Improving the Estimation of Ship Length via ISAR

John R. Bennett

arxiv: 2603.02183 · v2 · submitted 2026-03-02 · 📡 eess.SP

Improving the Estimation of Ship Length via ISAR

John R. Bennett This is my paper

Pith reviewed 2026-05-15 16:36 UTC · model grok-4.3

classification 📡 eess.SP

keywords ISARship length estimationaspect anglemotion compensationautofocusradar trackingsynthetic aperture radar

0 comments

The pith

ISAR AutoTrack estimates ship aspect angle from motion compensation velocity to measure length within 10 percent.

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

The paper develops the ISAR AutoTrack algorithm to extract ship aspect angle from adaptive motion compensation data during ISAR imaging. Average mocomp velocity gives the in-range velocity error while the linear trend gives the cross-range component, and intelligent smoothing removes wave and system noise. This produces aspect angle estimates that support ship length measurements to within 10 percent for angles from 5 to 85 degrees across all azimuths and ranges. The approach cuts dedicated radar tracking resources because length estimates form inside each ISAR dwell and remain valid even if the ship maneuvers.

Core claim

The IAT algorithm treats the average adaptive motion compensation velocity as the residual in-range ship velocity error and the linear time trend of that velocity as the cross-range ship velocity component. Two implementations, Search and Analytical, apply an intelligent smoothing process that strips random noise, ocean-wave effects, and system biases without distorting the derived aspect angle. When this angle is combined with the known ISAR image dimensions, ship length is recovered to the target accuracy of 10 percent for unsigned aspect angles between 5 and 85 degrees.

What carries the argument

The ISAR AutoTrack (IAT) algorithm, which derives aspect angle from the average and linear trend of adaptive motion compensation velocity together with intelligent smoothing.

If this is right

Radar resources for continuous ship tracking can be substantially reduced.
Length estimates remain valid during ship maneuvers because they are formed inside each ISAR time window.
Both Search and Analytical implementations become available for operational use after smoothing.
The method applies over the full range of aircraft azimuths and slant ranges.
Aspect-angle accuracy improves without requiring additional radar dwells.

Where Pith is reading between the lines

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

The velocity-extraction principle could be tested on other extended moving targets such as aircraft or vehicles when similar mocomp data exist.
Combining IAT outputs with existing maritime surveillance radars would allow length tagging of contacts with minimal extra processing.
Performance in high sea states could be checked by controlled trials that vary wave height while holding ship speed and aspect fixed.

Load-bearing premise

The adaptive motion compensation velocity correctly isolates the true in-range and cross-range ship velocity components and the intelligent smoothing step removes ocean-wave and system errors without altering the aspect-angle estimate.

What would settle it

Direct comparison of IAT-derived ship lengths against independent ground-truth measurements on the same vessels at known aspect angles between 5 and 85 degrees; errors consistently above 10 percent would disprove the accuracy claim.

Figures

Figures reproduced from arXiv: 2603.02183 by John R. Bennett.

**Figure 3.** Figure 3: is a scatter plot of the LOA error for 43 MSR2 cases (see Section V for this definition), including both broadside and forward looks. The aspect angles for these cases are computed from the AIS ship heading reports and the known radar pointing, in contrast to the IAT results reported later. The mean ship length here is 250 meters and the RMS error is 20 meters for a relative error of 8 percent. There is a … view at source ↗

**Figure 4.** Figure 4: Apparent rotation rate - Aux vs 3D ISAR [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: outlines a hypothetical full 3-D ATR algorithm for ship ID using ISAR. The blue arrows denote data flows, understood to be cumulative in the sense that a downstream algorithm can use any of the upstream outputs. For example, the tracker produces estimates of the ship speed and heading and its Lat/Lon position at the start of the ISAR dwell. However, this information would normally be used only in the ISAR … view at source ↗

**Figure 29.** Figure 29: Mean radial velocity, ISAR vs GPS, for the Tybee [PITH_FULL_IMAGE:figures/full_fig_p018_29.png] view at source ↗

**Figure 32.** Figure 32: Aspect Angle IAT vs GPS for the Tybee in SCATR [PITH_FULL_IMAGE:figures/full_fig_p020_32.png] view at source ↗

read the original abstract

A method for estimating the aspect angle of ships at sea from an ISAR is developed. The ISAR AutoTrack (IAT) algorithm uses the information from the adaptive motion compensation velocity to improve the tracker estimation of the ship aspect angle and thus to improve the estimation of ship length. The IAT is based on classical methods of autofocus for synthetic aperture radar. The average mocomp velocity yields the error in the in-range component of the ship velocity; the linear time trend of the velocity determines the cross-range component of the ship velocity. The IAT has two methods for implementing the algorithm, the Search and Analytical methods. Both methods benefit from an intelligent smoothing process that removes system errors, random noise, and ocean waves. The goal of the IAT is to measure ship length to within 10 percent over all azimuth angles and ranges relative to the aircraft and for (unsigned) aspect angles from 5 to 85 degrees. Using the IAT allows a major reduction in the radar resources dedicated to tracking; and since the IAT creates its estimates during the ISAR time window it is unaffected by ship maneuvers. Recommendations for further development and testing of the IAT are presented.

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.

Desk Editor's Note private letter to a colleague

The IAT extends classical SAR autofocus to ship aspect angle estimation from motion compensation velocities but supplies no data or tests to support the 10% length accuracy target.

read the letter

The main point is that this paper describes an ISAR AutoTrack method that takes the average and linear trend from adaptive motion compensation velocity to separate in-range and cross-range ship velocity components, then uses either a Search or Analytical implementation plus smoothing to get aspect angle and ship length. The target is 10% length error across azimuths and for unsigned aspects from 5 to 85 degrees, with the side benefit of cutting radar tracking resources since the estimate runs inside the ISAR window and is not thrown by maneuvers. That is a direct, practical extension of established autofocus techniques to the maritime case, and the two named implementations plus the smoothing step are spelled out clearly enough to follow the logic. The paper also notes the need for further development, which keeps the tone realistic. The obvious gap is the total lack of any supporting evidence. No equations appear, no simulated or measured data, no error statistics, and no comparison against ground-truth lengths. Without those, it is impossible to judge whether the velocity components stay clean enough under wave motion or whether the smoothing step preserves the angle estimate rather than biasing it. The 10% figure therefore remains a stated goal rather than a demonstrated result. This kind of incremental processing idea would mainly interest radar engineers already working on operational maritime ISAR systems who want to reduce dwell time on tracking. A reader with background in SAR autofocus could probably code the method from the description and run their own checks. I would send it to peer review because the core idea is coherent and the application is narrow enough that referees could quickly point out what experiments are needed, even though the current version is not ready for publication without added validation.

Referee Report

2 major / 1 minor

Summary. The paper proposes the ISAR AutoTrack (IAT) algorithm to estimate ship aspect angle from adaptive motion compensation velocity components in ISAR data. It outlines Search and Analytical implementations that use average mocomp velocity for in-range error and linear velocity trend for cross-range component, combined with intelligent smoothing to remove ocean-wave and system errors, with the stated goal of achieving ship length estimates within 10% accuracy for unsigned aspect angles 5–85° across all azimuth angles and ranges.

Significance. If the accuracy claim holds, the approach would reduce radar resources needed for ship tracking and yield estimates unaffected by maneuvers during the ISAR dwell. The adaptation of classical SAR autofocus relations to aspect-angle extraction is conceptually sound, but the complete absence of any quantitative validation, error analysis, or test cases prevents assessment of whether the method delivers the claimed performance.

major comments (2)

[Abstract] Abstract: the central claim that ship length can be measured to within 10% for aspect angles 5–85° is presented without any supporting equations, Monte Carlo results, error metrics, or ground-truth comparisons, leaving the performance assertion untestable from the manuscript.
[IAT Algorithm] IAT algorithm description: the assumption that adaptive mocomp velocity isolates undistorted in-range and cross-range components (after intelligent smoothing) is load-bearing for the aspect-angle estimate, yet no explicit equations, derivation, or sensitivity analysis is supplied to show how smoothing avoids distorting the velocity trends used for the angle calculation.

minor comments (1)

[IAT Algorithm] The two implementation methods (Search and Analytical) are named but not contrasted quantitatively or with pseudocode, making it difficult to evaluate their relative merits.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review of our manuscript on the ISAR AutoTrack (IAT) algorithm. The comments correctly identify areas where the presentation can be clarified and strengthened. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that ship length can be measured to within 10% for aspect angles 5–85° is presented without any supporting equations, Monte Carlo results, error metrics, or ground-truth comparisons, leaving the performance assertion untestable from the manuscript.

Authors: We agree that the abstract states the 10% accuracy target without accompanying validation data. The manuscript develops the IAT as a conceptual extension of classical SAR autofocus methods, where the target accuracy follows from the expected isolation of velocity components over the 5–85° aspect range. No Monte Carlo simulations or ground-truth comparisons appear in the current version because the work focuses on algorithm formulation and ends with explicit recommendations for further testing. We will revise the abstract to state clearly that the 10% figure is the design goal of the method rather than an empirically validated result. revision: yes
Referee: [IAT Algorithm] IAT algorithm description: the assumption that adaptive mocomp velocity isolates undistorted in-range and cross-range components (after intelligent smoothing) is load-bearing for the aspect-angle estimate, yet no explicit equations, derivation, or sensitivity analysis is supplied to show how smoothing avoids distorting the velocity trends used for the angle calculation.

Authors: The manuscript describes the Search and Analytical implementations, in which the average mocomp velocity supplies the in-range error and the linear velocity trend supplies the cross-range component, followed by intelligent smoothing to suppress ocean-wave and system errors. We acknowledge that the current text does not supply the full set of equations or a sensitivity study showing that smoothing preserves the underlying trends. In the revision we will add an appendix containing the explicit derivations for both implementations together with a basic sensitivity analysis that quantifies the effect of residual noise on the extracted aspect angle. revision: yes

Circularity Check

0 steps flagged

No significant circularity; aspect angle derived from classical velocity relations without reduction to fitted inputs or self-citations

full rationale

The manuscript describes the IAT algorithm as using adaptive motion compensation velocity to isolate in-range error (from average mocomp velocity) and cross-range component (from linear time trend), followed by intelligent smoothing to remove ocean-wave and system errors. Aspect angle is then obtained via classical autofocus relations for SAR to support ship length estimation. No equations are shown that define the output length or aspect angle in terms of themselves, no fitted parameters are renamed as predictions, and no self-citation chains or uniqueness theorems are invoked as load-bearing. The 10% accuracy target is presented as a design goal rather than a derived result. The derivation chain remains independent of the target quantity and relies on external classical methods.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on domain assumptions about how motion-compensation velocity components map to ship velocity and on the effectiveness of post-processing smoothing; no free parameters are explicitly named but smoothing thresholds are implied.

free parameters (1)

smoothing parameters
Intelligent smoothing process that removes system errors, random noise, and ocean waves; specific thresholds or filter coefficients are not stated but must be chosen to achieve the target accuracy.

axioms (2)

domain assumption Average mocomp velocity yields the error in the in-range component of the ship velocity
Directly invoked as the basis for extracting velocity information from the autofocus process.
domain assumption Linear time trend of the velocity determines the cross-range component of the ship velocity
Used to separate velocity components for aspect-angle calculation.

pith-pipeline@v0.9.0 · 5498 in / 1425 out tokens · 37930 ms · 2026-05-15T16:36:54.380012+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The IAT algorithm uses the information from the adaptive motion compensation velocity to improve the tracker estimation of the ship aspect angle... average mocomp velocity yields the error in the in-range component... linear time trend... cross-range component... intelligent smoothing process that removes system errors, random noise, and ocean waves.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

LOA = RE/Cosine(AspectU) = RE*Secant(AspectU)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

Focus3D: A Practical Method to Adaptively Focus ISAR Data and Provide 3 -D Information for Automatic Target Recognition

John R. Bennett. 2025. “Focus3D: A Practical Method to Adaptively Focus ISAR Data and Provide 3 -D Information for Automatic Target Recognition ”. http//arxiv.org/abs/2504.13321

work page arXiv 2025
[2]

An Automatic Ship Classification System for ISAR Imagery

Murali M. Menon, Eric R. Boudreau, and Paul J. Kolodzy. “An Automatic Ship Classification System for ISAR Imagery”. Volume 6, Number 2,1993, THE LINCOLN LABORATORY JOURNAL

work page 1993
[3]

The length estimation of ship targets in ISAR images

Hongxin Yang,Fulin Su, Jianjun Gao. (2015). “The length estimation of ship targets in ISAR images”. 2015. 1910-1913. 10.1109/ICOSP.2014.7015325

work page doi:10.1109/icosp.2014.7015325 2015
[4]

Radar ATR of Maritime Targets

Hartmut Schimpf. “Radar ATR of Maritime Targets”. NATO Paper SSTO-EN-SET-172-2013 3 – 1.pdf. 28 pp

work page 2013
[5]

ISAR Target Parameter Estimation with Application for Automatic Target Recognition

Kenneth A. Melendez and John R. Bennett. 1998. “ISAR Target Parameter Estimation with Application for Automatic Target Recognition ”. Proceedings of SPIE, W. Miceli Ed., Vol. 3162, pp. 2-13, San Diego

work page 1998
[6]

Automatic recognition of ISAR ship images

S. Musman, D. Kerr, C. Bachmann. “Automatic recognition of ISAR ship images”, IEEE Transactions on Aerospace and Electronic Systems, Year: 1996 | Volume: 32, Issue: 4

work page 1996
[7]

Optimizing ship length estimates from ISAR images,

F. E. McFadden and S. A. Musman. "Optimizing ship length estimates from ISAR images," Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium, Como, Italy, 2000, pp. 163-168 vol.1

work page 2000
[8]

Robust 3D ISAR ship classification

C. Y. Pui, S. Ghio,, B. Ng, E. Giusti and L. Rosenberg. “Robust 3D ISAR ship classification”, IEEE Radar Conference 2023

work page 2023
[9]

Three-Dimensional Target Geometry and Target Motion Estimation Method Using Multistatic ISAR Movies and Its Performance,

K. Suwa, T. Wakayama, and M. Iwamoto,.“Three-Dimensional Target Geometry and Target Motion Estimation Method Using Multistatic ISAR Movies and Its Performance,” IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 6, pp. 2361–2373, 2011

work page 2011
[10]

3D-ISAR Using a Single Along Track Baseline,

C. Y. Pui, B. Ng, L. Rosenberg, and T.-T. Cao.“3D-ISAR Using a Single Along Track Baseline,” in 2021 IEEE Radar Conference (RadarConf21), 2021, pp. 1–6

work page 2021
[11]

3D ISAR for an Along- Track Airborne Radar,

C. Y. Pui, B. Ng, L. Rosenberg, and T. Cao, “3D ISAR for an Along- Track Airborne Radar,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 4, pp. 2673–2686, 2022

work page 2022
[12]

High-Resolution Inverse Synthetic Aperture Radar Imaging and Scaling with Sparse Aperture

Gang Xu, Meng-Dao Xing, Xiang-Gen, Xia, Qian-Qian Chen, Lei Zhang, Zheng Bao. “High-Resolution Inverse Synthetic Aperture Radar Imaging and Scaling with Sparse Aperture ”. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Year: 2015 | Volume: 8, Issue: 8

work page 2015
[13]

https://www.telephonics.com/uploads/standard/46045-TC-Maritime- Classification-Aid-Brochure.pdf

work page
[14]

Novel approach for ISAR image cross-range scaling

Marco Martorella. “Novel approach for ISAR image cross-range scaling”. IEEE Transactions on Aerospace and Electronic Systems, Year: 2008 | Volume: 44, Issue: 1

work page 2008
[15]

Dall (1992)

J. Dall (1992). “A fast autofocus algorithm for synthetic aperture radar processing. IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings, 3, 5 - 8

work page 1992
[16]

This site includes all the code and ISAR results for the Tybee case in Section IX , the code for the simulation discussed in the Introduction, and the simulations in Section X

en.wikipedia.org/wiki/Automatic_identification_system DATA AVAILABILITY The software and data for the Tybee data is in github.com/mulebennett5-source/IAT_Published_Tybee. This site includes all the code and ISAR results for the Tybee case in Section IX , the code for the simulation discussed in the Introduction, and the simulations in Section X. The raw d...

work page 1972

[1] [1]

Focus3D: A Practical Method to Adaptively Focus ISAR Data and Provide 3 -D Information for Automatic Target Recognition

John R. Bennett. 2025. “Focus3D: A Practical Method to Adaptively Focus ISAR Data and Provide 3 -D Information for Automatic Target Recognition ”. http//arxiv.org/abs/2504.13321

work page arXiv 2025

[2] [2]

An Automatic Ship Classification System for ISAR Imagery

Murali M. Menon, Eric R. Boudreau, and Paul J. Kolodzy. “An Automatic Ship Classification System for ISAR Imagery”. Volume 6, Number 2,1993, THE LINCOLN LABORATORY JOURNAL

work page 1993

[3] [3]

The length estimation of ship targets in ISAR images

Hongxin Yang,Fulin Su, Jianjun Gao. (2015). “The length estimation of ship targets in ISAR images”. 2015. 1910-1913. 10.1109/ICOSP.2014.7015325

work page doi:10.1109/icosp.2014.7015325 2015

[4] [4]

Radar ATR of Maritime Targets

Hartmut Schimpf. “Radar ATR of Maritime Targets”. NATO Paper SSTO-EN-SET-172-2013 3 – 1.pdf. 28 pp

work page 2013

[5] [5]

ISAR Target Parameter Estimation with Application for Automatic Target Recognition

Kenneth A. Melendez and John R. Bennett. 1998. “ISAR Target Parameter Estimation with Application for Automatic Target Recognition ”. Proceedings of SPIE, W. Miceli Ed., Vol. 3162, pp. 2-13, San Diego

work page 1998

[6] [6]

Automatic recognition of ISAR ship images

S. Musman, D. Kerr, C. Bachmann. “Automatic recognition of ISAR ship images”, IEEE Transactions on Aerospace and Electronic Systems, Year: 1996 | Volume: 32, Issue: 4

work page 1996

[7] [7]

Optimizing ship length estimates from ISAR images,

F. E. McFadden and S. A. Musman. "Optimizing ship length estimates from ISAR images," Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium, Como, Italy, 2000, pp. 163-168 vol.1

work page 2000

[8] [8]

Robust 3D ISAR ship classification

C. Y. Pui, S. Ghio,, B. Ng, E. Giusti and L. Rosenberg. “Robust 3D ISAR ship classification”, IEEE Radar Conference 2023

work page 2023

[9] [9]

Three-Dimensional Target Geometry and Target Motion Estimation Method Using Multistatic ISAR Movies and Its Performance,

K. Suwa, T. Wakayama, and M. Iwamoto,.“Three-Dimensional Target Geometry and Target Motion Estimation Method Using Multistatic ISAR Movies and Its Performance,” IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 6, pp. 2361–2373, 2011

work page 2011

[10] [10]

3D-ISAR Using a Single Along Track Baseline,

C. Y. Pui, B. Ng, L. Rosenberg, and T.-T. Cao.“3D-ISAR Using a Single Along Track Baseline,” in 2021 IEEE Radar Conference (RadarConf21), 2021, pp. 1–6

work page 2021

[11] [11]

3D ISAR for an Along- Track Airborne Radar,

C. Y. Pui, B. Ng, L. Rosenberg, and T. Cao, “3D ISAR for an Along- Track Airborne Radar,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 4, pp. 2673–2686, 2022

work page 2022

[12] [12]

High-Resolution Inverse Synthetic Aperture Radar Imaging and Scaling with Sparse Aperture

Gang Xu, Meng-Dao Xing, Xiang-Gen, Xia, Qian-Qian Chen, Lei Zhang, Zheng Bao. “High-Resolution Inverse Synthetic Aperture Radar Imaging and Scaling with Sparse Aperture ”. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Year: 2015 | Volume: 8, Issue: 8

work page 2015

[13] [13]

https://www.telephonics.com/uploads/standard/46045-TC-Maritime- Classification-Aid-Brochure.pdf

work page

[14] [14]

Novel approach for ISAR image cross-range scaling

Marco Martorella. “Novel approach for ISAR image cross-range scaling”. IEEE Transactions on Aerospace and Electronic Systems, Year: 2008 | Volume: 44, Issue: 1

work page 2008

[15] [15]

Dall (1992)

J. Dall (1992). “A fast autofocus algorithm for synthetic aperture radar processing. IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings, 3, 5 - 8

work page 1992

[16] [16]

This site includes all the code and ISAR results for the Tybee case in Section IX , the code for the simulation discussed in the Introduction, and the simulations in Section X

en.wikipedia.org/wiki/Automatic_identification_system DATA AVAILABILITY The software and data for the Tybee data is in github.com/mulebennett5-source/IAT_Published_Tybee. This site includes all the code and ISAR results for the Tybee case in Section IX , the code for the simulation discussed in the Introduction, and the simulations in Section X. The raw d...

work page 1972