PaperlayerView exact revision on arXiv

Source-linked AI summary

From Echoes to Evidence: Cooperative Fusion for Integrated Sensing and Communication

Xingqin Lin

arXiv:2610.10994v1cs.NI

TL;DR

Multipath can make nodes agree on virtual targets while useful weak echoes remain unexploited. This paper separates association confirmation, state refinement, and residual recovery, and its San Francisco ray-tracing evaluation reports 92.46% detection with a 0.40% false-output fraction.

  • Problem

    Multipath can make reports agree on virtual targets while locally rejected weak direct echoes could resolve uncertainty, complicating cooperative ISAC evidence use.

    Source: §I · p. 1

  • Method

    The framework confirms associations with strong reports, refines confirmed states using bias-aware weak-report risk, and uses unused anchors for recovery while modeling acquisition cost.

    Source: §I · p. 2

  • Results

    92.46% detection with a 0.40% false-output fraction; common-target 90th-percentile position error fell from 8.54 to 3.50 m.

    Source: §VII · p. 12

  • Takeaways & Limitations

    The results support separating association validity from refinement utility when designing cooperative ISAC fusion.

    Source: §VII · p. 12

Abstract

from arXiv · show

Cooperative integrated sensing and communication (ISAC) can support shared situational awareness for unmanned aerial vehicles (UAVs), road vehicles, and industrial mobile robots such as automated guided vehicles (AGVs). Yet multipath can make nodes agree on a virtual target while useful weak echoes remain unexploited. This paper develops cooperative fusion that separates association confirmation, state refinement, and residual recovery. A cellular reference signal model accommodates arbitrary node counts, three-dimensional motion, monostatic and bistatic links, nuisance parameters, and correlated errors. We characterize report distinguishability under bounded bias and shared-reflector ambiguities that survive additional nodes. Minimax estimation yields directional weak-report refinement that preserves confirmed associations and limits bias-sensitive innovations; acquisition accounts for request and upload costs. Controlled experiments accompany UAV evaluations under a Third Generation Partnership Project (3GPP) stochastic channel model and a ray tracing environment representing San Francisco. In the latter environment, matched-budget fusion raises detection from observable site selection's 88.75% to 92.46% and reduces the false-output fraction from 11.06% to 0.40%. Against the strongest full-band fixed site, the 90th-percentile position error on commonly detected targets falls from 8.54 to 3.50 m. Association controls, local rejection ablations, and refinement studies distinguish the sources of these gains.

I. Introduction · II. General Signal and Measurement Model · A. Nodes, Motion, and Reference Signals

The paper addresses multipath cases where reports agree on a virtual target while a weak echo could resolve another node’s uncertainty. It separates association confirmation, bias-aware refinement, and candidate acquisition and recovery.

I. Introduction

  • Cellular ISAC uses known reference symbols for delay, Doppler, and angle measurements across complementary node views, with spatial-diversity benefits depending on visibility, scattering strength, and velocity observability.Applications include UAV operations, vehicle awareness, and AGV coordination.Source: §I · p. 1
  • Multipath can make reflected reports agree precisely on a virtual target, while a locally rejected weak direct echo could resolve another node’s uncertainty but may bias confirmed states.The framework links association confirmation, refinement at acceptable bias risk, and further acquisition.Source: §I · p. 1
  • Strong reports confirm associations, additional views refine confirmed states under a declared risk model, and unused anchors recover objects through candidate-specific access.The access model specifies candidate requests, exact residual-search equivalence conditions, and bidirectional acquisition cost.Source: §I · p. 2
  • The observation/report model characterizes bias-aware distinguishability and reflected-path equivalence that report consistency cannot resolve, even with additional nodes or signal energy.The paper connects these ambiguities to propagation and report evidence.Source: §I · pp. 1–2
  • A weighted innovation-risk formulation separates random error from unknown bias, accounts for correlation, and derives directional weak-report refinement while preserving confirmed associations.The declared bias radius regulates weak-report influence on confirmed estimates.Source: §I · pp. 1–2
  • Controlled geometry, bias, correlation, and signaling experiments precede stochastic-channel and mapped-city evaluations, with shared-observation controls and set-error, detection, and common-target accuracy metrics.The controls compare local rejection, association, and refinement.Source: §I · p. 2

A. Nodes, Motion, and Reference Signals

  • For each association hypothesis, target position and unrestricted three-dimensional velocity define a six-dimensional state with constant-velocity motion and a specified speed bound.The model assumes surveyed node positions and velocities, known array orientations, and an unknown target count and path classification.Source: A. Nodes, Motion, and Reference Signals · p. 2
  • Known cellular reference symbols and spatial weights drive link observations whose target paths have complex amplitudes, delays, and Dopplers; geometric reports require timing/frequency registration but not inter-node carrier-phase coherence.For an isolated return, bandwidth, timing, and their coupling—not sample count alone—determine delay/Doppler precision.Source: A. Nodes, Motion, and Reference Signals · p. 2

B. Monostatic and Bistatic Report Geometry

The section defines direct-return report geometry for moving targets and monostatic links, then specifies how reports combine predictions with calibration, bias, and random error. It also gives the link Jacobian structure used to describe local measurement sensitivity.

B. Monostatic and Bistatic Report Geometry

  • Each report predicts path length, receive azimuth and elevation, and path-length rate from target-to-endpoint geometry at the report epoch.Path length and rate use propagation speed and carrier wavelength; positive rate denotes recession.Source: B. Monostatic and Bistatic Report… · p. 2
  • Fixed monostatic nodes report half the path length as range and half the path-length rate as radial speed, with uncertainty transformed accordingly.Angles are expressed in a common surveyed frame.Source: B. Monostatic and Bistatic Report… · p. 2
  • Measured reports equal predicted reports plus calibration sensitivity, deterministic bias, and zero-mean random error with positive-definite covariance.Cross-report covariance can represent shared-receiver, waveform, and interference correlations; same-clock monostatic measurements cancel absolute clock offsets, unlike bistatic relative clock or frequency errors,. Known unbiased quantization contributes to covariance, while bounded quantization and nonlinear remainder contribute to bias.Source: B. Monostatic and Bistatic Report… · p. 3
  • The stacked report Jacobian uses link gradients, including angle and path-rate position gradients formed from endpoint-relative motion projected perpendicular to each link direction.At zenith, a nonsingular local direction coordinate replaces azimuth.Source: B. Monostatic and Bistatic Report… · p. 3

A. Geometry, Clock Nuisance, and Bias

The section separates geometric observability from bias-aware report distinguishability: registered views constrain motion only when geometry is sufficient, while overlapping bias-affected reports cannot be separated by improved precision alone.

A. Geometry, Clock Nuisance, and Bias

  • Full local observability requires rank-six information after nuisance projection,; two simultaneous views cannot identify unrestricted 3D velocity, but three spanning views can.Multiple epochs add Doppler sensitivity, while unresolved independent path-rate offsets can absorb all path-rate equations regardless of node count; geometry and reference registration must be reported together.Source: A. Geometry, Clock Nuisance, and Bias · p. 3
  • The minimax sum of decision-error probabilities is 2Φ(−d*/2), where d* is the minimum whitened separation between admissible projected mean sets.The result assumes two fixed states, common Gaussian covariance, unrestricted nuisance, and independently adversarial biases bounded by radius ρ.Source: A. Geometry, Clock Nuisance, and Bias · p. 3
  • If projected admissible mean sets overlap, the minimax error sum remains one despite reduced random error; disambiguation requires added information or narrower justified bias and nuisance classes.An overlapping set permits the same report distribution under both states.Source: A. Geometry, Clock Nuisance, and Bias · p. 3

B. Spatial Signatures and a Persistent Image Ambiguity · IV. Bias-Aware Refinement of Confirmed Targets · A. Risk of a Weak-Report Update

The paper shows that spatially coded reports can retain a shared-reflector ambiguity across nodes, while deriving a bias-aware minimax update for refining confirmed targets. It characterizes when report signatures distinguish paths and when weak-report refinement can strictly improve on no update.

B. Spatial Signatures and a Persistent Image Ambiguity

  • One resource yields zero profiled departure information; multiple resources help only through different normalized signatures, while collinear signatures remain indistinguishable.Separation need not increase with angular difference; multiple transmit polarizations require a matrix-valued signature and nuisance subspace.Source: B. Spatial Signatures and a Persistent… · p. 4
  • A valid reciprocal reflected path can produce direct-report geometry for its image at any number of nodes, preserving path length, Doppler, and final-segment direction.Across epochs, this persists while the reflection family remains visible; a bistatic extension requires the same image map on both legs.Source: B. Spatial Signatures and a Persistent… · p. 4, Figure 2 · p. 5
  • Identical report distributions for two admissible hypotheses impose a report-only minimax risk floor, attained by the midpoint estimate.The image construction gives identical four-coordinate reports for admissible states with unclassified path amplitudes, without equating complete scene responses.Source: B. Spatial Signatures and a Persistent… · p. 4
  • Map information, independent signatures, and visibility changes can break the image equivalence, but additional nodes or higher SNR alone need not.Departure-arrival disagreement is an established multipath discriminator, although a reciprocal reflected path can preserve both directions.Source: B. Spatial Signatures and a Persistent… · p. 4

A. Risk of a Weak-Report Update

  • The weak-report model combines a zero-mean baseline error with fixed additional reports, deterministic ellipsoidal bias, and potentially correlated baseline and weak-report noise.Coverage of path errors, quantization, and nonlinear remainders requires separate justification.Source: A. Risk of a Weak-Report Update · p. 4
  • The risk expansion does not require Gaussianity, but data-dependent association and covariance proxies require empirical validation.The result assumes fixed hypotheses, gain, moments, and bias set during expectation, or conditioning on independent calibration.Source: A. Risk of a Weak-Report Update · p. 4
  • The exact multi-report minimax refinement attains its optimized risk reduction through a convex bias-energy allocation problem.The admissible allocation matrices are positive semidefinite with trace at most ρ².Source: A. Risk of a Weak-Report Update · p. 4
  • For finite bias radius, refinement strictly improves on no update exactly when W^1/2A is nonzero; the weighted optimal gain is unique.Here A is the signed baseline coupling between estimation error and innovation.Source: A. Risk of a Weak-Report Update · pp. 4–5

B. Directional Admission and Spectral Refinement

The section derives mode-wise spectral admission for directional refinement and compares it with an optimized uniform scalar gain. It also characterizes how increasing bias uncertainty suppresses updates while leaving bias-free report combinations available.

B. Directional Admission and Spectral Refinement

  • For ρ > 0 and M ≠ 0, a unique spectral cap κ determines mode admission factors s_j = min(1, κ/√μ_j), with s_j = 1 when μ_j = 0.The cap allocates refinement directionally across modes.Source: B. Directional Admission and Spectral… · p. 5
  • Directional admission strictly outperforms the optimized scalar rule when the nonzero eigenvalues of M are unequal, and matches it when they are all equal.The cap law has uniform shrinkage exactly when the positive eigenvalues coincide; for a six-state target, sorting or bisecting computes the update after whitening.Source: B. Directional Admission and Spectral… · p. 5
  • As ρ → ∞, full-rank bias uncertainty suppresses the weighted update, including the complete update when W ≻ 0; bias-free combinations survive projection away from whitened bias directions.Before optimization, unbounded reference nuisance uses the same projection with its nuisance directions.Source: B. Directional Admission and Spectral… · p. 5

C. Joint Report Selection

Joint report selection maximizes robust reduction under acquisition costs and a communication budget, while correlated-noise cancellation can make requesting reports together valuable even when their individual signal-to-noise ratios are low.

C. Joint Report Selection

  • Selection uses optimized subset reduction Vρ(J), which is monotone when extra reports may receive zero gain, subject to acquisition costs and a communication budget.Source: C. Joint Report Selection · p. 5
  • Robust value cannot generally inherit a greedy guarantee, despite precedents for Fisher-based selection –.Source: C. Joint Report Selection · p. 5
  • With baseline error variance P = 1 and two unit-sensitivity reports, nominal reduction is 1/101 for either report alone and 2/3 for both at ρ = 0.When B = T, all three values are divided by 1 + ρ^2.Source: C. Joint Report Selection · p. 5
  • Correlated-noise cancellation makes joint value exceed the sum of individual values at every finite radius, so group requests can help despite low individual signal-to-noise ratios.Source: C. Joint Report Selection · p. 6

V. Reference-Signal Receiver, Evidence Decisions, and Reporting · A. Local Processing and Validity Tiers · B. Association, Confirmation, and Protected Refinement

The receiver separates strong and eligible reports using local consistency checks, while cooperative processing confirms associations before refining weak reports. Group fitting accounts for measurement geometry, nuisance parameters, and residual gates.

A. Local Processing and Validity Tiers

  • Seven local consistency checks screen thresholded peaks for spatial, temporal, resource-amplitude, CPI-half, and companion-return consistency, but do not establish direct-path probability.The threshold budgets false alarms over search cells; the factorial ablation evaluates all 27 check coalitions and allocates interaction credit with Shapley-weighted reductions.Source: A. Local Processing and Validity Tiers · p. 6
  • Strong sets contain reports passing all local checks, while eligible sets retain weaker candidates and diagnostics, with reports carrying four coordinates, epoch, stable ID, source, and covariance or weight.Noise-subtracted observed SNR determines effective precision weight, while the separate bias model governs refinement influence.Source: A. Local Processing and Validity Tiers · p. 6

B. Association, Confirmation, and Protected Refinement

  • Monostatic reports convert range and angles into apparent position and propagate their covariance; bistatic queries use transmitter-receiver geometry rather than treating half-delay as monostatic range.Monostatic prediction and covariance use the monostatic scaling matrix, while bistatic prediction uses the bistatic measurement model.Source: B. Association, Confirmation, and… · p. 6
  • A compatible report group requires cross-node pair edges and, for admissibility, at least two nodes, one report per node, all pair edges, and a successful joint fit.Compatibility accounts for apparent-position cross-covariance and a motion allowance for speed bounds and epoch differences; evaluated independent proxies set cross-covariance to zero.Source: B. Association, Confirmation, and… · p. 6
  • Joint fitting uses robust Huber residual loss, registers nuisance references or fits unresolved nuisance terms jointly, wraps angle residuals, and applies design gates on residuals and fitted speed.The gates are not calibrated chi-square probabilities, and unobservable velocity directions are flagged.Source: B. Association, Confirmation, and… · p. 6
  • The common admissible-group family compares strict consensus, permissive confirmation, anchored confirmation, and staged anchored recovery, with deterministic greedy exclusive selection that need not be globally optimal.Staged anchored recovery preserves strict consensus before recovering residual anchored groups.Source: B. Association, Confirmation, and… · p. 6
  • Risk-aware refinement preserves confirmed associations while limiting the directional influence of weak augmentations through a finite radius.It refines weak reports only when their strong membership matches the confirmed group, excluding records already consumed by recovery.Source: B. Association, Confirmation, and… · p. 6

C. Residual Access and Communication Cost

Residual screening preserves the recovered anchored groups under stated fixed conditions, while staged acquisition saves communication payload only under a specific payload-size threshold. Reliable fusion also requires report metadata beyond point estimates, including uncertainty and bias information.

C. Residual Access and Communication Cost

  • With fixed gates, cached values/weights, stable IDs, complete replies, and uncapped enumeration, screening preserves the residual anchored group family and yields identical residual outputs under identical deterministic fitting/selection.This recovery property does not concern one-pass association confirmation or refinement traffic.Source: C. Residual Access and Communication… · p. 7
  • For Na > 0, staged acquisition saves payload over full push only when bc/bw < (Nw−Nq)/[(K−1)Na] under unicast requests to K−1 other nodes.Nw, Nq, and Na count eligible weak reports, distinct recovery replies, and residual anchors; bw and bc are weak-report and cue payload sizes.Source: C. Residual Access and Communication… · p. 7
  • Fusion reports need endpoint poses and resource identity, epochs and frame, delay/rate conventions, ambiguity status, uncertainty and cross-report correlation, validity and consistency, and calibration/bias provenance.Covariance cannot replace a declared path-bias envelope; compressed reports must preserve the quantization rule, and these fields also support fusion from multiple bistatic UEs.Source: C. Residual Access and Communication… · p. 7

VI. Channel Construction and Evaluation … C. PRS Waveform, Timing, and Evaluation Protocol

The evaluation contrasts diffuse stochastic channels with mapped San Francisco ray tracing, then tests PRS-based sensing under a shared waveform, matched resource budgets, and controlled association and estimation protocols.

VI. Channel Construction and Evaluation

  • Both environments generate channel fields for a common receiver, with stochastic channels capturing diffuse target paths and ray tracing retaining persistent reflector geometry.The study presents these as complementary channel constructions, not a propagation-only comparison.Source: §VI · p. 7

A. 3GPP Stochastic Channel Construction

  • The 3GPP model pairs one-way LOS or NLOS links into sensing paths, retaining LOS–LOS, LOS–diffuse, diffuse–LOS, and permuted diffuse–diffuse ray pairs under a 40 dB cutoff,.It uses a 15 dB LOS Ricean factor, outdoor UMa fast fading, reciprocal monostatic legs, 20 rays per cluster, and prescribed subdelays.Source: A. 3GPP Stochastic Channel Construction · p. 7
  • Paired 3GPP delays combine geometric round-trip time, one-way excess delays, and diffuse-link delays, while Doppler follows the two outward target directions.The additional diffuse delay follows log10(Δ/s) ∼ N(−7.4, 0.22). Three independent UMa-NLOS virtual reference channels provide stationary background.Source: A. 3GPP Stochastic Channel Construction · p. 8

B. Mapped-City Ray-Tracing Construction

  • The San Francisco ray-tracing benchmark uses a 4,735-object scene and depth-three tracing, allowing one target interaction and up to two urban reflections.Diffuse scattering, diffraction, refraction, and moving background are disabled; target and background budgets are 220 and 105 rays per call.Source: Figure 3 · p. 7, B. Mapped-City Ray-Tracing Construction · p. 8

C. PRS Waveform, Timing, and Evaluation Protocol

  • PRS evaluation uses three one-port resources per site, comb-2 early/late phase views, and occasions every 4 ms across a 128-ms CPI,.The waveform allocation and timing are shown in Fig. 4; the configuration is listed in Table II.Source: C. PRS Waveform, Timing, and… · p. 8, Table II · p. 8, Figure 4 · p. 9
  • Each environment contains 1,024 occupied and 1,024 empty drops, with five UAVs per occupied drop and horizontal speeds from 0–50 m/s.The experiments set vertical velocity to zero, fit five states, and require rank-two noise-weighted horizontal sightlines; city draws maintain at least 1 m roof/terrain clearance.Source: C. PRS Waveform, Timing, and… · p. 8
  • Full-band fixed-site and aggregate matched cooperation use equal transmitted budgets, while cooperation adds three receive apertures; observable selection ranks sites without fitting or truth.Policies receive identical reports within an allocation, and report-level controls vary admission, refitting, loss, gates, and pair thresholds.Source: C. PRS Waveform, Timing, and… · p. 9
  • Evaluation defines truth matches within 30 m and reports detection, false-alarm, P90, controlled-study MSE and CRB, and RMS GOSPA with a 30 m cutoff.Pointwise 95% intervals use 2,000 paired whole-drop bootstrap resamples; zero empty alarms in 1,024 trials gives an exact one-sided 95% upper bound of 0.2921%.Source: C. PRS Waveform, Timing, and… · p. 9

D. Geometry, Bias, and Correlation Controls

Geometry, bias, and correlation controls show that additional views do not guarantee precise or informative updates: geometry affects velocity observability, while directional refinement limits worst-case risk and correlated innovations can carry no baseline-error information.

D. Geometry, Bias, and Correlation Controls

  • At a 15◦ span, twelve nodes still yield 78.9 m/s RMS unconstrained velocity CRB, versus 0.54 m/s with three full-circle nodes.Two views have deficient 3D velocity rank, while narrow-angle rank-six geometry can have poor precision; views separated by 50 ms achieve rank six through displacement information.Source: D. Geometry, Bias, and Correlation… · p. 9
  • Directional refinement lowers worst normalized MSE to 2.997 at design radius two, beating optimized scalar shrinkage (3.227) and locking (3.860).Nominal addition yields 8.531; directional refinement improves worst risk by 22.3% over locking and 7.1% over scalar shrinkage. At shared-error loading ζ=1, innovations contain no baseline-error information, but ignoring correlation still admits an erroneous update.Source: D. Geometry, Bias, and Correlation… · p. 9

E. Local Rejection and Cooperation in the 3GPP Environment · F. Target Returns and Sensing in the Mapped City

In the 3GPP environment, cooperative policies trade some coverage for stronger corroboration and more precise matched-target estimates, while local rejection suppresses false outputs. In the mapped city, SAR improves detection and false-output performance over matched selection, and target-interacting reflections remain a source of ambiguity.

E. Local Rejection and Cooperation in the 3GPP Environment

  • At full-band TRP0 in 3GPP, seven checks reduce unmatched outputs from 30.671 to 0.303 per occupied drop and FA2 from 84.82% to 5.16%, while detection falls from 97.52% to 94.41%.Temporal, spatial, TX-signature, and delayed-companion checks provide the largest interaction-adjusted reductions; split-speed and split-power contribute little at this setting.Source: E. Local Rejection and Cooperation in… · pp. 9–10, Figure 6 · p. 10
  • In 3GPP, matched SAR improves detection over the strongest fixed site by 1.543 percentage points, interval [0.918,2.168], while shared-truth position P90 drops from 8.607 to 2.522 m.The position comparison covers 4,771 shared truths; multiple receive apertures and geometric estimation improve precision despite split transmitted resources.Source: E. Local Rejection and Cooperation in… · p. 10, Figure 8 · p. 11
  • In 3GPP, observable selection detects 5,014 truths with 32 unmatched outputs, SC 4,926 with 2, and SAR 4,956 with 5, versus PC’s 4,956 with 77.Strong anchoring suppresses most all-weak false groups, while corroboration costs coverage relative to selection; independent 128-drop validation gives SC 615/0 and AC/SAR 619/0 matched/unmatched outputs.Source: E. Local Rejection and Cooperation in… · p. 10, Figure 7 · p. 11

F. Target Returns and Sensing in the Mapped City

  • In the mapped city, native target paths occur at all three sites for 4,936 of 5,120 UAVs, but all-three-site locally matched strong reports occur for only 2,856.Local rejection cuts full-band TRP0 false count from 8.742 to 1.904 per drop, while detection decreases from 84.20% to 80.59%; spatial, temporal, and TX consistency checks contribute most, unlike the stochastic ranking.Source: F. Target Returns and Sensing in the… · pp. 10–11
  • In the mapped city, matched SAR raises detection from 88.75% to 92.46% and cuts FA2 from 11.06% to 0.396%; common-target position P90 falls from 8.536 to 3.497 m.The position comparison covers 4,511 common truths; the detection advantage over the strongest fixed site is unresolved, with a 0.625-point difference and interval [−0.176,1.445].Source: F. Target Returns and Sensing in the… · p. 11, Figure 8 · p. 11
  • In a 64-drop, 320-target city path control, removing stationary background leaves scored outputs unchanged, while target-interacting reflections account for remaining ambiguity.Keeping only direct target paths changes SC from 281/0 to 294/0 and SAR from 290/1 to 295/0 matched/unmatched outputs; all coded fusion methods have zero observed empty alarms.Source: F. Target Returns and Sensing in the… · p. 11

G. Association Sensitivity and Estimator Comparisons … VII. Conclusion

The paper separates association confirmation, bias-aware refinement of confirmed states, and recovery of additional targets, while accounting for acquisition costs. Across its UAV evaluations, cooperative fusion improves detection, false-output fraction, and common-target position accuracy in the San Francisco ray-tracing environment.

G. Association Sensitivity and Estimator Comparisons

  • LS preserves Huber’s counts and matched truth IDs while slightly improving GOSPA; halving the covariance-pair threshold raises GOSPA by 0.828/1.140 m in stochastic/city cases.Both paired intervals for the threshold change exclude zero; doubling the threshold changes only two net matches per environment, while over-tight screening discards useful views before fitting.Source: G. Association Sensitivity and… · p. 11, Table IV · p. 12
  • An exploratory 30 m gate yields 4,955/2 and 4,736/5 matched/unmatched outputs, with competitive detection and fewer false outputs than nominal covariance gates; city GOSPA improves by 0.300 m [0.174, 0.444].The fixed 30 m gate transferred unchanged to independent 128-drop stochastic validation and preserved the nominal groups and metrics; the initially specified Euclidean 15 m gate removes ghosts but loses targets.Source: G. Association Sensitivity and… · p. 12

H. Bias-Aware Refinement and Common-Target Accuracy

  • At radius two, city common-truth position and velocity MSE changes are −0.0517 m2 [−0.0747, −0.0280] and −0.0196 (m/s)2 [−0.0284, −0.0123], with matched and false counts unchanged.The comparisons use the strong Euclidean-30 m baseline and 63 stochastic and 268 city refinable states; both intervals exclude zero. The covariance-gated baseline also improves by −0.0486 m2 and −0.0202 (m/s)2.Source: H. Bias-Aware Refinement and… · p. 12
  • Finite-radius refinement reduces position exposure while retaining velocity benefit, whereas infinite radius reproduces SAR exactly on all 4,096 original drops.Scalar shrinkage gives slightly lower city position MSE at radius two; Corollary 2 concerns worst weighted risk under specified bias and moments, as the fixture verifies, while waveform reports show the practical tradeoff.Source: H. Bias-Aware Refinement and… · p. 12

I. Reporting Payload and Request Overhead

  • Locked covariance-gated SAR uploads 13,809/13,434 stochastic/city strong records; weak uploads fall from 1,367/1,558 to 35/213, requiring 644/2,966 unicast cue copies.Equation (27) gives cue/report size breakpoints 2.068/0.4535; equal-size records reduce stochastic traffic 4.53% but increase city traffic 10.81%, while quarter-size city cues save 4.03%, excluding framing and acknowledgments. Compact requests determine net savings; this payload differs from the 5.3375% radiated PRS overhead.Source: §I · p. 12

VII. Conclusion

  • In the San Francisco ray-tracing environment, cooperative fusion achieves 92.46% detection and a 0.40% false-output fraction, reducing common-target 90th-percentile position error from 8.54 to 3.50 m.The conclusion frames these results as support for separating association validity from refinement utility in sensing reports and network processing.Source: §VII · p. 12
  • The conclusion connects report distinguishability, shared-image ambiguity, correlated-innovation risk, and acquisition cost in a general cooperative fusion framework.It describes strong reports as establishing associations, additional views as refining confirmed states under a declared bias model, and unused anchors as recovering further targets; future work will incorporate map-informed bias sets and bistatic reference errors into adaptive fusion and acquisition.Source: §VII · p. 12
Loading 2610.10994v1…