PaperlayerView exact revision on arXiv

Source-linked AI summary

Spaceborne differential photogrammetry for control-free measurement of large-gradient deformation with structural immunity and a predictable accuracy envelope

Yueqiang Zhang, Chang Ma, Shuixin Pan, Haibo Liu

arXiv:2609.29550v1cs.CV

TL;DR

Optical image correlation measures deformation in large-gradient regimes where InSAR can fail, but standard pairwise workflows lack a pre-acquisition error budget and often depend on extensive stable terrain. This paper models repeat-pass optical correlation as differential estimation without surveyed ground control, and experiments validate the model’s predicted noise floor and other measurement properties. The paper also identifies an information boundary: control-free optical methods cannot recover mean along-track displacement.

  • Problem

    Repeat-pass optical workflows lack a model for predicting accuracy before acquisition and calibrated uncertainty afterward, while some deformation settings do not permit surveyed ground control.

    Source: §1 · pp. 3–4

  • Method

    The paper jointly estimates surface displacement and revisit-bias coefficients in a differential model, using nominal georeferencing, stable-area constraints, and displacement priors.

    Source: §3.1 · p. 8, §8 · p. 32

  • Results

    Three control-free real-data cases validate the predicted noise floor, closure-based error decomposition, pair-specific matching-uncertainty calibration, cross-view effects, and agreement with ITS_LIVE velocities.

    Source: §1 · p. 5, §8 · p. 32

  • Takeaways & Limitations

    The framework turns pairwise optical correlation into a measurement with a predictive error budget and calibrated per-point uncertainty.

    Source: §1 · p. 4, §8 · p. 32

    Mean along-track displacement is unobservable to control-free optical methods; recovering a dense along-track signal requires ground control or joint inversion with InSAR.

    Source: Honest boundaries · p. 30

Abstract

from arXiv · show

Optical satellite image correlation measures wide-area deformation in regimes where coherent interferometric synthetic aperture radar fails because displacement gradients are too large. However, standard pairwise workflows lack a pre-acquisition error budget and rely on extensive stable terrain. We formulate repeat-pass optical correlation as a differential estimation problem without surveyed ground control. Nominal georeferencing defines the coordinate frame, stable-area constraints and displacement priors resolve the datum, and surface displacement is estimated jointly with inter-epoch revisit-bias coefficients. The model yields a predictive accuracy envelope and calibrated per-point posterior uncertainty, bounds along-track uncertainty through a displacement prior, and represents pushbroom jitter using per-line revisit offsets. Simulations and Sentinel-2 and WorldView-2 experiments on the 2019 Ridgecrest earthquake, the 2023 Kahramanmaraş earthquake, and the Baltoro glacier validate the predicted noise floor, control-free accuracy margin, and leakage caused by view-angle and digital elevation model errors. The measured noise floor reaches approximately $0.05$ pixel at $10$,m ground sampling distance. With only five stable tiles, conventional destriping changes the estimated Baltoro trunk velocity from $106$ to $1251$myr$^{-1}$, whereas the prior-constrained estimate remains $87$myr$^{-1}$. Closure analysis attributes approximately $88\%$ of pair-error variance to individual scenes, consistent with $25{,}354$ ITS_LIVE glacier-velocity triplets. Three matching methods lead to the same conclusions. The framework therefore turns pairwise correlation into a robust measurement with a predictive error budget, reduced dependence on stable terrain, and conclusions independent of the matching method.

1. Introduction

Optical correlation measures surface change across wide areas and in high-gradient regimes, but conventional workflows lack a unified model that predicts accuracy and calibrated uncertainty. This paper extends differential estimation to repeat-pass satellite imaging, addressing constraints that include sparse stable terrain and pushbroom jitter.

1. Introduction

  • No operator can lay ground control across a fault zone, accumulation basin, or disaster site, although deformation measurements inform earthquake, glacier, and landslide studies.The paper notes coseismic slip constrains rupture physics and seismic hazard, glacier velocities inform ice-mass budgets, and landslide acceleration can serve as an early-warning quantity.Source: §1 · p. 3
  • Optical correlation estimates two horizontal displacement components without phase ambiguity, complementing InSAR where large displacements or steep gradients degrade phase unwrapping and coherence.InSAR can achieve millimeter-per-year precision over coherent terrain undergoing slow deformation.Source: §1 · p. 3
  • The differential satellite model estimates inter-epoch change with revisit geometry and provides an accuracy budget and calibrated matching uncertainty, addressing gaps in pairwise optical workflows.The paper frames this as a predictable measurement whose accuracy can be known before acquisition and matching uncertainty calibrated per pair afterward.Source: §1 · pp. 3–4

2.1. Optical offset tracking: from COSI-Corr to continental products

  • Existing optical offset-tracking workflows generally apply empirical trend removal and destriping, then assess accuracy through external comparison rather than a predictive error budget.The paper identifies the missing elements as an estimation-theoretic account of correction, pre-acquisition accuracy prediction, and calibrated per-point posterior uncertainty.Source: §1 · pp. 3–4, §2.1 · p. 6

2.2. Coseismic and landslide applications

  • Across deformation applications, downstream inversions need error covariance and stability checks across epochs, quantities a differential model delivers.The cited applications include coseismic and landslide motion; the paper also notes InSAR and optical correlation have largely disjoint sensitivity ranges for near-field Ridgecrest validation.Source: §2.2 · pp. 6–7, §2.3 · p. 7

2.3. InSAR and its large-gradient boundary

  • In Ridgecrest’s near field, InSAR cannot directly validate the optical result: decorrelation occurs along the rupture, while mid-field motion is below the optical noise floor.The paper relies on an independent field survey of surface offsets for near-field validation.Source: §2.3 · p. 7

2.4. Pushbroom geometry and jitter

  • For pushbroom jitter, the differential formulation represents per-line geometric offsets as a time-varying revisit offset whose identifiability comes from the displacement prior.This estimation view complements forward-model corrections of individual acquisitions.Source: §2.4 · p. 8

2.5. Differential vision metrology

  • The work carries close-range photogrammetry’s treatment of calibration and orientation as adjusted parameters with stated precision into satellite change measurement.It derives a prior-screened saturation effect for an along-track chain under satellite geometry and pushbroom line rate.Source: §2.5 · p. 8

3. Differential Model for Repeat-Pass Imaging

The model treats repeat-pass optical displacement as a differential estimation problem, jointly accounting for displacement, revisit bias, terrain error, and matching noise. Stable-area constraints and displacement priors help resolve the datum, while the prior also bounds along-track uncertainty and supports per-line jitter estimation.

3.1. Observation model

  • The observation model represents image-match differences using displacement, revisit-bias coefficients, DEM-height error, and matching noise, with terrain leakage propagated into the noise model.The empirical revisit-bias basis uses low-order image-coordinate polynomials plus per-line terms; its coefficients are not assigned individual orbital meanings.Source: §3.1 · pp. 8–9

3.2. Informed differential estimator

  • Revisit-bias coefficients and displacements are jointly estimated by a Gaussian-prior MAP model, whose posterior covariance provides displacement uncertainty.The displacement prior constrains inter-epoch change itself, a state unavailable to independent per-epoch position estimates.Source: §3.2 · p. 9

3.3. Immunity of per-orbit biases

  • Per-orbit offsets are assigned to revisit bias rather than displacement, but separation depends on stable-area references and displacement priors, and displacement aligned with the bias basis can be absorbed as offset.The paper therefore requires fitting the correction on stable ground only; without the reference and prior, the along-track mean is unidentifiable.Source: §3.3 · p. 10

3.4. Prior-screened along-track chain

  • A displacement prior makes along-track uncertainty saturate rather than accumulate along a settlement chain.In the weak-prior limit, the interior variance approaches v∞ ≈ σ0σd/2 and the correlation length is ℓc ≈ σd/σ0 segments; as σd grows without bound, the random walk is recovered.Source: §3.4 · p. 11

3.5. Pushbroom: the revisit offset becomes ξ(t)

  • For pushbroom imagery, a low-order or per-line revisit-offset function models time-varying attitude jitter, with the displacement prior providing identifiability.The paper reports that low-order offsets leak jitter, whereas per-line offsets hold the noise floor flat across jitter grades.Source: §3.5 · p. 11

4. Accuracy Envelope by Simulation

A first-order, single-component pushbroom simulation evaluates a five-part accuracy envelope.

4.1. E1. Immunity

  • Adding 5 m orbit, 10″ attitude, and 2″ drift yields an RMSE ratio of 0.989 [0.972, 1.002], statistically inseparable from unity.Source: §4.1 · p. 11

4.2. E2. Pushbroom ξ(t)

  • Per-line revisit offsets hold the along-track floor at 9.6 cm across 0.05″–1″ jitter; constant-plus-linear offsets leak jitter fully.Source: §4.2 · p. 12, Table 1 · p. 12

4.3. E3. Control-free margin

  • Without control, RMSE is 5.85 m versus 9.6 cm (62×); with eight anchors, absolute RPC correction is 79–81 cm versus 8–16 cm differential (5–10×).Source: §4.3 · p. 12

4.4. E4. Noise floor and DEM leakage

  • At 10 m GSD, 2σ minimum detectable deformation is 38 cm per component at one point and 2.7 cm for a jointly averaged 100-point patch.The patch figures assume independent matching noise across points and components; spatially correlated error and prior-induced shrinkage bias are excluded.Source: §4.4 · p. 12
  • A 5° cross-view pair with a 10 m DEM leaks 87 cm per point; cross-view pairs require increasingly accurate elevation data as view-angle difference increases.Source: §4.4 · p. 12

4.5. E5. Engineering ladder and the observability boundary

  • The L2 informed estimator matches the destriping ladder on sparse deformation and outperforms it on dense, large-scale fields; dense smooth along-track mean remains unidentifiable without control.In that dense-field case, both methods return the RMS signal amplitude as error.Source: §4.5 · p. 13, Table 2 · p. 13
  • In the chain regime, error is flat when displacement-prior scale is [0.5, 2]× the true magnitude; tightening to 0.1× costs 2.45×, while loosening to 10× raises error 1.7×.Source: §4.5 · p. 13

5. Real-Data Validation

Three control-free cases test complementary conditions: stable terrain at Ridgecrest, cross-view geometry at Kahramanmaraş, and a moving-majority glacier scene with limited stable terrain at Baltoro. Across these cases, measured floors, field comparisons, and closure tests assess the accuracy envelope and the estimator’s behavior under each condition.

5.1. Ridgecrest 2019: 10 m, coseismic, no control

  • 0.48–0.54 m (0.05 pixel) was the Ridgecrest informed-estimator floor, statistically equal to the 0.51 m destriping floor and within a factor of 1.3 of the predicted 0.38 m.The measured match noise was 0.05 pixel, better than the simulation’s conservative 0.1-pixel assumption.Source: §5.1 · pp. 14–15

5. Real-Data Validation

  • A Ridgecrest closure ratio of 0.60 implies approximately 88% of pair-error variance is scene-associated; ITS_LIVE triplets independently give a 0.61 ratio in both components.The archive analysis used 25,354 closed triplets, supporting the same scene-error pattern in an operational velocity product.Source: §5.1 · p. 15, §5.3 · p. 19

5.1. Ridgecrest 2019: 10 m, coseismic, no control

  • Two-band redundancy calibrated empirical single-band uncertainty across correlation-quality bins, spanning 0.25–1.39 m, with a plateau and decorrelation knee rather than a universal power law.The authors frame this as a pair-specific calibration procedure for converting correlation quality into per-point standard deviation.Source: §5.1 · p. 16, Figure 4 · p. 19

5.2. Kahramanmaraş 2023: 0.52 m, cross-view

  • 0.27 pixel across-look versus 1.73 pixel along-look shows strongly anisotropic noise in the Kahramanmaraş cross-view pair; height regression removes only 2% of the excess.The residual is attributed to look-direction resolution degradation and is uncorrectable by a DEM; the authors recommend same-view pairing for sub-meter measurement.Source: §5.2 · pp. 16–17

5.3. Baltoro glacier 2024: 10 m, flow regime, three-scene triplet

  • The Baltoro 10-day pair’s 0.47 m bedrock floor accompanied centerline speeds tracking the ITS_LIVE autumn median, with a 15% median relative difference over the trunk.The comparison spans 50–118 m yr−1 for this work versus 38–120 m yr−1 for ITS_LIVE; trunk structure was resolved in a single pass.Source: §5.3 · p. 19
  • The 13 October snowfall scene raised pair noise floors to approximately 1.3–1.9 m and biased accumulation-zone speeds, so the 10-day pair excluding it is primary.Bright-snow area was 19% for that scene versus 9% for the others; scene statistics can flag this baseline-design issue before correlation.Source: §5.3 · p. 20
  • The 2025 persistence forecast’s trunk-speed difference had a 28 m yr−1 MAD, below the 37 m yr−1 expected from the two measurement floors; the forecast held within measurement noise.The median speed ratio of 0.86 is not claimed as a slowdown because a shared systematic of that size cannot yet be excluded from two seasons.Source: §5.3 · p. 21

6. Limits of destriping and benefits of the displacement prior

The section tests how displacement priors change destriping’s dependence on stable terrain, separating matching-kernel effects from geometric correction and evaluating injected truth, natural cut-outs, and automatically set priors.

6.1. Kernel versus post-processing

  • Across three window-correlation kernels, noise floors vary within a factor of 1.3, while post-processing changes the signal by a factor of two.On Baltoro, full-field destriping gives 58 m yr−1 versus 106 m yr−1 for the masked estimator with the same kernel; strong prefiltering lowers the floor but attenuates the signal.Source: §6.1 · pp. 22–23, Table 4 · p. 23

6.2. Thinning the stable area: explain, then improve

  • With five stable tiles, Baltoro trunk speed is 1251 m yr−1 under destriping versus 87 m yr−1 with the informed estimator.With all 54 bedrock tiles, destriping returns 106 m yr−1; the informed estimator returns 86 m yr−1 even with no stable tile, against an ITS_LIVE reference of 90–120.Source: §6.2 · p. 24, Figure 8 · p. 25

6.3. Controlled truth: injected deformation on a real background

  • For injected strip-aligned deformation, a 20 m unknown-tile prior gives 1.14–1.30 m RMSE versus 0.74–0.80 m; an uninformative prior of at least 50 m removes the loss.For a smooth field, destriping RMSE rises to 2.5–2.8 m as stable tiles are thinned, while the informed estimator holds at 1.19 m; the prior therefore trades signal absorption against regularization.Source: §6.3 · pp. 24–25, Table 5 · p. 26

6.4. Natural cut-outs: two seasons, two scenes

  • On 2025 bedrock-free Baltoro windows, automatic-prior shape RMS is 0.34–0.83 m versus 0.85–1.22 m for destriping; at 24 km on Ridgecrest, destriping is equal or better.In the original Baltoro cut-outs, the informed estimator returns trunk speeds of 82–95 m yr−1 in corner-bedrock windows, while plane-plus-strip destriping gives 337–778 m yr−1.Source: §6.4 · pp. 26–27, Figure 9 · p. 27

6.5. Priors by rule, not by hand

  • The offset-only empirical-Bayes rule matches hand-set controlled-truth results within 0.05–0.2 m and keeps the Ridgecrest floor at 0.50–0.57 m as destriping rises to 1.31 m.On the Ridgecrest headline pair, the automatic informed floor is 0.48–0.54 m, statistically similar to destriping; on Baltoro, robust weighting costs about 20% of trunk speed at five stable tiles.Source: §6.5 · pp. 27–28

Identifiability limits and the strict-hybrid estimator.

The estimator matches destriping where the problem is identifiable, but unsupported strips leave strip-aligned deformation to the prior; a strict hybrid and joint network solution address distinct aspects of that boundary.

Identifiability limits and the strict-hybrid estimator.

  • On unsupported strips, strip-aligned deformation is indistinguishable from revisit offset, so the outcome is decided by the prior alone.The injected band favors destriping at 0.80 m versus 1.33 m, while real Baltoro strips favor the informed estimator at 87 versus 1251 m yr−1.Source: Identifiability limits and the… · p. 28
  • The strict hybrid reproduces destriping where supported and applies the prior only to the unsupported remainder, lifting Baltoro estimates when destriping fails.At five stable tiles it returns 92 m yr−1 versus destriping’s 1251; it also inherits destriping’s clustered-plane and noisy-strip-median failure modes.Source: Identifiability limits and the… · p. 29

6.6. From pairs to a network

  • Jointly solving triplet displacements with exact closure reduces Ridgecrest held-out noise floors by 4–10% but produces no measurable reduction for Baltoro.The primary benefit is consistency: each interval has one displacement field, and added epochs, control observations, or InSAR measurements can enter as observation equations.Source: §6.6 · p. 29

Positioning against InSAR and offset tracking.

The differential model complements InSAR in large-gradient optical-offset settings, but its contribution is not an unconditional single-pair accuracy gain.

Positioning against InSAR and offset tracking.

  • InSAR is most effective for small deformation over coherent terrain, while differential optical measurement addresses large gradients and low radar coherence.Source: Positioning against InSAR and offset… · p. 29
  • The differential model is not an unconditional improvement in single-pair accuracy; for Ridgecrest, the two approaches agree within observed scatter.Source: Positioning against InSAR and offset… · p. 30
  • The model supplies a predictive error budget and pair-specific matching-uncertainty calibration, with a simulated 2σ minimum detectable displacement of 0.38 m at 10 m GSD.For Ridgecrest, stable-area MAD noise floors are 0.51 m for destriping and 0.48–0.54 m for the informed estimator under the automatic prior rule.Source: Positioning against InSAR and offset… · p. 30

Honest boundaries..

The paper identifies boundaries on what its validation establishes and outlines extensions toward multi-year monitoring and an operational product.

Honest boundaries..

  • The sub-meter envelope is verified across-look for one cross-view pair; the along-track mean of dense deformation remains unobservable without ground control or joint InSAR inversion.The reported Sentinel-2 North floors are upper bounds because the per-line revisit-offset basis omits detector-module offsets.Source: Honest boundaries · p. 30

Outlook: from single pairs to a monitoring instrument.

  • The outlook proposes multi-year glacier series, vertical-change estimation, added sensor resolutions, and optical–InSAR fusion using per-point posterior uncertainty.The multi-year Baltoro triplet covers one season; attributing velocity changes to climate requires a mass-balance model.Source: Outlook: from single pairs to a… · p. 31

From first examples to an operational product.

  • An operational product requires sensor-specific per-line attitude models, DEM-coupled cross-view geometry, and populated per-sensor parameter tables.The measured six-fold anisotropy quantifies the cross-view geometry error these steps must address.Source: From first examples to an operational… · p. 31

8. Conclusion

The conclusion presents control-free differential estimation as a framework for optical deformation measurements with quantified uncertainty and tested limits. The study’s public imagery and reference datasets support reproduction, while scripts and experiment logs are available on request.

8. Conclusion

  • The formulation estimates deformation without surveyed control, validates predicted noise floors across three real-data cases, and identifies dense-field mean along-track displacement as unobservable without added information.The experiments also validate closure-based error decomposition, pair-specific uncertainty calibration, cross-view geometry effects, and agreement with ITS_LIVE glacier velocities.Source: §8 · p. 32

Data and code availability

  • Imagery and reference datasets are publicly accessible, and processing scripts and experiment logs are available from the corresponding author upon reasonable request.The scripts regenerate each main-text real-data figure.Source: Data and code availability · pp. 32–33

S1. Uncertainty calibration on four scene pairs

The supplement reports scene-specific uncertainty calibration, explains why the intraseasonal glacier analysis supports no deceleration conclusion, and adds tests at 2 m and 0.45 m resolution.

S1. Uncertainty calibration on four scene pairs

S2. Why the intraseasonal analysis is not reported

  • Intraseasonal trunk-velocity estimates vary by up to a factor of two across 5-, 10-, and 15-day intervals, with 0.5–1 m residual coregistration offsets leaking into displacement estimates.With only 54 usable bedrock tiles, weakly determined corrections make formal uncertainty understate actual error by about an order of magnitude; no intraseasonal deceleration conclusion is drawn.Source: S2. Why the intraseasonal analysis is… · pp. 41–42

S3. Additional sensors at 2 and 0.45 m resolution

  • At 2 m resolution, the CBERS-04A dune-field noise floor is 0.13–0.20 m, and the estimated migration azimuth is 220° versus 225° expected from trade winds.The Sentinel-2 pair over the same window gives an azimuth of 209°.Source: S3. Additional sensors at 2 and 0.45 m… · p. 42, Figure S3 · p. 42
  • At 0.45 m resolution, the same-view GeoEye-1 null pair has directional noise floors of 0.30 and 0.36 pixels and an anisotropy ratio of 1.21.The evaluated resolutions are 0.45, 0.52, 2, and 10 m; the 16 m wide-swath class remains unevaluated.Source: S3. Additional sensors at 2 and 0.45 m… · p. 42

S4. Simulation protocol and complete results

The supplement documents the simulation setup and reproducibility materials, then examines prior sensitivity and comparisons using image subsets and alternative prior choices.

S4. Simulation protocol and complete results

  • The simulation envelope uses 40 trials, 2,000 bootstrap resamples per statistic, a 20 × 20 ground grid, and matching noise of 0.1 px.The protocol also specifies a 500 km altitude, 5 cm baseline orbit error, 2″ attitude, 1″ per-epoch drift, 0.2″ line jitter, and 10 m DEM error.Source: S4. Simulation protocol and complete… · p. 43

S5. Reproducibility

  • The real-data figures can each be regenerated with a corresponding script, and experiment logs record prespecified criteria and corrections, including withdrawn claims.Scripts and logs are available from the corresponding author upon reasonable request.Source: S5. Reproducibility · p. 43

S6. Sensitivity to the prior scale

  • Baltoro trunk median velocity is 82–85 m yr−1 at σd = 4 m, 85–89 m yr−1 at σd = 20–30 m, and 96–135 m yr−1 at σd = 100 m.A prior scale of approximately ten times the expected displacement compromises between deformation attenuation and insufficient regularization.Source: S6. Sensitivity to the prior scale · p. 44

S7. Natural image subsets from a second season and a coseismic scene

  • Table S7 evaluates natural cut-outs without thinning and automatic priors against full-scene masked solutions using trunk median or cross-fault step and shape RMS difference.The caption identifies Baltoro 2025 AB and Ridgecrest B04 as the two comparisons.Source: Table S7 · p. 45

S8. Comparison of manually and automatically selected priors

  • For Ridgecrest B04, the cross-fault step is +3.16 m with destriping, +2.50 m with hand-set priors, and +3.14 m with automatic priors.Table S8 compares hand-set and automatic priors across prior-constrained experiments.Source: Table S8 · p. 46

S9. Triplet adjustment with a closure constraint

Across S9–S11, the analyses distinguish held-out automatic-prior statistics from main-text closure statistics, specify the strict-hybrid comparison, and test correction behavior on a zero-deformation CBERS-04A scene. In that scene, full-field and stable-terrain masked corrections agree closely, while destriping performance depends on sensor-specific strip geometry.

S9. Triplet adjustment with a closure constraint

  • Held-out automatic-prior statistics use held-out halves of the stable set, unlike main-text closure statistics, which use the full stable set and baseline estimator.Table S9 reports floors and closure values as Gaussian-scaled MADσ of the fault-parallel component on held-out stable tiles.Source: S9. Triplet adjustment with a closure… · p. 47, Table S9 · p. 47

S10. Strict hybrid estimator

  • The strict hybrid is compared with masked destriping and the fully prior-constrained estimator with automatic priors on the same experiments and metrics.The hybrid applies masked destriping on supported strips and, when stable tiles span the window, the plane; informed priors are used only on unsupported strips.Source: Table S10 · p. 48

S11. Zero-deformation control for CBERS-04A imagery

  • The CBERS-04A control uses a 22×22 km savanna-and-cropland window; 33.4% of nodes yield valid offsets, and 19,606 stable nodes are held out after a random split.The window is 98.6% clear in both epochs; matching uses 64-pixel chips and a 32-pixel step.Source: S11. Zero-deformation control for… · p. 49
  • The 2 m floors are 0.065–0.085 px on dunes and 0.081–0.156 px in the adjacent scene, both within the predicted 0.04–0.27 px band.The roughly twofold scene-to-scene spread motivates an accuracy envelope expressed as a band rather than a single value.Source: S11. Zero-deformation control for… · pp. 49–50
  • 0.179 and 0.180 pixels are the noise floors for the full-field and stable-terrain masked corrections, which agree within 0.001 pixels.The experiment has no measurable deformation and sufficient stable terrain; 58 of 60 along-track strips contain at least three valid nodes.Source: S11. Zero-deformation control for… · p. 49, Table S11 · p. 50
  • 7.5° explains 84% of detrended residual variation, while destriping at the Sentinel-2 azimuth of 12° incurs about a 30% floor penalty.The reported floors are 0.250/0.467 m at the Sentinel-2 azimuth and 0.162/0.311 m at the estimated azimuth.Source: S11. Zero-deformation control for… · p. 49, Figure S11 · p. 50
Loading 2609.29550v1…