unlike baseline systems that would suffer from rapid divergence.

6. 】Improved Long-Term Accuracy via Bias Correction:

7. 】By treating accelerometer bias as a state variable and using this new acceleration update measurement, the filter can converge on much more accurate long-term estimates of sensor biases (e.g., the z-axis accelerometer bias improved by 53% in sea tests). This leads to significantly better navigation solutions over extended missions.

8. 】Faster Convergence Rates:

9. 】The system exhibits a dramatically faster convergence rate for error states compared to the baseline approach (up to 57% improvement in convergence time for straight-line trajectories). For dynamic maneuvers (like the figure-of-eight), this improvement is even more pronounced (up to 54% improvement), meaning the AUV can reach a high level of accuracy much sooner.

10. 】Superior Performance in Dynamic Environments:

11.】The improved estimation of orientation and leveling angles during highly dynamic motion (e.g., the eight-figure trajectory) demonstrates that the system can better handle complex rotational dynamics, leading to higher precision in mapping and inspection tasks where precise attitude knowledge is critical.

12. 】Enabling Lower-Grade Sensor Utilization:

13.】The overall performance enhancement suggests that this method allows for the reliable operation of lower-grade sensors or less expensive IMUs by compensating for their inherent errors more effectively, leading to the development of simpler, low-cost navigation systems suitable for micro/small platforms.

This improved AI system can perform:

1. Accurate, drift-free navigation in complex underwater environments (oceanographic surveys, mapping).

2. Reliable operation during periods of DVL signal loss or beam blockage (e.g., navigating near structures or complex terrain).

3. High-precision localization and attitude estimation for critical tasks like subsea inspection and autonomous underwater construction, achieving accuracy levels that surpass standard INS/DVL fusion systems by substantial margins (up to 50% improvement in bias error).