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TRACE: Learning to Self-Calibrate Wireless Digital Twins from ISAC Measurements

Saad Masrur, Saeed R. Khosravirad, Ismail Guvenc

arXiv:2609.32923v2cs.AIeess.SP

TL;DR

Imperfect map-derived geometry can make a wireless digital twin misrepresent the physical environment, and prior approaches do not directly repair a known approximate twin from network RF. TRACE aligns measured and twin-rendered RF and learns gated building-level residual updates. It reduces simulated position error and transfers to measured NIST RF without measured-data fine-tuning.

  • Problem

    Wireless learning depends on environmental representations that may not match the physical scene, while existing approaches do not directly correct an approximate twin with known buildings from its RF disagreement.

    Source: §1 · pp. 1–2

  • Method

    TRACE backprojects measured and twin-rendered RF into a common frame, extracts building-centered GeoCrops, and predicts gated geometric residuals for the existing twin.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    TRACE reduces 3D position RMSE from 2.202 m to 0.302 m on unseen simulated scenes and mean planar wall-position error from 1.00 m to 7.8 cm on measured NIST RF.

    Source: §6.4 · p. 9, §8 · p. 10

  • Takeaways & Limitations

    The results show that disagreement between measured and twin-rendered RF can provide evidence for updating an imperfect digital twin.

    Source: §8 · pp. 9–10

    TRACE assumes buildings to be corrected already exist in the twin and evaluates rectangular buildings, leaving other static and dynamic objects for future work.

    Source: §7 · p. 9

Abstract

from arXiv · show

Wireless digital twins (DTs) rely on 3D environment models to predict radio propagation and support wireless-network decisions, yet these models are often initialized from imperfect 3D maps. Errors in building position, height, footprint, and orientation can therefore cause a high-fidelity propagation engine to simulate the wrong physical environment. In this paper, we study how a deployed wireless network can repair an existing DT using its own radio frequency (RF) measurements. In particular, we introduce Twin Residual Alignment and Calibration Engine (TRACE), a physics-grounded learning-based self-calibration framework that treats twin maintenance as residual alignment between the physical world and the current DT. Using the same sensing configuration as the physical measurements, TRACE ray-traces the current DT, coherently backprojects the measured and simulated RF onto a common world grid, and extracts the same local region around each building's current DT position. A multi-view corrector then fuses evidence across sensing nodes and neighboring buildings to predict a gated six-parameter correction per building, without relying on absolute layout or sensor ordering, and supports iterative correction through re-rendering. On 5,400 held-out samples from unseen simulated scenes at 28 GHz, TRACE reduces 3D position RMSE from 2.202 m to 0.302 m and yaw RMSE from 4.978{\deg} to 0.894{\deg}, outperforming ViT and U-Net baselines under changes in layout, building count, sensing-node count, and SNR. On measured 28 GHz RF data from the NIST outdoor courtyard, a model trained only on synthetic RF reduces mean planar wall-position error from 1.00 m to 7.8 cm, without measured-data fine-tuning or geometric labels. These results show that the discrepancy between measured and twin-rendered RF can serve as a learning signal for repairing a wireless DT.

1 INTRODUCTION

Wireless predictions depend on environmental geometry, but outdoor digital twins derived from maps can differ from the physical scene. TRACE treats maintenance as correcting known buildings in an existing twin from the disagreement between measured and simulated RF.

1 INTRODUCTION

  • Imperfect environmental representations can misstate radio propagation and downstream predictions because geometry supplies spatial context for wireless learning.Outdoor map-derived twins can contain footprint offsets and missing height tags; geometric errors can distort signal strength, delay, and link reliability.Source: §1 · pp. 1–2
  • Existing approaches either make forward predictors tolerate inaccurate geometry or infer scene structure, leaving correction of a known, approximate twin as a distinct problem.TRACE calls this residual twin maintenance: the network and twin observe the same ISAC acquisition, and their RF disagreement supplies evidence for geometric error.Source: §1 · p. 2
  • TRACE combines world-frame backprojection and building-centered GeoCrop with a multi-view corrector to update an existing twin across layouts and varying building counts.The corrector predicts gated six-parameter building corrections without fixed sensor or building slots.Source: §1 · p. 2

2 RELATED WORK

Prior wireless methods use environmental geometry as a conditioning representation, while RF-based geometry recovery and optimization address related inverse problems. TRACE instead learns residual updates to a known approximate building-level twin.

2 RELATED WORK

  • Wireless prediction methods condition on environmental geometry, implicitly or explicitly, while generally assuming that the environment representation is sufficiently accurate.Examples include geometry-conditioned path-loss methods, learned scene fields, ray-surface interactions, point clouds, and mesh representations.Source: §2 · p. 3
  • RF-based scene recovery and differentiable-rendering approaches infer or optimize geometry, whereas TRACE starts from known building correspondences and predicts residual updates to that existing twin.TRACE learns a reusable corrector rather than solving a new optimization problem for each deployment.Source: §2 · p. 3
  • Geometric RF signatures depend on sensing viewpoint: lateral shifts can be hard to infer near boresight, while radial shifts appear more directly in delay.Even displacements up to 4 m leave physical and stale-twin channels 96.5% coherent, motivating phase-preserving processing and complementary views.Source: §2 · p. 3

3 RESIDUAL TWIN MAINTENANCE

TRACE represents each known building with a six-parameter state and estimates the residual needed to align the current twin with the physical scene. It compares RF measured and ray-traced under the same sensing configuration, then applies gated updates that can be re-rendered iteratively.

3 RESIDUAL TWIN MAINTENANCE

  • Each building state contains its center coordinates, height, footprint dimensions, and yaw, and the complete twin is the set of these building states.The physical scene uses the same representation; TRACE estimates per-building corrections rather than reconstructing it from scratch.Source: §3 · p. 3
  • For each sensing node, TRACE compares measured complex CSI with CSI ray-traced from the current twin under the same known sensing configuration.Using the same configuration makes the RF responses directly comparable, so their mismatch provides the geometric-correction signal.Source: §3 · p. 3
  • Coherent backprojection places measured and simulated RF on a shared world grid at multiple focus heights, aligning evidence from different sensing nodes in physical coordinates.The learned corrector uses these maps and the current twin state to predict a gate and raw residual; the applied correction is their product.Source: §3 · pp. 3–4
  • After applying an update, TRACE re-renders the corrected twin so the same correction rule can be applied iteratively.Because each prediction becomes the next input, stable closed-loop correction depends on avoiding scene- or sensor-specific shortcuts.Source: §3 · p. 4

4 TRACE

TRACE uses a deterministic RF-alignment front end and a learned multi-view corrector. It compares local measured and twin-rendered RF evidence, combines sensing-node and building context, and predicts gated geometric updates.

4 TRACE

  • Only the corrector is learned; ray tracing, backprojection, and GeoCrop deterministically form paired building-centered RF inputs for gated six-parameter updates.The front end registers both RF branches in a common world frame before extracting each building’s GeoCrops.Source: §4 · p. 4

4.1 DETERMINISTIC FRONT END

  • Coherent backprojection focuses complex measurements at candidate world points by compensating expected propagation delays and summing them, registering RF observations spatially.Applying it to both branches and all nodes on a common metric grid at multiple heights preserves height-dependent structure and phase.Source: §4.1 · p. 4
  • GeoCrop extracts matched measured and simulated RF windows centered on each building’s current twin position, making displacement, resizing, or rotation appear as local mismatch.The crop uses the current twin position, not the unknown true position, and avoids exposing absolute scene layout to the corrector.Source: §4.1 · p. 5

4.2 THE LEARNED CORRECTOR: FOUR DESIGN DECISIONS

  • The corrector preserves complex RF cues, compares measured tokens with rendered tokens, and fuses complementary sensing-node views as an unordered set.Pose conditioning supports viewpoint-dependent cues; geometry-aware attention uses relative building arrangements while excluding absolute coordinates.Source: §4.2 · p. 5

4.3 GATED RESIDUAL HEAD AND TRAINING

  • A gate determines whether to apply the predicted six-parameter residual; training uses MSE for residual correction and binary cross-entropy for the gate.The gate suppresses unnecessary updates when measured RF is already consistent with the current twin.Source: §4.2 · p. 5, §4.3 · pp. 5–6

5 EXPERIMENTAL SETUP

The evaluation uses synthetic 28 GHz scenes to test correction under scene and sensing shifts, plus measured NIST courtyard RF to assess transfer without measured-data training.

5 EXPERIMENTAL SETUP

  • The synthetic benchmark uses three separated rooftop monostatic sensing nodes, 8 × 8 arrays, and 122.88 MHz bandwidth at 28 GHz.Physical-scene variation and twin corruption are generated separately; receiver noise is added only to the physical branch.Source: §5 · p. 6
  • Testing uses 5,400 scene-disjoint samples and evaluates transfer without retraining across unseen layouts, building counts, SNR, out-of-range errors, and changed sensing-node poses.Building counts are 4, 8, and 10 versus 6 in training; SNR ranges from −5 dB to 20 dB.Source: §5 · p. 6
  • For measured-data evaluation, the frozen corrector is trained only on synthetic courtyard RF pairs and tested with measured 28 GHz NIST RF against a corrupted Sionna twin.The physical branch uses measured RF; the twin branch is ray-traced under the same acquisition configuration, and LiDAR supplies reference geometry for construction and evaluation.Source: §5 · p. 6
  • The corrupted twin is the no-correction reference, and full-scene ViT and U-Net baselines use the same splits, noise model, targets, loss, and schedule.Evaluation reports per-parameter RMSE and the percentage of initial error removed.Source: §5 · p. 6

6 RESULTS

TRACE’s building-centered RF representation generalizes across layouts, and its complete corrector outperforms full-scene baselines. Tests of RF inputs, sensing shifts, and measured courtyard data show correction across varied conditions and downstream beam-selection benefits.

6.1 THE RF REPRESENTATION DESIGN AND CORRECTION PERFORMANCE

  • TRACE lowers 3D position RMSE from 2.202 m to 0.302 m and yaw RMSE from 4.978° to 0.894°, outperforming full-scene ViT and U-Net baselines.Against the stronger U-Net, TRACE further reduces residual RMSE by 62.9% in position, 65.5% in height, and 75.9% in yaw.Source: Table 2 · p. 7, §6.1 · p. 7
  • With BP+GeoCrop, layout-shifted 2D RMSE is 0.213 m versus 0.205 m on standard scenes, while raw CSI reaches 2.111 m OOD-Layout RMSE.World-frame backprojection registers measured and rendered RF; GeoCrop extracts matched building-centered regions, reducing the layout shortcut.Source: §6.1 · pp. 6–7, Table 1 · p. 7

6.2 THE CORRECTOR USES THE INTENDED PHYSICAL EVIDENCE

  • Blinding either RF branch raises 3D position RMSE from 0.302 m to 0.835 m with only Ireal and 2.63 m with only Itwin; blinding both yields 2.46 m.Shuffling Ireal across scenes raises RMSE to 3.723 m, worse than the 2.202 m uncorrected twin, while shuffling Itwin yields 0.889 m.Source: §6.2 · pp. 7–8, Table 3 · p. 7

6.3 TRACE GENERALIZATION ACROSS SCENE COMPLEXITY AND SENSING CONDITIONS

  • Without retraining, TRACE removes 80.1%–86.3% of initial error across tested building counts and 52.8% at −5 dB, while U-Net and ViT worsen the twin at that SNR.With one sensing node, TRACE removes 71.8% of initial error, exceeding U-Net with all three nodes at 61.6%.Source: §6.3 · p. 8, Figure 3 · p. 8
  • For errors beyond the training range, one pass removes 79.2% of initial 3D position error, rising to 93.1% after re-rendering and applying the frozen corrector again.Separated sensing nodes provide complementary views that TRACE preserves and fuses per building.Source: §6.3 · p. 8

6.4 TRACE EVALUATION ON REAL 28 GHZ MEASUREMENTS AND DOWNSTREAM TASKS

  • On measured NIST 28 GHz RF, TRACE reduces mean planar wall-position error from 1.00 m to 7.8 cm without measured-data training or fine-tuning.Across 100 samples, 69% of estimates are within 10 cm and 84% within 15 cm of the LiDAR reference.Source: §6.4 · p. 9, Figure 4 · p. 9
  • At the 4 m mean OSM footprint offset, TRACE correction raises P10 beam-selection spectral-efficiency retention from 14% to 61%.As geometric error increases from 1 m to 6 m, corrupted-twin retention falls from 81% to 9%, while corrected-twin retention is 60–67% at 4 m to 6 m.Source: §6.4 · p. 9, Figure 4 · p. 9

7 DISCUSSION AND LIMITATIONS

TRACE corrects existing buildings but does not add missing buildings or remove obsolete ones; the experiments use rectangular buildings and leave other static and dynamic objects for future work.

7 DISCUSSION AND LIMITATIONS

  • TRACE assumes buildings to be corrected already exist in the twin, and the experiments cover rectangular buildings rather than bridges, vegetation, vehicles, or pedestrians.It therefore cannot add a missing building or remove one that no longer exists.Source: §7 · p. 9

8 CONCLUSION

The conclusion summarizes TRACE’s approach to repairing imperfect wireless digital twins by aligning measured RF with twin simulations and using relative building geometry to predict gated updates. It also highlights complex RF backprojection, which improves geometric calibration over amplitude-only input and uses phase to provide sensitivity to small displacements.

8 CONCLUSION

  • On unseen simulated scenes, TRACE reduces 3D position RMSE from 2.202 m to 0.302 m; on measured 28 GHz NIST RF, it reduces mean planar wall-position error from 1.00 m to 7.8 cm.The measured-data model is trained entirely on synthetic data, without measured-RF fine-tuning; corrected geometry also improves downstream beam selection. The simulated-scene result removes 86.3% of the initial error.Source: §8 · p. 10

A PROBLEM FORMULATION AND NOTATION

  • TRACE compares measured and twin-rendered RF under matched acquisition settings, backprojects both onto a shared world grid, and extracts building-centered GeoCrops to expose local misalignment.The residual is defined per building and assumes correspondence between twin and physical-scene elements; structures present in only one fall outside the formulation.Source: A PROBLEM FORMULATION AND NOTATION · pp. 12–14

B REPRESENTATIVE SCENE, WORLD-FRAME BACKPROJECTION, AND GEOCROP

  • Multiple sensing viewpoints provide complementary RF evidence, while stacking backprojections at several focus heights exposes how a building’s response changes with height.Each node’s GeoCrop selects the same physical region, but visibility and occlusion make some views weak or ambiguous; crops use the current twin position, not ground truth.Source: B REPRESENTATIVE SCENE, WORLD-FRAME… · pp. 14–15

C.1 PAIRED INPUTS AND THE COHERENT RESIDUAL STREAM

  • For each building-node pair, TRACE supplies measured, rendered, and explicit residual GeoCrops to a shared complex encoder that preserves phase and supports varying building counts.Weight sharing lets the same checkpoint process four-, eight-, and ten-building scenes without modification.Source: §C.1 · pp. 15–16, §C.2 · p. 16

C.3 SENSOR-POSE FILM

  • Sensor-pose FiLM conditions a shared encoder on node position and orientation rather than a fixed sensor index, allowing different node counts and previously unseen sensing poses.The modulation begins at identity, then learns viewpoint dependence during training.Source: §C.3 · p. 16

C.4 REAL-TO-TWIN DISCREPANCY ATTENTION

  • Real-to-twin attention first compares tokens from the same building and viewpoint, then CueFusion preserves raw evidence alongside attention and both feature-space and coherent residual cues.The local comparison uses the noiseless rendered branch as a template for the noisy measured branch; the multiple comparison routes are deliberate.Source: §C.4 · p. 17, §C.5 · p. 17

C.6 CROSS-SENSOR FUSION

  • Cross-sensor fusion jointly attends to a building’s discrepancy tokens across nodes without sensor-index embeddings, making the output independent of node presentation order.Random sensing-node subsets are used during training so reduced node sets are in distribution.Source: §C.6 · p. 17

C.7 CURRENT SHAPE PRIOR

  • A current-shape prior adds the twin’s non-location geometry to the sensing-aggregated token, using double-angle yaw encoding to represent rectangular-footprint symmetry.Absolute map coordinates are excluded from this pathway.Source: §C.7 · p. 18

C.8 RELATIVE-GEOMETRY BUILDING ATTENTION

  • Relative-geometry building attention makes scene representations invariant to shared translations, reducing location-specific memorization and supporting generalization to unseen arrangements.The attention stage uses pairwise relative geometry rather than absolute scene coordinates.Source: §C.8 · p. 18

C.9 GATED PREDICTION HEADS AND SUB-PIXEL CORRECTION

  • TRACE’s gate applies corrections only where needed and suppresses unnecessary updates to buildings that are already well aligned.The movement and regression heads use the same token, and the gate is evaluated in soft form.Source: §C.9 · p. 19

D PRESERVING THE COMPLEX RF RESPONSE

  • 0.302 m versus 0.350 m 3D position RMSE shows complex backprojection outperforms amplitude-only input, reducing remaining error by 13.7%.The comparison holds the rest of the pipeline fixed on the scene-disjoint test split.Source: D PRESERVING THE COMPLEX RF RESPONSE · p. 19, Table 5 · p. 19
  • At 28 GHz, phase changes with round-trip path length at a wavelength of about 1.07 cm, making it sensitive to fractional-wavelength displacements where magnitude may barely change.This phase sensitivity is useful once the twin is already approximately right, when magnitude is least informative.Source: D PRESERVING THE COMPLEX RF RESPONSE · p. 19

E EFFECT OF THE NUMBER OF BACKPROJECTION FOCUS HEIGHTS

The section tests whether multiple backprojection focus heights improve geometric correction by withholding planes at test time from models trained with all six. More heights improve accuracy, with the largest effect on building height.

E EFFECT OF THE NUMBER OF BACKPROJECTION FOCUS HEIGHTS

  • Models are trained with all six planes, then evaluated with frozen weights while unavailable planes are zeroed; performance averages all subsets at each size.This keeps the model architecture and learned weights unchanged as available focus heights vary.Source: E EFFECT OF THE NUMBER OF… · pp. 19–20, Table 6 · p. 20
  • TRACE mean 3D position RMSE falls from 1.489 m with one focus height to 0.302 m with all six; U-Net and ViT follow the trend but finish substantially higher.The model is trained with all six heights and evaluated with frozen weights; results average subsets of each size.Source: Table 6 · p. 20, E EFFECT OF THE NUMBER OF… · p. 20, Figure 6 · p. 20
  • Building-height RMSE drops from 1.268 m with one focus plane—slightly worse than the 1.151 m uncorrected twin—to 0.221 m with six.The largest benefit from additional heights appears in building-height estimation.Source: E EFFECT OF THE NUMBER OF… · pp. 20–21
  • Planar position RMSE improves from 0.720 m with one focus height to 0.205 m with six, a smaller change than height error.Source: E EFFECT OF THE NUMBER OF… · p. 21

F COMPARISON OF TRACE WITH CLASSICAL BASELINES

TRACE outperforms training-free registration and remains effective across component ablations, changing sensing conditions, and unseen sensing poses. Its paired building-centered RF representation and learned multi-view corrector support these results, though the cross-sensor ablation also changes model capacity.

F COMPARISON OF TRACE WITH CLASSICAL BASELINES

  • TRACE reduces 2D position error to 0.206 m, removing 89.0%, while phase correlation increases error from 1.878 m to 1.925 m and NCC removes 4.0%.The registration methods use the same building-centered regions but collapse complex RF to power images; phase correlation returns a median 0.20 m shift for displaced buildings needing a median 3.16 m correction. Per-scene renderer optimization also faces visibility changes and a highly non-convex discrepancy at 28 GHz.Source: F COMPARISON OF TRACE WITH CLASSICAL… · pp. 21–22, Table 7 · p. 22

G COMPONENT ABLATIONS AND MODEL DESIGN

  • Removing any single learned-corrector component increases error; without the most costly component, TRACE still removes 83.0% of initial 3D error, versus 61.6% for U-Net and 26.4% for ViT.The ablations retain the same front end and retrain each variant from scratch.Source: G COMPONENT ABLATIONS AND MODEL DESIGN · p. 22

G.1 CROSS-SENSOR FUSION

  • Removing cross-sensor attention raises 3D position RMSE from 0.302 m to 0.375 m, a 23.8% increase, the largest component-ablation degradation.The ablated model has 2.93 M parameters versus 3.98 M for TRACE, so the comparison does not fully isolate fusion from model capacity; the error gap also widens as sensing conditions become harder.Source: §G.1 · pp. 22–23, Table 8 · p. 23

G.2 MOVEMENT GATE

  • Removing the movement gate increases 3D position RMSE from 0.303 m to 0.332 m, a 9.6% increase, as unnecessary updates are no longer suppressed.The comparison retains the movement head and training signal, isolating use of the gate at inference.Source: §G.2 · p. 23

G.3 SENSOR-POSE FILM AND COMPLEMENTARY COMPARISON PATHS

  • Removing sensor-pose FiLM raises 3D position RMSE from 0.303 m to 0.317 m, while removing the coherent residual stream or real-to-twin attention raises it to 0.315 m or 0.310 m.FiLM conditions a shared encoder on sensing-node position and orientation; the two comparison paths overlap with other available cues, so removing either alone has a small effect.Source: §G.3 · pp. 23–24

G.4 REPLACING THE ATTENTION-BASED CORRECTOR WITH A U-NET

  • At −5 dB, TRACE with the attention-based corrector removes 52.8% of initial 3D position error, twice the 25.6% removed by a U-Net using the same GeoCrop front end.At high SNR, the GeoCrop U-Net already removes most of the error; the gap widens as SNR decreases.Source: §G.4 · p. 24, Table 9 · p. 24

G.5 GENERALIZATION TO UNSEEN SENSING POSES

  • Under the tested sensing-pose perturbations, frozen TRACE removes at least 79.6% of initial 3D position error, versus 54.8% for U-Net and 18.1% for ViT.The worst case is a 38 m displacement stress test; in the worst rotation/tilt condition, TRACE reaches 0.407 m RMSE, below U-Net’s 0.846 m nominal-pose error.Source: §G.5 · p. 24, Table 10 · p. 25

G.6 PERMUTATION INVARIANCE

  • Across all six input permutations of three sensing nodes, TRACE’s output is unchanged to three decimal places.Shared node encoding, pose conditioning through FiLM, and permutation-invariant pooling make predictions independent of node order.Source: §G.6 · pp. 24–25

H ADDITIONAL FALSIFICATION RESULTS

Input blinding tests whether the corrector depends on paired measured and twin-rendered RF evidence. The reported footprint and yaw results show substantially lower errors with both branches than with either branch alone.

H ADDITIONAL FALSIFICATION RESULTS

  • With both RF branches, footprint length, footprint width, and yaw RMSE are 0.273 m, 0.260 m, and 0.894°; measured-RF-only errors rise to 0.600 m, 0.615 m, and 5.30°.Figure 7 shows results across geometric parameters; 3D position is reported separately in Sec. 6.2.Source: Figure 7 · p. 25, H ADDITIONAL FALSIFICATION RESULTS · pp. 25–26
  • With twin-rendered RF alone, footprint length, footprint width, and yaw errors rise further to 1.11 m, 1.01 m, and 6.80°.The rendered branch gives the current twin hypothesis but no independent observation of the physical scene.Source: H ADDITIONAL FALSIFICATION RESULTS · p. 26
  • When both RF branches are blinded, the model can still predict an ungrounded residual that worsens error, unlike the no-correction baseline, which applies no update.The twin-only input likewise lacks independent physical evidence to indicate how the current geometry should change.Source: H ADDITIONAL FALSIFICATION RESULTS · p. 26

I OUT-OF-DISTRIBUTION ERROR AND CLOSED-LOOP CORRECTION

TRACE generalizes to layout and corruption shifts beyond training support, and re-rendering the corrected twin lets the same frozen corrector further reduce residual error. The iterative procedure reuses the measured branch and does not require true geometry.

I OUT-OF-DISTRIBUTION ERROR AND CLOSED-LOOP CORRECTION

  • Under OOD-Layout, TRACE removes 88.70% of initial 3D position error, versus 56.33% for U-Net and 23.59% for ViT.OOD-Layout shifts building positions outside training support while keeping twin corruption in distribution.Source: I OUT-OF-DISTRIBUTION ERROR AND… · p. 26
  • OOD-Error requires corrections larger than the ±4 m training range, leaving part of the largest corrections after the first pass.The same frozen corrector is reapplied after updating the twin, re-rendering it, and recentering the GeoCrops.Source: I OUT-OF-DISTRIBUTION ERROR AND… · pp. 26–27
  • For OOD-Error, TRACE removes 79.16% of initial error in one pass and 93.08% after a second pass using the same frozen corrector.The second pass follows updating and re-rendering the twin; Table 11 identifies this step in the OOD results.Source: I OUT-OF-DISTRIBUTION ERROR AND… · pp. 26–27, Table 11 · p. 26
  • Each additional correction pass re-renders and backprojects only the twin branch; the measured branch is acquired once and reused, with no true geometry required.The added per-pass cost is one ray-tracing and backprojection of the current twin per sensing node.Source: I OUT-OF-DISTRIBUTION ERROR AND… · p. 27

J MEASURED NIST BENCHMARK

The NIST benchmark evaluates planar wall-position correction from measured RF paired with a ray-traced corrupted twin, using LiDAR-derived geometry for reference rather than as corrector input. Its scope is synthetic-to-measured transfer at a known site, not cross-site generalization.

J MEASURED NIST BENCHMARK

  • The NIST courtyard benchmark uses a fixed transmitter and mobile receiver platform carrying RF, LiDAR, and camera sensors, with each evaluation estimate fusing eight receiver positions.Figure 8 depicts the acquisition and planar wall-recovery setup; eight positions is the stated benchmark configuration.Source: Figure 8 · p. 27, J MEASURED NIST BENCHMARK · p. 27
  • LiDAR supplies the reference site model and wall geometry for scoring, while the corrector receives RF evidence and the current twin state.The measured result is RF-driven correction evaluated against a LiDAR reference, not RF-plus-LiDAR fusion.Source: J MEASURED NIST BENCHMARK · p. 27
  • At test time, measured NIST RF forms the physical branch, while the corrupted courtyard twin is ray-traced under the same transmitter and receiver configuration.Two walls are independently displaced horizontally by up to ±2 m; the remaining geometry is held at the reference.Source: J MEASURED NIST BENCHMARK · p. 28
  • The measured benchmark assesses planar wall-position correction; wall height and other geometric attributes remain at reference, and no measured sample is used for training or fine-tuning.Measured-to-rendered residuals may also reflect material, antenna, synchronization, clutter, and other modeling mismatch; training uses the NIST courtyard twin, so the test is at a known site.Source: J MEASURED NIST BENCHMARK · p. 28

K.1 SYNTHETIC SCENE AND SENSING CONFIGURATION

  • Synthetic scenes vary layout and twin corruption independently, enabling separate tests of layout diversity and correction difficulty.Scene generation perturbs buildings to form the physical scene, then corrupts a random subset of one to three buildings in the twin.Source: §K.1 · p. 29

K.2 WORLD-FRAME BACKPROJECTION AND GEOCROP

  • The GeoCrop window is 22.8 m square and is designed to contain generated buildings and training-range planar displacement; shared intensity scaling preserves relative branch brightness and height-dependent contrast.The same scaling is applied to measured, rendered, and coherent-difference streams rather than normalizing the branches separately.Source: Table 13 · p. 29, §K.2 · p. 30

K.3 LEARNED CORRECTOR

  • One encoder is shared across buildings, sensing nodes, and branches, keeping parameter count independent of the numbers of buildings and sensing nodes.The six input channels of the first complex stage correspond to the six focus heights.Source: §K.3 · p. 30, Table 14 · p. 30

K.4 TRAINING AND EVALUATION PROTOCOL

Training and evaluation use scene-disjoint splits and dimension-balanced checkpoint selection, while the baseline comparison holds the training recipe fixed and contrasts global scene-descriptor strategies. Under layout shift, U-Net outperforms ViT, and the compared models have closely matched parameter counts.

K.4 TRAINING AND EVALUATION PROTOCOL

  • Training splits are disjoint by true scene, and checkpoint selection uses a dimension-balanced validation score rather than an aggregate distance dominated by position.Evaluation noise is resampled per run when differencing ablation costs.Source: §K.4 · p. 30

K.5 BASELINES

  • Both baselines consume the full backprojected scene as ordinary real-valued channels and share the training recipe, isolating differences in input representation and fusion strategy.The inputs stack sensing nodes, focus heights, and three streams, with real and imaginary parts separated.Source: §K.5 · p. 31
  • 56.33% of initial error is removed by U-Net under layout shift, versus 23.59% by ViT.The U-Net retains local spatial structure; the ViT uses globally attending patches with learned absolute positional embeddings.Source: §K.5 · p. 31
  • 83.0% of initial 3D error is removed by the 2.93 M-parameter TRACE variant, versus 61.6% for U-Net; model sizes are matched within about 4%.The TRACE variant removes cross-sensor attention.Source: §K.5 · p. 31

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