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Benchmarking EMlog Calibration for Autonomous Surface Vehicles

Samuel Cohen-Salmon, Itzik Klein

arXiv:2609.39203v1cs.RO

TL;DR

DVL measurements can become unavailable under operational altitude constraints, while raw EMLog readings require calibration to correct systematic errors. This paper compares four calibration models through two estimation pipelines on real-world MARVEL ASV telemetry. EM3 achieved a 71% EMlog1 RMSE reduction, and the paper reports that high-excitation maneuvers improve calibration generalization over straight-line paths.

  • Problem

    Comparative evidence is limited on how different EMLog error models and estimation approaches perform under dynamic sea conditions and changing calibration trajectories.

    Source: §I · p. 1

  • Method

    The paper evaluates four EMLog error models through least-squares and Kalman-filter estimation pipelines using MARVEL ASV telemetry with two EMLogs and DVL recordings.

    Source: §I · p. 2

  • Results

    71%: EM3 reduced EMlog1 baseline RMSE from 0.576 m/s to 0.167 m/s, while KF-EM3 achieved 0.170 m/s RMSE with 70% improvement.

    Source: D. Results · p. 6, §V · p. 8

  • Takeaways & Limitations

    High-excitation circular and figure-8 maneuvers are structurally necessary to raise the information matrix to full rank, and their calibration parameters generalized better across unseen trajectories.

    Source: D. Results · p. 7, §V · p. 8

    Uniform non-accelerating transits yield a rank-deficient information matrix, confounding steady speed offsets with electronic zero-drift and producing 27% cross-validation error inflation.

    Source: 1) Limitations of straight-line transits · p. 7

Abstract

from arXiv · show

Accurate velocity measurement is a fundamental requirement for autonomous surface and underwater vehicles. Commonly, velocity is provided by a Doppler velocity log (DVL) sensor, yet it becomes unavailable due to operational altitude constraints. In such situations, electromagnetic logs (EMLogs) provide a critically robust alternative for continuous velocity estimation. However, raw EMLog measurements are inherently corrupted by systematic errors, which need to be calibrated prior mission begins. Currently, a benchmarking comparative evaluation of how different calibration models perform under rapidly changing dynamic sea conditions is missing in the literature. To bridge this gap, this paper presents a comparative model-based calibration methodology that evaluates four distinct calibration models using two different estimation pipelines. The proposed framework is rigorously validated on a unique 221 minutes of continuous real-world telemetry collected from the MARVEL surface vehicle during dynamic sea trials. The dataset contains two different EMLogs and DVL recordings. Experimental results demonstrate that the bias and scale error model implemented with the Kalman filter improves the speed estimation by 71%. We also demonstrate that dynamical manoeuvres further improve the accuracy compared to standard straight-line paths, ultimately delivering a validated, real-time online calibration EMLog approach for autonomous surface vehicles.

I. INTRODUCTION

DVLs support precise velocity measurement but can lose bottom-track under altitude constraints, making EMLogs an alternative whose systematic errors require calibration. This paper addresses the lack of common-condition comparisons of EMLog error models and estimation approaches, and introduces least squares as a static-model parameter estimator.

I. INTRODUCTION

  • DVL bottom-track can become unavailable when vehicles operate too far from or too close to the seabed, while EMLogs provide an alternative velocity measurement.EMLogs measure speed-through-water from voltage induced by conductive seawater flowing past hull-mounted electrodes.Source: §I · p. 1
  • Raw EMLog readings contain systematic errors associated with hydrodynamic flow, boundary-layer disturbances, installation angles, and electronic zero-drift, motivating calibration.Proposed approaches range from post-mission matrix algorithms and static bias corrections to recursive alignment filters.Source: §I · p. 1
  • The literature lacks systematic comparisons of EMLog error models and estimation pipelines under dynamic sea conditions, including how maneuver trajectories affect parameter observability.Existing work also offers limited comparison between batch post-processing and recursive estimation.Source: §I · p. 1
  • The paper proposes four EMLog error models and seven estimation models across least-squares and Kalman-filter pipelines, evaluated using 221 minutes of MARVEL ASV telemetry.The telemetry includes two commercial EMLogs and high-precision DVL measurements across five dynamic trajectories.Source: §I · p. 2

A. Least squares formulation

  • Least squares estimates static-model parameters by minimizing the discrepancy between observations and predictions, assuming a non-singular design-matrix normal equation for a unique solution.The formulation uses an observation vector, a design matrix, and a parameter vector.Source: A. Least squares formulation · p. 2

B. Kalman filter

The Kalman filter estimates a dynamic system’s state recursively from noisy measurements using a linear stochastic state-space model. Its recursion alternates between projecting the state and covariance forward and incorporating each new measurement to refine the estimate.

B. Kalman filter

  • The Kalman filter models a dynamic system with a linear stochastic difference equation and estimates its state recursively from noisy measurements.The process noise is modeled as zero-mean multivariate normal with covariance Q, and the measurement noise is independent, zero-mean multivariate normal with covariance R.Source: B. Kalman filter · p. 2
  • In the prediction phase, the filter projects the current state estimate and its error covariance forward using the state transition and process-noise covariance.The resulting estimates are a priori values for the current time step.Source: B. Kalman filter · p. 2
  • In the update phase, the filter uses the new measurement and Kalman gain to refine the state estimate and error covariance.The gain weights the measurement innovation relative to the prior estimate.Source: B. Kalman filter · p. 2

III. PROPOSED APPROACH

The proposed approach models EMLog errors from additive bias and multiplicative scale to a second-order polynomial, then examines when those parameters can be identified. Constant-speed operation makes the information matrix singular, whereas dynamic speed variation can make it full rank and separate scale from bias.

A. Error models

  • EM1 models constant additive bias, while EM2 assumes zero offset and models multiplicative gain error.EM1 bias is associated with electronic zero-drift; EM2's gain error addresses hydrodynamic scaling or incorrect installation angles.Source: A. Error models · p. 3
  • EM3 combines scale and bias as a general linear case that captures hydrodynamic gain errors and electronic or installation offsets.The paper identifies it as a common approximation for marine speed logs.Source: A. Error models · p. 3
  • EM4 extends the linear-affine model to a second-order polynomial for nonlinear hydrodynamic effects, including boundary-layer separation and hull-curvature disturbances.The paper states these effects must be compensated for during EMLog calibration.Source: A. Error models · p. 3

B. Parameter Identifiability Analysis

  • Dynamic speed variation can raise the information matrix to full rank, decoupling scale factor m from zero-drift bias b.Under constant speed, the matrix is singular and rank-deficient; the polynomial formulation also collapses under that condition.Source: B. Parameter Identifiability Analysis · p. 3

C. Methodology

The methodology compares seven calibration variations across least-squares and Kalman-filter estimation. Its least-squares implementations use design matrices and parameter vectors matched to the targeted error profiles.

C. Methodology

  • Seven calibration methodologies combine four least-squares variations and three Kalman-filter variations to compare error representations and estimation frameworks.The variants range from isolated bias or scale disturbances to coupled linear-affine and higher-order hydrodynamic models.Source: C. Methodology · p. 3

1) Least squares calibration:

  • The least-squares variants construct design matrices and parameter vectors for bias-only, scale-only, combined bias-and-scale, and polynomial error profiles.The polynomial design expands the vector to capture nonlinearities.Source: 1) Least squares calibration · p. 3

2) Kalman filter calibration:

The Kalman-filter calibration estimates speed alongside sensor-error parameters using a pseudo-linear operating-point approach. Three state-vector variants model bias, scale, or both, with identity state transitions assuming static or random-walk error states.

2) Kalman filter calibration:

3) Summary:

The paper summarizes seven estimator variations spanning least squares and Kalman filtering, with error models and estimator outputs organized in a common architecture. Its analysis and results section evaluates the framework using MARVEL dynamic-sea-trial data and reports performance across the seven models.

3) Summary:

  • Four error models map to seven parallel estimator variations using least squares and Kalman filtering, with outputs representing calibration parameters and dynamic states.The architecture is shown in Fig. 1.Source: Figure 1 · p. 4, 3) Summary · p. 4

IV. ANALYSIS AND RESULTS

  • The empirical evaluation uses MARVEL ASV dynamic sea-trial data and presents performance results across all seven estimation models.The section also covers the setup, recorded trajectories, preprocessing, synchronization, and evaluation metrics; Fig. 2 depicts the platform and safety boat.Source: §IV · p. 4, Figure 2 · p. 4

A. Experimental setup

Dynamic sea trials used the MARVEL ASV with two commercial EMlogs and DVL references. The recorded dataset spans five trajectory segments with distinct motion profiles.

A. Experimental setup

  • EMlog1 measured longitudinal and transverse water speed at 1 Hz, while EMlog2 provided water-speed outputs at 5 and 10 Hz.The Rowe SeaPILOT DVL operated at 10 Hz.Source: A. Experimental setup · p. 4
  • The DVL served as the absolute ground-truth reference because ambient currents were negligible, reaching at most 0.286 m/s.A secondary EMlog was also used for relative inter-sensor calibration.Source: A. Experimental setup · pp. 4–5

1) Dataset:

  • The five segments comprised transit to the trial location, figure-8 maneuvers, straight lines, circular maneuvers, and a shortened return transit.The figure-8 segment included transient speed fluctuations, variable slip angles, and alternating port/starboard turns; only 30 minutes of the return transit were recorded.Source: 1) Dataset · p. 5
  • The dataset contains 221 minutes of recorded data from both EMlogs and DVL; Fig. 3 presents horizontal positions of five trajectories recorded using MARVEL.Two commercial EMlogs were deployed simultaneously; the absolute-velocity reference was a high-precision Rowe SeaPILOT DVL.Source: A. Experimental setup · p. 4, 1) Dataset · p. 5

2) Implementation details:

The implementation initializes Kalman-filter states and covariances, aligns asynchronous sensor streams, and evaluates corrected speed using RMSE.

2) Implementation details:

  • Measurement-noise variance R is initialized from sensor specifications, while the initial filter covariance and process noise are set to nominal values.The stated initialization uses P0 = 0.25 · I and Q = 10^-7 · I.Source: 2) Implementation details · p. 5

3) Temporal synchronization and lag optimization:

  • Cross-correlation alignment estimated delays of 3.2 s for EMlog1 and 0.45 s for EMlog2 before estimator ingestion.The optimization addressed asynchronous sampling rates and phase shifts during dynamic maneuvers.Source: 3) Temporal synchronization and lag… · p. 5

C. Evaluation metric

1) Root mean square error:

2) Filter consistency and normalized innovation squared:

Filter consistency is assessed with normalized innovation squared, while five-fold cross-validation evaluates calibration on trajectories withheld from training.

2) Filter consistency and normalized innovation squared:

  • The normalized innovation squared (NIS) evaluates filter consistency through observable measurements and helps test whether covariance bounds estimation errors.The stated check is whether NIS fluctuates around its expected level.Source: 2) Filter consistency and normalized… · p. 5

3) Combinatorial cross-validation paradigm:

  • Five-fold cross-validation trains each estimator on one trajectory, freezes its estimates, and evaluates them on the other four unseen trajectories.Each evaluation compares calibrated and pre-calibration RMSE; Fig. 4 illustrates the workflow.Source: 3) Combinatorial cross-validation… · p. 6, Figure 4 · p. 6

D. Results

The bias-and-scale EM3 model delivered the strongest reported speed correction, while Kalman-filter implementation approached batch least-squares accuracy. Calibration on dynamic, high-excitation paths also improved generalization to unseen trajectories compared with straight-line calibration.

D. Results

  • LS-EM3 and KF-EM3 consistently yielded the highest accuracy among the evaluated estimator formulations.The speed comparison on clean trajectory 3 shows calibrated EMlog outputs tracking the DVL reference more closely than raw measurements.Source: D. Results · p. 6, Figure 7 · p. 7
  • KF-EM3 achieved 0.170 m/s RMSE for EMlog1 (70% improvement), with rapid convergence, statistical stability, and performance near the least-squares methods.The NIS fluctuated around its expected level of 1 across the trial.Source: D. Results · p. 6, Figure 5 · p. 7, Figure 6 · p. 7
  • 71%: LS-EM3 reduced EMlog1 RMSE from 0.576 m/s to 0.167 m/s when trained on figure-8 dynamics and evaluated on straight transits.Table I covers calibration on the figure-8 run applied to trajectory 3.Source: Table I · p. 6, D. Results · p. 6
  • 30%: High-excitation circular and figure-8 calibration maneuvers improved out-of-sample generalization accuracy over standard straight transits.Training on straight-line trajectory 3 instead produced a 27% error inflation (RMSE = 0.507 m/s) when tested on circular paths.Source: D. Results · p. 7

E. Discussion

Calibration-path geometry affects parameter stability: straight, non-accelerating transits leave the information matrix rank-deficient, while dynamic maneuvers improve parameter decoupling. The conclusion reports that EM3 substantially improves EMlog1 accuracy, with a trade-off between calibration accuracy and energy-optimal travel.

E. Discussion

  • Spatial path geometry governs the numerical stability of estimated navigation parameters by changing their observability in the state-space estimation framework.Source: E. Discussion · p. 7

1) Limitations of straight-line transits:

  • Uniform, non-accelerating transits produce a rank-deficient information matrix and 27% cross-validation error inflation; KF-EM3 converges within 15 seconds of dynamic turn entry.The paper attributes the straight-transit corruption to steady current becoming collinear with electronic zero-drift bias.Source: 1) Limitations of straight-line transits · p. 7

2) Ambient current suppression in circular loops:

  • Continuous circular maneuvers expose the sensor to current from every relative orientation, making steady-current speed error a zero-mean periodic signal that the Kalman filter averages over time.The paper says this suppresses contamination of the estimated electronic zero-drift bias.Source: 2) Ambient current suppression in… · p. 7

3) Dual-axis excitation in figure-8 maneuvers:

  • Figure-8 maneuvers combine transient acceleration with alternating turns, raising the information matrix to full rank and driving scale-factor and bias correlation toward zero.Alternating port and starboard turns also help isolate asymmetric boundary-layer distortions and installation misalignment.Source: 3) Dual-axis excitation in figure-8… · pp. 7–8

V. CONCLUSION

  • EM3 (bias and scale) reduced EMlog1 baseline RMSE from 0.576 [m/s] to 0.167 [m/s] (71% improvement) and improved out-of-sample generalization 30% over straight-line transits.The conclusion identifies EM3 as the most robust optimization framework for the examined EMlogs.Source: §V · p. 8
  • High-excitation calibration maneuvers require temporarily leaving energy-optimal straight-line transits, and EMlog reliability degrades when vehicle speed approaches ambient-current speed.EMlogs measure speed relative to water, so the ambient current-to-vehicle speed ratio bounds reliability.Source: §V · p. 8
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