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arxiv: 2605.02235 · v1 · submitted 2026-05-04 · 📡 eess.SY · cs.DC· cs.MA· cs.SY· eess.SP· math.OC

Distributed Observer-based Fault Detection over Intelligent Networked Multi-Vehicle Systems

Mohammadreza Doostmohammadian , Hamid R. Rabiee This is my paper

Pith reviewed 2026-05-08 17:35 UTC · model grok-4.3

classification 📡 eess.SY cs.DCcs.MAcs.SYeess.SPmath.OC
keywords fault detection and isolationdistributed observersconnected autonomous vehiclesmixed traffic networksresidual thresholdssensor attacksprobabilistic designconsensus-based estimation
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The pith

Connected autonomous vehicles can each detect sensor faults locally using distributed state estimation and probabilistic residual thresholds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how a network of connected autonomous vehicles can track the states of nearby human-driven vehicles through distributed consensus observers, even when no individual CAV has enough local sensors to observe the HDVs on its own. Building on this estimation, each CAV runs its own fault detection logic on the residuals between predicted and measured sensor values to identify possible faults or attacks. Two versions of this logic are given: one that uses only the current residual and another that incorporates its history, both using thresholds set by probabilistic analysis rather than fixed bounds. This setup allows every vehicle to monitor its sensors independently, which is useful in real traffic where a central computer might not be reliable or available. The method avoids assuming that measurement noise is strictly bounded, making it more applicable to actual driving conditions with random disturbances.

Core claim

The authors establish that local residual-based fault detection and isolation can be performed at each CAV using residuals from distributed consensus-based observers, with probabilistic threshold design that does not require bounded noise support, enabling decentralized detection of sensor anomalies in mixed human-driven and autonomous vehicle networks where individual vehicles lack full local observability.

What carries the argument

Distributed consensus-based observers that allow state estimation of HDVs from partial measurements across the CAV network, paired with local residual generators for FDI.

Load-bearing premise

The distributed consensus observers converge despite each CAV having only partial observability of the human-driven vehicles.

What would settle it

A simulation or real test where sensor faults are injected into CAV measurements and the local FDI logic fails to flag them above the probabilistic threshold, or where the distributed state estimation error does not decrease over time.

Figures

Figures reproduced from arXiv: 2605.02235 by Hamid R. Rabiee, Mohammadreza Doostmohammadian.

Figure 1
Figure 1. Figure 1: This figure shows a mixed traffic NMVS of 4 HDVs and 4 CAVs. The idea is view at source ↗
Figure 2
Figure 2. Figure 2: This figure illustrates the FDI strategy in this paper. For the normalized residual view at source ↗
Figure 3
Figure 3. Figure 3: This figure presents the position state of the view at source ↗
Figure 4
Figure 4. Figure 4: This figure presents the velocity state of the view at source ↗
Figure 5
Figure 5. Figure 5: This figure compares the MSE performance of proposed distributed estimator view at source ↗
Figure 6
Figure 6. Figure 6: This figure presents the residuals r i k , for i = 1, . . . , 4 under the distributed observer (8)-(9). The faulty measurement at CAV 2 is detected by FAR less than 5% via the proposed stateless FDI. measured state of HDV 2 is erroneous or biased due to adversarial condi￾tions or possible attacks. To model this, we consider f2,k ∼ N (1.5, 0.25) for k ≥ 300 (or t ≥ 15). First, we check the instantaneous res… view at source ↗
Figure 7
Figure 7. Figure 7: This figure presents the distance measures view at source ↗
Figure 8
Figure 8. Figure 8: This figure presents the weighted distance measures view at source ↗
Figure 9
Figure 9. Figure 9: This figure presents the weighted distance measures view at source ↗
Figure 10
Figure 10. Figure 10: This figure shows the position of the i-th HDV, denoted by px,i, for i = 1, . . . , 4 and the estimated position, ˆp j x,i by the j-th CAV j = 1, . . . , 4 via the distributed observer (8)-(9). the state of HDVs despite large uncertainty. It should be clarified that the HDV parameters by free-flow and Helly’s car-following models are generally unknown to the CAVs, and CAVs only track the HDVs based on the… view at source ↗
Figure 11
Figure 11. Figure 11: This figure shows the velocity of the i-th HDV, denoted by vx,i, for i = 1, . . . , 4 and the estimated velocity, ˆv j x,i by the j-th CAV j = 1, . . . , 4 via the distributed observer (8)-(9) view at source ↗
Figure 12
Figure 12. Figure 12: This figure shows the distance measures ψ T i,k, for i = 1, . . . , 4 and T = 20 time￾steps (or 1sec). The fault at CAV 1 is detected by FAR less than 5% via the proposed stateful FDI. 27 view at source ↗
Figure 13
Figure 13. Figure 13: This figure shows the weighted distance measures view at source ↗
read the original abstract

Decentralized strategies are of interest for local decision-making over multi-vehicle networks. This paper studies mixed traffic networks of human-driven and autonomous vehicles with partial sensor measurements. The idea is to enable the group of connected autonomous vehicles (CAVs) to track the state of a group of human-driven vehicles (HDVs) via distributed consensus-based observers/estimators. Particularly, we make no assumption that the group of HDVs is locally observable in the direct neighborhood of any CAV. Then, the main contribution is to design local residual-based fault detection and isolation (FDI) at every CAV to detect possible faults/attacks in the sensor measurements. This distributed detection strategy enables every CAV to locally find possible anomalies in its taken sensor measurement with no need for a central processing unit. Two FDI logics are proposed with and without considering the history of the residuals. These FDI techniques are based on probabilistic threshold design on the residuals (in contrast to the existing deterministic threshold FDI techniques) with no assumption that the noise is of bounded support. This is more realistic in real-world multi-vehicle transportation systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript develops distributed consensus-based observers enabling a group of CAVs to estimate the states of HDVs in mixed traffic networks even when no individual CAV has local observability of the HDVs. It then designs local residual-based FDI at each CAV using probabilistic thresholds (with and without residual history) to detect sensor faults or attacks, without a central processor and without assuming bounded noise support, contrasting this with deterministic threshold methods.

Significance. If the observer convergence and residual distributions are rigorously established, the work offers a realistic decentralized FDI framework for intelligent transportation systems that relaxes common bounded-noise and full-observability assumptions, potentially improving fault resilience in partially observable multi-vehicle networks.

major comments (2)
  1. [Abstract / Observer design] The distributed observer design (as described in the abstract and setup) explicitly permits cases with no local observability of HDVs by any CAV yet provides no graph-theoretic conditions (e.g., joint observability of the union of measurement graphs or existence of a spanning tree in the CAV communication graph) guaranteeing asymptotic convergence of the consensus-based estimators. This is load-bearing because the FDI residuals are generated from estimation errors; without convergence, the residuals do not necessarily converge to the noise distribution and the probabilistic thresholds are ill-posed.
  2. [FDI logics] The two FDI logics rely on probabilistic threshold design on the residuals, but the manuscript provides no derivation steps or stability analysis showing how the thresholds are obtained from the limiting residual distribution (or how history is incorporated without introducing circularity). This undermines the claim of rigorous contrast to deterministic methods.
minor comments (1)
  1. [Abstract] The abstract states the design goals but omits any mention of simulation results, numerical validation of the probabilistic thresholds, or explicit statements of the noise model; adding a concise summary of these would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight areas where additional rigor will strengthen the presentation of the distributed observer convergence and the FDI threshold derivations. We address each point below and will incorporate the necessary clarifications and proofs in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract / Observer design] The distributed observer design (as described in the abstract and setup) explicitly permits cases with no local observability of HDVs by any CAV yet provides no graph-theoretic conditions (e.g., joint observability of the union of measurement graphs or existence of a spanning tree in the CAV communication graph) guaranteeing asymptotic convergence of the consensus-based estimators. This is load-bearing because the FDI residuals are generated from estimation errors; without convergence, the residuals do not necessarily converge to the noise distribution and the probabilistic thresholds are ill-posed.

    Authors: We agree that explicit graph-theoretic conditions are essential to guarantee asymptotic convergence of the distributed observers and thereby justify the limiting residual distributions used for the probabilistic thresholds. The original manuscript relies on standard multi-agent consensus results but does not state the required conditions (e.g., the CAV communication graph containing a directed spanning tree and collective observability of the HDV states via the union of local measurement graphs). In the revision we will add a dedicated theorem and proof establishing these conditions and the resulting convergence of the estimation errors to the noise statistics, ensuring the FDI analysis is well-posed. revision: yes

  2. Referee: [FDI logics] The two FDI logics rely on probabilistic threshold design on the residuals, but the manuscript provides no derivation steps or stability analysis showing how the thresholds are obtained from the limiting residual distribution (or how history is incorporated without introducing circularity). This undermines the claim of rigorous contrast to deterministic methods.

    Authors: We acknowledge that the derivation of the probabilistic thresholds from the limiting residual distribution and the handling of residual history require more explicit steps. The thresholds are obtained from the asymptotic Gaussian (or sub-Gaussian) distribution of the residuals once observer convergence is established; history is incorporated via a finite-length moving window whose statistics remain independent of future samples. In the revised manuscript we will insert the full derivation, including the Lyapunov-based stability argument for the observer error and the moment analysis or central-limit result for the residual distribution, together with a clear statement that the windowed history avoids circularity. This will provide the requested rigorous contrast to deterministic bounded-noise methods. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's chain proceeds from standard distributed consensus observer design (under partial observability) to residual generation and then to probabilistic threshold FDI logics. No equations or steps reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the thresholds and gains are derived from noise statistics and consensus error analysis rather than being tuned on the same detection-performance data. The approach rests on external control-theoretic results for residuals and is self-contained against those benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The work implicitly relies on standard assumptions from distributed estimation (network connectivity, existence of a spanning tree, and convergence of consensus under partial measurements) that are not enumerated here.

axioms (2)
  • domain assumption The communication graph among CAVs permits distributed state estimation of the HDV group even without local observability at any single CAV.
    Stated explicitly in the abstract as the setting in which the observers are designed.
  • domain assumption Sensor noise has known statistical properties sufficient to set probabilistic thresholds.
    Required for the probabilistic threshold design; no bounded-support assumption is made.

pith-pipeline@v0.9.0 · 5509 in / 1478 out tokens · 62186 ms · 2026-05-08T17:35:17.400597+00:00 · methodology

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