<p>Distributed state estimation under a hard communication budget is limited not only by local packet generation but also by the network-level decision of which candidate packets can actually be admitted during congestion. This paper develops a fairness-regularized value-based admission strategy for bandwidth-constrained cooperative state estimation. Each active node runs a standard local Kalman filter, forms a candidate packet according to an innovation trigger, and reports an uncertainty-reduction value together with its transmission cost. A starvation-sensitive compensation factor reshapes the packet utility so that short-term information gain and long-horizon access fairness are balanced under a strict stepwise byte budget. The resulting admission problem is a binary knapsack problem that is solved online by a low-complexity value-density scheduler and coupled with a covariance-intersection backend for conservative fusion under unknown cross-correlation. The analysis includes a bounded-admission-gap sufficient condition for covariance boundedness and a practical tuning rule for the fairness parameters. The evaluation covers adaptive and exact-knapsack baselines, scalability tests for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$N=8,12,20,30$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>8</mn> <mo>,</mo> <mn>12</mn> <mo>,</mo> <mn>20</mn> <mo>,</mo> <mn>30</mn> </mrow> </math></EquationSource> </InlineEquation> nodes, two-dimensional <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>–<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\tau _{\max }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mo movablelimits="true">max</mo> </msub> </math></EquationSource> </InlineEquation> sensitivity, and a time-varying-budget scenario with content-dependent packet costs. The results show that the proposed method keeps RMSE and ANEES comparable to utility-only and exact utility-only admission, while clearly reducing long admission gaps and improving Jain fairness. In the default congested evaluation window, FRUA reduces the maximum silence length from 18.2 to 14.0 steps and improves the Jain index from 0.952 to 0.974 relative to UOA. When the network size increases to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$N=30$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>30</mn> </mrow> </math></EquationSource> </InlineEquation>, FRUA keeps the maximum silence length below 18 steps, whereas UOA and exact UOA exceed 150 steps. These results indicate that fairness-aware admission is a useful system-level complement to local communication-efficient estimation when congestion, packet competition, and unknown cross-correlation coexist.</p>

Fairness-Regularized Value-Based Admission for Bandwidth-Constrained Cooperative State Estimation

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发表日期：

2026年7月19日

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Yuanyuan Chi,
Haoliang Guan,
Huili Wang

摘要

Distributed state estimation under a hard communication budget is limited not only by local packet generation but also by the network-level decision of which candidate packets can actually be admitted during congestion. This paper develops a fairness-regularized value-based admission strategy for bandwidth-constrained cooperative state estimation. Each active node runs a standard local Kalman filter, forms a candidate packet according to an innovation trigger, and reports an uncertainty-reduction value together with its transmission cost. A starvation-sensitive compensation factor reshapes the packet utility so that short-term information gain and long-horizon access fairness are balanced under a strict stepwise byte budget. The resulting admission problem is a binary knapsack problem that is solved online by a low-complexity value-density scheduler and coupled with a covariance-intersection backend for conservative fusion under unknown cross-correlation. The analysis includes a bounded-admission-gap sufficient condition for covariance boundedness and a practical tuning rule for the fairness parameters. The evaluation covers adaptive and exact-knapsack baselines, scalability tests for $N=8,12,20,30$ $N = 8, 12, 20, 30$ nodes, two-dimensional $\beta $ $β$ – $\tau _{\max }$ $τ_{max}$ sensitivity, and a time-varying-budget scenario with content-dependent packet costs. The results show that the proposed method keeps RMSE and ANEES comparable to utility-only and exact utility-only admission, while clearly reducing long admission gaps and improving Jain fairness. In the default congested evaluation window, FRUA reduces the maximum silence length from 18.2 to 14.0 steps and improves the Jain index from 0.952 to 0.974 relative to UOA. When the network size increases to $N=30$ $N = 30$ , FRUA keeps the maximum silence length below 18 steps, whereas UOA and exact UOA exceed 150 steps. These results indicate that fairness-aware admission is a useful system-level complement to local communication-efficient estimation when congestion, packet competition, and unknown cross-correlation coexist.