pith. sign in

arxiv: 1907.02897 · v1 · pith:LT56RJX3new · submitted 2019-07-05 · 🧮 math.OC

Preliminary Results in Current Profile Estimation and Doppler-aided Navigation for Autonomous Underwater Gliders

Jonathan Jonker , Andrey Shcherbina , Richard Krishfield , Lora Van Uffelen , Aleksandr Aravkin , Sarah E. Webster This is my paper

Pith reviewed 2026-05-25 02:07 UTC · model grok-4.3

classification 🧮 math.OC
keywords autonomous underwater gliderADCPcurrent profile estimationDoppler navigationocean currentsstate-space modeldead reckoningSeaglider
0
0 comments X

The pith

Two post-processing methods using ADCP and hydrodynamic models estimate consistent ocean current profiles and improve AUG positioning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops two related formulations for estimating ocean current profiles from autonomous underwater glider data. One solves an explicit inverse problem for the currents, while the other uses a state-space model to jointly infer glider states and currents. Both rely on ADCP relative velocity measurements and through-the-water velocity estimates from a hydrodynamic model, along with GPS fixes. When applied to 49 days of data from a Seaglider off Alaska, the methods agree and produce current profiles along the trajectory plus over-the-ground velocities for better subsea positioning, validated against moored ADCP in the top 40 meters. This addresses the challenge of navigation when ocean currents are comparable in speed to the glider's progress.

Core claim

Both approaches agree on their estimates of the ocean current profile through which the AUG was flown using measurements of current relative to the AUG from the ADCP, and estimates of the AUGs TTW velocity from a hydrodynamic model. The result is a complete current profile along the AUGs trajectory, as well as over-the-ground (OTG) velocities for the AUG that can be used for more accurate subsea positioning.

What carries the argument

The two formulations: an explicit inverse problem for current profiles only, and a deconvolution problem using a state-space model to infer both states and current profiles.

If this is right

  • Complete current profile along the glider's trajectory is obtained.
  • Over-the-ground velocities enable more accurate subsea positioning.
  • The two independent methods agree, supporting the reliability of the estimates.
  • Results are shown for a 49-day deployment with 1 MHz ADCP data compared to 600 kHz moored ADCP ground truth.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These post-processed velocities could potentially be adapted for real-time navigation corrections if computational demands allow.
  • Similar methods might apply to other buoyancy-driven or low-speed underwater vehicles facing current advection.
  • Extended use could contribute to mapping ocean current variability over larger regions from repeated glider missions.

Load-bearing premise

The hydrodynamic model must supply sufficiently accurate through-the-water velocity estimates that can be subtracted from ADCP relative-velocity measurements to recover absolute current profiles.

What would settle it

A mismatch between the estimated current profiles in the top 40 meters and the independent measurements from the moored upward-facing 600 kHz ADCP would falsify the agreement and accuracy of the methods.

Figures

Figures reproduced from arXiv: 1907.02897 by Aleksandr Aravkin, Andrey Shcherbina, Jonathan Jonker, Lora Van Uffelen, Richard Krishfield, Sarah E. Webster.

Figure 1
Figure 1. Figure 1: Ready for launch, Seagliders SG196 and SG198 are loaded on the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SG196 (green) and SG198 (red) were deployed at the shelf break north [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Zooming in on the upper 100m of the profiles in Figure 4, we use [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the full results from the method of Section III (black [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Updated velocities after processing the ADCP data. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: We compare position estimates from a glider trajectory computed [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

This paper describes the development and experimental results of navigation algorithms for an autonomous underwater glider (AUG) that uses an on-board acoustic Doppler current profiler (ADCP). AUGs are buoyancy-driven autonomous underwater vehicles that use small hydrofoils to make forward progress while profiling vertically. During each dive, which can last up to 6 hours, the Seaglider AUG used in this experiment typically reaches the depth of 1000 m and travels 3-6 km horizontally through the water, relying solely on dead-reckoning. Horizontal through-the-water (TTW) progress of AUG is 20-30 cm/s, which is comparable to the speed of the stronger ocean currents. Underwater navigation of an AUG in the presence of unknown advection therefore presents a considerable challenge. We develop two related formulations for post-processing. Both use ADCP observations, through the water velocity estimates, and GPS fixes to estimate current profiles. However, while the first solves an explicit inverse problem for the current profiles only, the second solves a deconvolution problem that infers both states and current profiles using a state-space model. Both approaches agree on their estimates of the ocean current profile through which the AUG was flown using measurements of current relative to the AUG from the ADCP, and estimates of the AUGs TTW velocity from a hydrodynamic model. The result is a complete current profile along the AUGs trajectory, as well as over-the-ground (OTG) velocities for the AUG that can be used for more accurate subsea positioning. Results are demonstrated using 1 MHz ADCP data collected from a Seaglider AUG deployed for 49 days off the north coast of Alaska during August and September 2017. The results are compared to ground truth data from the top 40 meters of the water column, from a moored, upward-facing 600 kHz ADCP.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper develops two post-processing methods for estimating full-depth ocean current profiles from 1 MHz ADCP data collected on a Seaglider AUG: an explicit inverse problem using ADCP relative-velocity measurements and hydrodynamic-model TTW velocity estimates, and a state-space deconvolution that jointly infers states and currents. Both formulations are shown to agree with each other and with independent moored 600 kHz ADCP ground truth in the upper 40 m; the resulting OTG velocities are proposed for improved subsea positioning. Results are demonstrated on 49 days of data from a 2017 deployment off Alaska reaching 1000 m depth.

Significance. If the hydrodynamic-model TTW estimates prove sufficiently accurate, the work supplies a practical route to absolute current profiles along AUG trajectories and better dead-reckoning corrections, addressing a recognized navigation limitation when TTW speeds (20-30 cm/s) are comparable to ocean currents. The agreement between two independent formulations is a positive internal consistency check.

major comments (1)
  1. [Abstract] Abstract and methods description: both formulations recover absolute currents by subtracting hydrodynamic-model TTW velocities from ADCP relative-velocity measurements. The abstract states that TTW speeds are comparable to ocean currents yet supplies no independent validation, error covariance, or sensitivity analysis for the model. Ground-truth comparison is restricted to the upper 40 m, leaving the assumption untested for the 1000 m profiles that constitute the central claim. If model error exceeds a few cm/s, the recovered currents and OTG velocities will be biased at all depths.
minor comments (2)
  1. [Abstract] The abstract would benefit from quantitative summary statistics (e.g., RMS difference between the two methods or versus the moored ADCP) rather than qualitative statements of agreement.
  2. Notation for TTW velocity, relative velocity, and absolute current should be introduced consistently with symbols and units at first use.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the constructive review. The central concern about lack of independent validation and sensitivity analysis for the hydrodynamic TTW model is addressed below. We propose targeted revisions to improve the manuscript while acknowledging inherent data limitations.

read point-by-point responses

  1. Referee: [Abstract] Abstract and methods description: both formulations recover absolute currents by subtracting hydrodynamic-model TTW velocities from ADCP relative-velocity measurements. The abstract states that TTW speeds are comparable to ocean currents yet supplies no independent validation, error covariance, or sensitivity analysis for the model. Ground-truth comparison is restricted to the upper 40 m, leaving the assumption untested for the 1000 m profiles that constitute the central claim. If model error exceeds a few cm/s, the recovered currents and OTG velocities will be biased at all depths.

    Authors: We agree that the accuracy of the Seaglider hydrodynamic TTW model is a foundational assumption and that the manuscript would benefit from greater transparency on this point. The model is the standard flight dynamics formulation used in the Seaglider community. While no independent deep-water validation exists for this deployment, the two formulations (inverse problem and state-space deconvolution) are mathematically distinct yet produce consistent current profiles, providing an internal cross-check. OTG velocities are further validated against the moored 600 kHz ADCP in the upper 40 m. In revision we will add: (i) a dedicated sensitivity analysis perturbing TTW estimates by representative error levels (e.g., ±3–5 cm/s) and quantifying impact on recovered currents at all depths, (ii) explicit propagation of TTW uncertainty into the reported current error covariances, and (iii) a brief discussion of prior literature bounds on the hydrodynamic model. We cannot, however, supply independent ground truth below 40 m because no such instrumentation was present. revision: partial

standing simulated objections not resolved
  • Independent validation of the TTW hydrodynamic model at depths below 40 m, as no additional deep-water ground-truth sensors were deployed in the 2017 Alaska experiment.

Circularity Check

0 steps flagged

No significant circularity; estimates combine external model outputs with measurements

full rationale

The paper's two formulations estimate current profiles by subtracting TTW velocities (from a pre-existing hydrodynamic model) from ADCP relative-velocity measurements, then incorporating GPS fixes. No quoted step shows a result defined in terms of itself, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The hydrodynamic model is invoked as an external input, not derived here, and the abstract explicitly separates it from the estimation procedures. This is the common case of a self-contained method against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; the central claim rests on the unstated accuracy of the hydrodynamic through-water velocity model and on the assumption that ADCP relative-velocity measurements can be directly combined with surface GPS fixes without additional bias terms.

axioms (1)
  • domain assumption Hydrodynamic model supplies accurate through-the-water velocity estimates
    Invoked to convert ADCP relative velocities into absolute current profiles in both formulations.

pith-pipeline@v0.9.0 · 5897 in / 1414 out tokens · 27743 ms · 2026-05-25T02:07:26.740216+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

  1. [1]

    Surveying a subsea lava flow using the autonomous benthic explorer (abe),

    D. R. Yoerger, A. M. Bradley, B. B. Walden, H. Singh, and R. Bach- meyer, “Surveying a subsea lava flow using the autonomous benthic explorer (abe),” International Journal of Systems Science, vol. 29, no. 10, pp. 1031–1044, 1998

    work page 1998

  2. [2]

    Toward ice-relative navigation of underwater robotic vehicles under moving sea ice: Experimental evaluation in the arctic sea,

    C. J. McFarland, M. V . Jakuba, S. Suman, J. C. Kinsey, and L. L. Whit- comb, “Toward ice-relative navigation of underwater robotic vehicles under moving sea ice: Experimental evaluation in the arctic sea,” in Proc. IEEE Intl. Conf. Robot. Auto. (ICRA) , May 2015, pp. 1527–1534

    work page 2015

  3. [3]

    Deep ocean acoustic Doppler current profiling,

    E. Firing and R. L. Gordon, “Deep ocean acoustic Doppler current profiling,” in Proceedings of the IEEE Fourth Working Conference on Current Measurement, April 1990, pp. 192–201

    work page 1990

  4. [4]

    Deep velocity profiling with self-contained ADCPs,

    J. Fischer and M. Visbeck, “Deep velocity profiling with self-contained ADCPs,” Journal of Atmospheric and Oceanic Technology , vol. 10, no. 5, pp. 764–773, 1993

    work page 1993

  5. [5]

    Deep velocity profiling using lowered acoustic Doppler current profilers: Bottom track and inverse solutions,

    M. Visbeck, “Deep velocity profiling using lowered acoustic Doppler current profilers: Bottom track and inverse solutions,” Journal of Atmo- spheric and Oceanic Technology , vol. 19, no. 5, pp. 794–807, 2002

    work page 2002

  6. [6]

    Water profile navigation with an acoustic doppler current profiler,

    M. Stanway, “Water profile navigation with an acoustic doppler current profiler,” in Proc. IEEE/MTS OCEANS Conf. Exhib. , Sydney, Australia, May 2010, pp. 1–5

    work page 2010

  7. [7]

    Dead reckoning through the water column with an acoustic doppler current profiler: Field experiences,

    M. J. Stanway, “Dead reckoning through the water column with an acoustic doppler current profiler: Field experiences,” in Proc. IEEE/MTS OCEANS Conf. Exhib. , Kona, HI, Sep. 2011, pp. 1–8

    work page 2011

  8. [8]

    Water column current profile aided localisation for autonomous underwater vehicles,

    L. Medagoda, M. V . Jakuba, O. Pizarro, and S. B. Williams, “Water column current profile aided localisation for autonomous underwater vehicles,” in Proc. IEEE/MTS OCEANS Conf. Exhib., Sydney, Australia, May 2010, p. 10 pp

    work page 2010

  9. [9]

    Processing explorer ADCP data collected on Slocum gliders using the LADCP shear method,

    A. M. Thurnherr, D. Symonds, and L. St. Laurent, “Processing explorer ADCP data collected on Slocum gliders using the LADCP shear method,” in 2015 IEEE/OES Eleveth Current, Waves and Turbulence Measurement (CWTM), March 2015, pp. 1–7

    work page 2015

  10. [10]

    Poleward flows in the southern California Current system: Glider observations and numerical simulation,

    R. E. Todd, D. L. Rudnick, M. R. Mazloff, R. E. Davis, and B. D. Cornuelle, “Poleward flows in the southern California Current system: Glider observations and numerical simulation,” Journal of Geophysical Research: Oceans, vol. 116, no. C02026, pp. 2156–2202, 2011

    work page 2011

  11. [11]

    Ab- solute velocity estimates from autonomous underwater gliders equipped with doppler current profilers,

    R. E. Todd, D. L. Rudnick, J. Sherman, W. Owens, and L. George, “Ab- solute velocity estimates from autonomous underwater gliders equipped with doppler current profilers,” J. Atmos. Oceanic Tech. , vol. 34, no. 2, pp. 309–333, 2017

    work page 2017

  12. [12]

    On the coastal-upwelling overturning cell,

    R. E. Davis, “On the coastal-upwelling overturning cell,” J. Marine Res., vol. 68, no. 3-4, pp. 369–385, May 2010

    work page 2010

  13. [13]

    An inequality constrained nonlinear Kalman–Bucy smoother by interior point likelihood maximiza- tion,

    B. M. Bell, J. V . Burke, and G. Pillonetto, “An inequality constrained nonlinear Kalman–Bucy smoother by interior point likelihood maximiza- tion,” Automatica, vol. 45, no. 1, pp. 25–33, 2009

    work page 2009

  14. [14]

    Robust and trend-following stu- dent’s t Kalman smoothers,

    A. Aravkin, J. Burke, and G. Pillonetto, “Robust and trend-following stu- dent’s t Kalman smoothers,”SIAM Journal on Control and Optimization, vol. 52, no. 5, pp. 2891–2916, 2014

    work page 2014

  15. [15]

    Sparse/robust estimation and Kalman smoothing with nonsmooth log-concave densities: Model- ing, computation, and theory,

    A. Y . Aravkin, J. V . Burke, and G. Pillonetto, “Sparse/robust estimation and Kalman smoothing with nonsmooth log-concave densities: Model- ing, computation, and theory,” J. Mach. Learn. Res. , vol. 14, no. 1, pp. 2689–2728, 2013

    work page 2013

  16. [16]

    Gen- eralized Kalman smoothing: Modeling and algorithms,

    A. Aravkin, J. V . Burke, L. Ljung, A. Lozano, and G. Pillonetto, “Gen- eralized Kalman smoothing: Modeling and algorithms,” Automatica, vol. 86, pp. 63–86, 2017

    work page 2017

  17. [17]

    Fast robust methods for singular state-space models,

    J. Jonker, A. Aravkin, J. V . Burke, G. Pillonetto, and S. Webster, “Fast robust methods for singular state-space models,” Automatica, vol. 105, pp. 399–405, 2019

    work page 2019

  18. [18]

    Optimization viewpoint on kalman smoothing with applications to robust and sparse estimation,

    A. Y . Aravkin, J. V . Burke, and G. Pillonetto, “Optimization viewpoint on kalman smoothing with applications to robust and sparse estimation,” in Compressed sensing & sparse filtering. Springer, 2014, pp. 237–280

    work page 2014