Beyond the Flat Seafloor: A Closed-Form Two-View Constraint to Aid Sidescan Sonar Reconstruction

Beyond the Flat Seafloor: A Closed-Form Two-View Constraint to Aid Sidescan Sonar Reconstruction

Kalin Norman, Joshua G. Mangelson · N/A · 2026

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Summary

Sidescan sonar is a common sensor for both manned and autonomous marine exploration and mapping, yet very few methods build upon or exploit the geometric projection model of the sensor.

Abstract Summary

Sidescan sonar is a common sensor for both manned and autonomous marine exploration and mapping, yet very few methods build upon or exploit the geometric projection model of the sensor. As sidescan sonar is limited to a 1D range measurement, many approximations are frequently used, including the long-standing assumption of a flat seafloor. Rather than make similar approximations, this paper focuses on a multi-view geometry based approach and formalizes a two-view geometric constraint and proves that a shared feature is constrained to a locus within the intersection of a sphere and a plane. In addition, we characterize what governs the size of the ambiguity locus through Monte Carlo simulation that is grounded in real aperture and mounting geometry for both a surface vessel and an underwater vehicle. We translate additional simulations of relative trajectories for both vehicle platforms into concrete survey-planning guidance. Our results show that locus length is strongly governed by elevation misalignment, and peaks at a moderate oblique crossing angle of approximately 20 degrees, with minimal locus lengths obtained at near parallel and anti-parallel passes.

Key Points

  • Sidescan sonar is a common sensor for both manned and autonomous marine exploration and mapping, yet very few methods build upon or exploit the geometric projection model of the sensor.
  • As sidescan sonar is limited to a 1D range measurement, many approximations are frequently used, including the long-standing assumption of a flat seafloor.
  • Rather than make similar approximations, this paper focuses on a multi-view geometry based approach and formalizes a two-view geometric constraint and proves that a shared feature is constrained to a locus within the intersection of a sphere and a plane.
  • In addition, we characterize what governs the size of the ambiguity locus through Monte Carlo simulation that is grounded in real aperture and mounting geometry for both a surface vessel and an underwater vehicle.
  • We translate additional simulations of relative trajectories for both vehicle platforms into concrete survey-planning guidance.

Preliminaries

An SSS emits an acoustic ping at a known frequency (or range of frequencies) and measures the round-trip time of flight of any returns, converted via the local speed of sound into range measurements.

We adopt a local sensor coordinate frame, as in [ 10 ] , with the sensor oriented in the $+x$ direction, with $+y$ to the left of the sensor, and $+z$ up, and describe the location of a feature relative to the sensor in spherical coordinates $(r,\theta,\phi)$, the range, azimuth, and elevation, which are related to local Cartesian coordinates throu...

Preliminaries — Beyond the Flat Seafloor: A Closed-Form Two-View Constraint to Aid Sidescan Sonar Reconstruction
(a)

Closed-Form Geometric Constraint

Consider two SSS observations of the same feature from two distinct sensor poses, either from two separate measurements from the same vehicle, or observations from two different vehicles. Let $\mathbf{p}_{1}=[x_{1}\ y_{1}\ z_{1}]^{T}$ be the unknown location of the feature in the local frame of the first sensor.

Closed-Form Geometric Constraint — Beyond the Flat Seafloor: A Closed-Form Two-View Constraint to Aid Sidescan Sonar Reconstruction
(b)

Application and Analysis

Initially, we verified our approach on an idealized, unconstrained sensor pair and conducted a full-range Monte Carlo simulation over relative position and orientation.

However, we determined that this idealized sweep was not representative, as many of the sample relative orientations corresponded with vehicle attitudes that are either physically impossible or operationally impractical, such as an observation that comes from beneath the seafloor, or a vehicle rotated to be on its side.

Application and Analysis — Beyond the Flat Seafloor: A Closed-Form Two-View Constraint to Aid Sidescan Sonar Reconstruction
(c)

Sources and Demonstrations

Figures are reproduced from Norman et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.

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