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When Weak Reports Matter: Staged Anchored Fusion for Cooperative UAV Sensing

Xingqin Lin

arXiv:2610.07747v1cs.NI

TL;DR

Local multipath rejection can erase evidence needed for cooperative sensing, while forwarding every weak report increases search and traffic. SAR locks strong-only confirmations, then queries compatible weak reports with unused strong anchors. It recovers targets over strict consensus, matches anchored confirmation’s detection counts, and reduces weak uploads.

  • Problem

    Multipath and viewing angle can leave a target strong at one UAV transmit/receive point and weak at another, while requiring multiple locally accepted reports can miss it.

    Source: §I · p. 1

  • Method

    SAR locks strong-only confirmations, then uses unused strong anchors to query compatible weak reports, with lossless screening proved for any number of TRPs.

    Source: §I · p. 1

  • Results

    SAR recovers 30 truths over SC and matches AC at 4,956 truths with five unmatched outputs; validation recovers four truths with no unmatched outputs.

    Source: B. Detection, estimation, and reporting · p. 4

  • Takeaways & Limitations

    SAR preserves SC estimates while recovering rejected targets, with 97.4% fewer weak uploads and 4.5% less modeled payload than uploading all eligible reports.

    Source: §V · p. 4

Abstract

from arXiv · show

Local multipath rejection can erase evidence needed for cooperative sensing. We propose staged anchored recovery: preserve strong-only confirmations, then query compatible weak reports using unused strong anchors. For any number of sensing nodes, we prove lossless residual screening and derive corroboration and bidirectional cost laws. In 1,024 five-UAV drops, recovery adds 30 matched targets and three false outputs over strict consensus, matching one-pass anchored confirmation's detection counts while reducing weak uploads by 97.4%. Equal-sized cue/report records yield 4.5% less payload than uploading all eligible reports. Independent validation recovers four additional targets with no observed false outputs.

I. Introduction

Local multipath rejection can remove evidence that cooperative sensing could use, while accepting multiple reports can miss targets and forwarding every weak report increases search and traffic. Staged anchored recovery preserves strong-only confirmations and gives compatible weak reports a second chance through unused strong anchors.

I. Introduction

  • Multipath and viewing angle can make a target strong at one UAV transmit/receive point and weak at another, so requiring multiple locally accepted reports can miss it.Forwarding every weak report instead increases association search and traffic.Source: §I · p. 1
  • Prior work covers PRS sensing, multipath association, aerial localization, resource design, and selective reporting; this paper addresses selective recovery of locally rejected reports.The stated aim also accounts for query and response traffic while preserving confirmed estimates.Source: §I · p. 1
  • SAR locks objects confirmed by strong reports, then uses unused strong anchors to query compatible weak reports.It is proposed for any number of TRPs, with lossless screening and corroboration and bidirectional-cost laws.Source: §I · p. 1

A. Strong and weak evidence

  • Weak reports are locally rejected but remain eligible under lower fixed quality thresholds; strong reports pass all local checks.The figure distinguishes strong from eligible weak reports and shows that all-weak groups cannot confirm an object.Source: A. Strong and weak evidence · p. 1, Figure 1 · p. 2

B. Recovery after strict consensus

After strict consensus locks its accepted estimates and members, staged recovery queries compatible weak reports using unused strong reports, then confirms residual groups with a shared fitter and exclusive selection.

B. Recovery after strict consensus

  • SAR first runs strict consensus on strong reports and locks accepted estimates and member IDs, preventing locked reports from entering another group.The unused strong reports form the residual anchor set.Source: B. Recovery after strict consensus · p. 2
  • Each residual strong report queries the other TRPs for eligible weak reports passing the pair gate, and replies are deduplicated by stable ID.The resulting set contains queried weak reports for residual confirmation.Source: B. Recovery after strict consensus · p. 2
  • Residual groups must be pair-compatible, contain at least two TRPs, and include a residual strong anchor before shared fitting and exclusive selection.Accepted estimates are appended to the locked outputs.Source: B. Recovery after strict consensus · p. 2
  • The shared fitter estimates three-dimensional position and velocity from each report group using a forward measurement model.The model accounts for report and fusion epochs and each report’s TRP position.Source: B. Recovery after strict consensus · p. 2
  • Full velocity is reported only when the profiled velocity system has rank three and singular-value ratio at most 100; target confirmation does not require full velocity availability.Rank-deficient fits use a minimum-norm representative and report observable velocity projections with their basis.Source: B. Recovery after strict consensus · p. 2

A. Lossless screening and retention

For fixed reports and pair gates, screening weak reports through residual strong anchors preserves the candidate groups that could be formed by using all weak reports. With identical settings, complete cueing preserves residual outputs after the same strict-consensus locks.

A. Lossless screening and retention

  • For fixed reports and pair gates, residual-strong candidate groups formed from queried weak reports equal those formed from all weak reports.This is the stated lossless residual-screening result.Source: A. Lossless screening and retention · p. 2
  • With unchanged measurements, weights, stable IDs, and settings, complete cueing preserves residual outputs relative to uploading all weak reports after identical strict-consensus locks.The equivalence is for residual outputs; one-pass anchored confirmation has no prior strict-consensus locks.Source: A. Lossless screening and retention · p. 2
  • Appending r residual outputs gives 0 ≤ ΔM ≤ r and ΔF = r − ΔM ≥ 0 under maximum-cardinality truth matching.ΔM and ΔF are changes in matched and unmatched counts, respectively.Source: A. Lossless screening and retention · p. 2

B. Corroboration with an arbitrary number of views

The section characterizes corroboration for any number of views, distinguishing anchored recovery from strict and permissive confirmation. It also bounds how eligibility and shared evidence affect target and false corroboration.

B. Corroboration with an arbitrary number of views

  • The anchored gain over SC is exactly the event of one strong view corroborated by at least one weak view.Source: B. Corroboration with an arbitrary… · p. 2
  • The probability PC loses under anchoring is the all-weak event.For identical strong and eligible probabilities, the event analysis uses p_i=p and q_i=q.Source: B. Corroboration with an arbitrary… · p. 2
  • With compatible reports, objectwise association, and successful fits, SAR and AC both realize anchored evidence probability A_K; SAR locks multiple-strong objects first and recovers one-strong objects.This identifies when staged recovery matches one-pass anchored confirmation.Source: B. Corroboration with an arbitrary… · p. 2
  • For small probabilities and fixed K, anchored false corroboration scales with αβ, whereas permissive false corroboration scales with β².The selective advantage grows when strong false evidence is substantially rarer than eligible false evidence.Source: B. Corroboration with an arbitrary… · p. 2
  • At eligibility probability q, the marginal anchored corroboration gain is p/q times the permissive gain.When β rises from 0.005 to 0.01 with α=10^-4 and the strong threshold fixed, anchoring admits only 1–2% of that false-evidence increment for any K.Source: B. Corroboration with an arbitrary… · pp. 2–3
  • With shared evidence fraction η, a common strong false event contributes ηα regardless of K, so adding TRPs cannot remove this shared component.Figure 2 contrasts target and false evidence versus K under independent and shared evidence, with η=0.1.Source: B. Corroboration with an arbitrary… · p. 3, Figure 2 · p. 3

C. Bidirectional reporting cost

The section compares SAR's bidirectional reporting cost with uploading all eligible reports. Its accounting includes strong reports, weak reports, and query cues, and identifies a cost boundary for savings.

C. Bidirectional reporting cost

  • Unicast querying uses (K−1)N_a cues, while N_s counts uploaded strong reports, N_w eligible weak reports, N_a residual anchors, and N_p deduplicated weak replies.The cost model assigns b_r bits per report and b_c per cue.Source: C. Bidirectional reporting cost · p. 3
  • For N_a>0, SAR reduces bidirectional payload precisely when the cue/report bit-cost relation satisfies the derived boundary.The supplied passage does not state the boundary's full expression.Source: C. Bidirectional reporting cost · p. 3
  • When N_a=0, no query is sent and only N_s reports are uploaded; confirming first reduces the number of anchors and relaxes the cost boundary.The report/query model excludes protocol framing and acknowledgments.Source: C. Bidirectional reporting cost · p. 3

A. Configuration and experimental controls

The experiments use a fixed three-TRP, five-UAV sensing setup and shared acquisition settings across policies. The design population and scoring procedure support paired comparisons.

A. Configuration and experimental controls

B. Detection, estimation, and reporting

SAR recovers targets beyond strict consensus while matching anchored confirmation's detection counts, with fewer weak uploads and modest modeled-payload savings. Validation recovers four additional targets without unmatched outputs.

B. Detection, estimation, and reporting

V. Conclusion

SAR preserves strict-consensus estimates while recovering rejected targets, and matches anchored confirmation's detection counts in the evaluated populations. Against uploading all eligible reports, it reduces weak uploads and modeled bidirectional payload for equal-sized cue/report records.

V. Conclusion

  • SAR preserves SC estimates while recovering rejected targets, matching AC detection counts in the evaluated populations.Source: §V · p. 4
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