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Wave-Robust Passive AUV Localization Using FP-MUSIC

Usama Saqib, Ola Rønning, Andrzej Wąsowski

arXiv:2609.27712v1cs.RO

TL;DR

AUV localization with acoustic systems can require seabed transponders, while wave-driven buoy motion degrades direction estimation. The paper uses a buoy-mounted hydrophone array and IMU with FP-MUSIC and a receiver-passive pipeline; in simulation, it improves close-beacon resolution and supports tracking and orientation estimation through Sea State 4.

  • Problem

    Existing LBL systems require pre-deployed seabed transponders, while wave-induced array motion degrades acoustic direction estimation.

    Source: §I · p. 1, §II · p. 2

  • Method

    A receiver-passive buoy-mounted hydrophone array and IMU use fixed-point MUSIC to compensate wave-induced motion when estimating beacon directions.

    Source: §I · p. 1, §IV · p. 3

  • Results

    At 2 m beacon separation, FP-MUSIC raises resolution accuracy from approximately 45% with uncompensated MUSIC to approximately 75%.

    Source: B. Can the two beacons setup be… · p. 6

  • Takeaways & Limitations

    The combined framework achieves robust 3-D tracking and vehicle orientation estimation up to Sea State 4.

    Source: §VII · p. 8

    The evaluations use simulation, and validation with a physical buoy array in field trials remains future work.

    Source: §VII · p. 8

Abstract

from arXiv · show

Localizing an autonomous underwater vehicle without pre-deployed seabed transponders, or direct access to onboard vehicle sensors remains a core challenge. We present a receiver-passive 3-D localization and spatial mapping system utilizing a single floating surface buoy equipped with a hydrophone array and an inertial measurement unit (IMU). The central difficulty is that surface wave motion induces six-degree-of-freedom (6-DOF) perturbations that rotate the array between snapshots, degrading conventional subspace processing. We resolve this by introducing a fixed-point iterative MUltiple SIgnal Classification algorithm (FP-MUSIC) that uses IMU measurements to de-warp snapshot covariances prior to direction-of-arrival estimation. Furthermore, we employ a subspace-projected wideband matched filter to resolve beacon ranges and use power asymmetry for independent front-back identification. Evaluations across simulated sea states demonstrate that FP-MUSIC substantially reduces localization error relative to uncompensated methods and sustains robust 3-D tracking and vehicle orientation estimation under wave-induced motion. At moderate sea state, FP-MUSIC increases the 2-m beacon-separation accuracy from approximately 45% to 75%.

I. INTRODUCTION

Optical tracking is short-range, while established acoustic approaches impose deployment, synchronization, or multi-vehicle constraints. The paper proposes receiver-passive AUV localization with a buoy-mounted array and IMU, addressing wave-induced array rotation through iterative compensation.

I. INTRODUCTION

  • Optical systems use fiducial markers to track AUVs, but these markers are reliable only at short range, mostly in clean indoor pools, before visibility degrades.Source: §I · p. 1
  • LBL requires pre-deployed seabed transponders, while USBL uses two-way communication requiring accurate clock synchronization and cannot track multiple AUVs simultaneously, [5].These constraints make offshore installation and calibration expensive.Source: §I · p. 1
  • The proposed system uses one floating surface buoy with a hydrophone array and IMU to receive AUV beacons and reconstruct vehicle pose.The receiver-passive approach avoids seabed infrastructure and physical cables, and receives signals one way from the AUV.Source: §I · p. 1
  • Surface-wave motion rotates the array and corrupts high-resolution DOA estimation, motivating iterative fixed-point de-warping of the observations.The approach uses IMU data to compensate acoustic phase shifts while estimating beacon directions.Source: §I · p. 1

II. RELATED WORK

  • Prior floating-buoy acoustic localization recovers AUV position but not orientation, and does not explicitly account for wave perturbation.Resolving orientation requires detecting at least two hull-mounted beacons and assigning persistent front/back identities.Source: §II · p. 1
  • The proposed formulation keeps two beacons in a shared frequency band, avoiding dedicated frequency bands or time slots for source identity.The related-work discussion identifies MUSIC as attractive for resolving closely spaced beacons on a compact vehicle frame.Source: §II · p. 2
  • The framework applies motion correction directly to MUSIC’s covariance matrix under unconstrained stochastic 6-DOF buoy motion, rather than correcting a preestimated bearing.The paper states that rigid-body translation does not affect plane-wave DOA estimation, so only rotational degrees of freedom require compensation.Source: §I · p. 1, §II · p. 2

III. SYSTEM MODEL AND PROBLEM FORMULATION

The system models a floating rectangular hydrophone array observing submerged sources and uses two front-and-back AUV beacons that transmit windowed LFM chirps.

A. Array and Target Geometry

  • A uniform rectangular array of M hydrophones floats at the water surface, with its origin at the array center.Fig. 1 depicts the floating URA used for AUV localization.Source: A. Array and Target Geometry · p. 2, Figure 1 · p. 2
  • The underwater source position is expressed relative to the array center, with vertical coordinate z = −h for depth h > 0.The source lies below the floating array, so its elevation angle φ is in [−90°, 0°].Source: A. Array and Target Geometry · p. 2

B. Transmitted Wideband LFM Chirp

  • The vehicle carries two acoustic beacons, one at the front and one at the back, transmitting at different power levels.The beacons provide the pair used for AUV localization.Source: B. Transmitted Wideband LFM Chirp · p. 2
  • Each beacon emits a linear frequency modulated chirp, with a windowed transmit pulse.The passage introduces the pulse expression but does not provide its readable form.Source: B. Transmitted Wideband LFM Chirp · p. 2
  • The chirp is active for duration T_sig, and its operational bandwidth is B = f_high − f_low.The sweep boundaries define the lower and upper frequencies.Source: B. Transmitted Wideband LFM Chirp · p. 2
  • A Hanning window tapers the chirp pulse edges to keep transmission within the intended band.The nominal center frequency is f0 = (f_low + f_high)/2.Source: B. Transmitted Wideband LFM Chirp · p. 2

C. Received Signal Representation

The signal model represents two spatially separated beacons sharing a frequency band, with arrival directions estimated from direct-path acoustic signals and then combined with wideband ranging to obtain AUV pose.

C. Received Signal Representation

  • The two beacons transmit in a shared band and are separated spatially rather than by frequency allocation.The model treats sensor and ambient noise as separate received-signal components.Source: C. Received Signal Representation · p. 2
  • Under the far-field assumption, a planar wavefront gives each hydrophone a delay determined by its position projected onto the arrival direction.The direction is represented by the unit vector in Eq. (7).Source: C. Received Signal Representation · p. 3
  • The channel model includes only the direct arrival and defers reflected-path multipath to future work.The passage defines the underwater channel as generally containing direct and reflected arrivals.Source: C. Received Signal Representation · p. 3
  • In the frequency domain, convolution becomes multiplication and the direct-path channel becomes a per-hydrophone phase factor.The formulation leaves the operating band free, allowing ultrasonic or audible beacons.Source: C. Received Signal Representation · p. 3
  • Estimated arrival directions determine beacon delays, which combine with wideband ranging to yield ranges and then AUV pose.The passage identifies this as the link between DOA estimation and the ranging stage.Source: C. Received Signal Representation · p. 3

IV. DOA VIA FIXED-POINT MUSIC (FP-MUSIC)

FP-MUSIC forms narrowband array snapshots from each recording frame and applies MUSIC to estimate beacon directions using steering vectors and a loaded covariance matrix.

IV. DOA VIA FIXED-POINT MUSIC (FP-MUSIC)

  • Each frame is divided into short-time snapshots long enough to observe the complete chirp, and the hydrophone spectra at f0 are stacked into array vectors.A frame is a complete recording window across all hydrophones; experiments used 5-second frames.Source: §IV · p. 3
  • Because beacon gain is common across hydrophones, it factors out of the steering vector and is absorbed into the source amplitude.This leaves the steering vector to describe the direction-dependent phase pattern across the array.Source: §IV · p. 3
  • The steering vector collects the hydrophone phases expected for a plane wave arriving from a candidate direction.The delay for each hydrophone is evaluated at that arbitrary direction.Source: §IV · p. 3
  • MUSIC forms a sample spatial covariance with power-normalized diagonal loading, then searches for steering vectors nearly orthogonal to the noise subspace.The loading addresses L < M by ensuring a full-rank covariance and a well-defined noise subspace; two signal eigenvectors correspond to the two beacons.Source: §IV · p. 3

A. IMU Kinematics and Translational Invariance

The array rotation is represented by a snapshot-specific 3-D rotation matrix, while rigid-body translation leaves covariance-based DOA estimation unchanged. Consequently, compensation is needed only for rotation, and a gyroscope alone could provide it.

A. IMU Kinematics and Translational Invariance

B. Iterative Fixed-Point Motion Compensation Loop

FP-MUSIC iteratively de-warps snapshots using current DOA estimates and IMU-derived rotations, then updates the covariance and MUSIC directions. It averages source-conditioned covariances to handle multiple beacons without extra receivers or dedicated frequency bands.

B. Iterative Fixed-Point Motion Compensation Loop

  • FP-MUSIC alternates snapshot de-warping with covariance formation and MUSIC DOA updates, iterating until successive direction estimates differ by less than an angular tolerance.The procedure is inspired by IMU-guided iterative image deblurring.Source: B. Iterative Fixed-Point Motion… · p. 4
  • Each snapshot is corrected for rotational phase perturbation relative to flat geometry, preserving the rest-frame steering phase before covariance estimation.Source: B. Iterative Fixed-Point Motion… · p. 4
  • The updated covariance is eigendecomposed to obtain the noise subspace and signal-subspace projector used in the MUSIC direction update.Source: B. Iterative Fixed-Point Motion… · p. 4
  • The method averages source-conditioned covariances, preventing single-beacon preference despite direction-dependent residual phase, and resolves beacons without separate receivers or dedicated frequency bands.Source: B. Iterative Fixed-Point Motion… · p. 4
  • FP-MUSIC adds at most Kmax covariance updates at O(LM^2) cost per iteration, without requiring extra hydrophones, bandwidth, or array aperture.Source: B. Iterative Fixed-Point Motion… · p. 4

A. Subspace-Projected Wideband Filtering

The ranging stage projects wideband snapshots through the converged signal-subspace projector before matched filtering. The resulting envelope is evaluated along each resolved direction without requiring environmental replica fields.

A. Subspace-Projected Wideband Filtering

B. Range Peak Extraction & Beacon Tagging

The pipeline maps matched-filter delay to range, uses peak power to assign front/back identities, and derives vehicle heading and pitch from the tagged beacon baseline. Experiments use simulated wave-driven buoy motion and assess DOA performance, angular resolvability, and trajectory reconstruction.

B. Range Peak Extraction & Beacon Tagging

VI. EXPERIMENT RESULTS

  • The simulations use a 4×6, 24-element half-wavelength array and 50 trials, with WMO sea-state kinematics across Sea States 1–7.The IMU data are sampled at 400 Hz and interpolated to snapshot midpoints; its evaluation is outside scope, with AHRS orientation assumed at nominal factory accuracy.Source: §VI · pp. 5–6
  • The evaluation asks whether de-warping reduces DOA error, how beacon resolvability changes with geometry and noise, and whether the pipeline reconstructs AUV trajectories.Fig. 2 compares MUSIC and FP-MUSIC under 6-DOF motion at Sea State 1 using RMSE over 50 trials.Source: §VI · p. 6, Figure 2 · p. 6

A. Does FP-MUSIC compensate under all sea-state?

FP-MUSIC improves DOA estimation under wave motion and extends two-beacon resolvability across challenging separations and geometries. Its advantage varies with sea state and operating conditions.

A. Does FP-MUSIC compensate under all sea-state?

  • FP-MUSIC maintains superior accuracy through Sea State 4; at Sea States 5–7, elevation improves significantly while azimuth shows a minor crossover.The reported crossover is attributed to large initialization errors under severe motion.Source: A. Does FP-MUSIC compensate under all… · p. 6

B. Can the two beacons setup be resolved by FP-MUSIC

  • Resolution accuracy counts trials where both beacons yield distinct peaks within half their true angular separation, evaluated at Sea State 3 with 10 dB ambient and 30 dB sensor noise.Source: B. Can the two beacons setup be… · p. 6
  • At 2 m beacon separation, FP-MUSIC raises resolution accuracy from approximately 45% for uncompensated MUSIC to approximately 75%.The comparison is at 7 m depth and 10 m horizontal range; Fig. 3(a) evaluates beacon separation.Source: B. Can the two beacons setup be… · p. 6, Figure 3 · p. 7

A. Does FP-MUSIC compensate under all sea-state?

B. Can the two beacons setup be resolved by FP-MUSIC

  • FP-MUSIC maintains a 10–15% accuracy advantage over standard MUSIC in the 10–15 m transition regions as depth and horizontal range increase.The effective angular separation shrinks with greater depth and range, and DAS and MVDR fail almost immediately.Source: B. Can the two beacons setup be… · pp. 6–7

C. Is Two-Beacon Resolvability Robust to Oceanic Ambient

The evaluation examines two-beacon resolvability under ambient noise and full-pipeline trajectory reconstruction. FP-MUSIC supports tracking and orientation estimation in simulated wave conditions, with field validation still pending.

C. Is Two-Beacon Resolvability Robust to Oceanic Ambient

  • Across evaluated SNR levels, DAS fails to resolve targets due to the array’s Rayleigh limit; MVDR plateaus at approximately 90% accuracy even at high SNR, while standard MUSIC and FP-MUSIC improve sharply between −5 dB and 10 dB.Source: C. Is Two-Beacon Resolvability Robust… · p. 7

D. Can FP-MUSIC Reconstruct an End-to-End 3-D Trajec-

  • In the Sea State 2 trajectory session, power-asymmetry tagging classified front and back correctly in 100% of 50 resolved frames without inter-frame history.Compensation halves the reported 3-D position errors to 0.12 m and 0.14 m; Table II reports trajectory RMSE for this session.Source: D. Can FP-MUSIC Reconstruct an… · p. 7, Table II · p. 8
  • The end-to-end estimates trace the true 3-D path, and recovered front/back beacons remain aligned with ground-truth orientation over the session.The trajectory is evaluated under Sea State 2 at 7 m depth and 10.2 m horizontal range.Source: D. Can FP-MUSIC Reconstruct an… · p. 7

VII. CONCLUSION AND FUTURE WORK

  • FP-MUSIC combines fixed-point de-warping, wideband matched filtering, and power-asymmetry tagging to track position and orientation up to Sea State 4.Source: §VII · p. 8
  • Field trials with a physical buoy-array prototype remain future work; real AHRS error, IMU–acoustic timing offset, and multipath are not captured by the idealized direct-path channel.Source: §VII · p. 8
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