A Closed-loop, State-centric, Multi-agent Framework for Passenger Load Estimation from Heterogeneous Data Streams

Hao Zhou; Jingran Sun; Yiyao Xu; Yuhang Wang

arxiv: 2605.19834 · v1 · pith:25R4X7KVnew · submitted 2026-05-19 · 💻 cs.LG · cs.AI· cs.SY· eess.SY

A Closed-loop, State-centric, Multi-agent Framework for Passenger Load Estimation from Heterogeneous Data Streams

Yiyao Xu , Hao Zhou , Yuhang Wang , Jingran Sun This is my paper

Pith reviewed 2026-05-20 06:53 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.SYeess.SY

keywords passenger load estimationmulti-agent frameworkheterogeneous data streamsphysical feasibilitysensor fusionclosed-loop systemtransit operations

0 comments

The pith

A closed-loop multi-agent framework produces reliable passenger load estimates by enforcing physical feasibility on data from multiple sensors at each stop.

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

The paper proposes a framework for estimating how many passengers are on a transit vehicle when direct observation is impossible and sensors give imperfect or conflicting readings. It builds a unified stop-event backbone that processes information stop by stop, then runs a Perception-Physical-Fusion loop that respects physical rules about boarding and alighting while assigning changing levels of trust to different data sources. Any violations of those physical rules are turned into signals that retrain the system, making later estimates more robust. Transit agencies need accurate load trajectories to run operations and serve riders, yet current automatic counting systems still lose accuracy under heavy use or awkward station layouts.

Core claim

The central claim is that a closed-loop, state-centric, multi-agent framework, built around a unified stop-event backbone and a coupled Perception-Physical-Fusion loop, can enforce physical feasibility at every step, allocate trust dynamically among evidence sources, and feed physics-derived violation residuals back into training to improve robustness in passenger load estimation from heterogeneous data streams.

What carries the argument

The coupled Perception-Physical-Fusion loop inside the unified stop-event backbone, which carries out stop-by-stop inference, dynamically weights sensor evidence, and returns physical-violation residuals for further training.

If this is right

Load trajectories become usable for scheduling and passenger information even when sensors introduce incremental count errors or change reliability with station layout.
Conflicts between data sources are handled by shifting trust rather than by fixed averaging or discarding readings.
Training gains robustness because residuals from physical violations are fed back directly into model updates.
Trip-level macro-correction and closed-loop calibration modules can be added to refine estimates across an entire journey.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same stop-by-stop physical-constraint loop could be tested on other multi-sensor problems such as estimating vehicle occupancy in ride-sharing fleets.
A practical next check would be to run the system on live transit feeds and compare against fare-collection data to see whether the dynamic-trust mechanism identifies which sensors perform best under different crowding levels.
If the feedback loop works, agencies might reduce the need for expensive manual audits by letting the model self-correct from its own physical-rule violations.

Load-bearing premise

Physical feasibility constraints can be modeled and enforced inside the stop-event backbone and fusion loop without creating new inconsistencies across the different data streams.

What would settle it

Apply the framework to a transit line that has independent manual passenger counts as ground truth and measure whether estimated loads match the true counts more closely than standard methods while producing fewer physical-rule violations.

Figures

Figures reproduced from arXiv: 2605.19834 by Hao Zhou, Jingran Sun, Yiyao Xu, Yuhang Wang.

**Figure 2.** Figure 2: Dataset overview and motivating evidence characteristics. (a) Stop count distribution per trip. (b) Temporal coverage across operating hours. (c) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Composition of POI-based semantic clusters ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Representative failure modes and corrective mechanisms on held-out trips. (a) APC spike correction: raw APC (red dashed) induces an implausible [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

read the original abstract

To support operations and passenger-facing services, transit agencies need reliable passenger load trajectories. Currently, load estimates are typically inferred from imperfect sensing systems rather than fully observed, and the accuracy of modern automatic passenger counting (APC) systems still varies with station layout, flow intensity, and operating conditions. To address the challenges of robust passenger load estimation from heterogeneous data streams, including incremental count errors, evidence conflicts, and context-dependent sensor reliability, we propose a closed-loop, state-centric, multi-agent framework. This method enforces physical feasibility at every step, allocates trust dynamically among evidence sources, and feeds physics-derived violation residuals back into training for robustness improvement. The architecture consists of a unified stop-event backbone, a coupled Perception--Physical--Fusion loop for stop-by-stop inference, and optional trip-level macro-correction and closed-loop calibration modules.

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.

Desk Editor's Note private letter to a colleague

The paper lays out a closed-loop multi-agent architecture for transit passenger load estimation that ties physical constraints into sensor fusion, but it still needs concrete results to show the approach actually works.

read the letter

The main point is a framework that runs a unified stop-event backbone through a Perception-Physical-Fusion loop, dynamically weights evidence sources, and pushes physics-violation residuals back into the process to keep estimates feasible. That combination is the part that feels fresh for this domain. It directly targets the real headaches in automatic passenger counting: drifting errors, layout-dependent accuracy, and conflicting streams from different sensors. The optional trip-level corrections and closed-loop calibration give it some operational flexibility that pure data-driven models often lack. Credit to the authors for grounding the design in stop-level events rather than forcing everything into a single global model. The state-centric multi-agent setup also makes sense for allocating trust on the fly. The soft spot is the missing evidence. The description stays architectural with no equations shown for the residual term, no trust-allocation rule, and no error metrics or baseline comparisons on real data. Without those, it is hard to tell whether the physical constraints actually reduce inconsistencies or just add another layer that could drift. If the full manuscript has reproducible experiments on heterogeneous streams with clear gains over standard fusion methods, that gap closes. As written, the claim that residuals improve robustness is plausible but untested in the visible material. This is for transit researchers or applied ML groups working on sensor fusion in noisy physical systems. Someone already dealing with APC data or similar count-estimation problems could pull useful ideas from the loop structure. It is worth a serious referee because the problem is concrete, the architecture is coherent on its own terms, and the field needs more work that mixes physics constraints with learning rather than treating them separately.

Referee Report

2 major / 1 minor

Summary. The paper proposes a closed-loop, state-centric, multi-agent framework for robust passenger load estimation in transit systems from heterogeneous data streams. The architecture centers on a unified stop-event backbone together with a coupled Perception-Physical-Fusion loop that performs stop-by-stop inference; optional trip-level macro-correction and closed-loop calibration modules are also described. The central claims are that the method enforces physical feasibility at every step, dynamically allocates trust among evidence sources, and feeds physics-derived violation residuals back into training to improve robustness.

Significance. If the described mechanisms can be shown to work on real data, the framework would offer a principled way to integrate imperfect APC counts, evidence conflicts, and context-dependent sensor reliability while respecting physical constraints. Such an approach could meaningfully improve the reliability of passenger-load trajectories used for operations and passenger-facing services. The explicit use of a state-centric backbone and residual feedback distinguishes it from purely data-driven or open-loop fusion methods.

major comments (2)

Abstract: the manuscript supplies no experimental results, error metrics, or validation against real passenger-counting data, so it is impossible to assess whether the Perception-Physical-Fusion loop or residual-feedback mechanism actually delivers the claimed robustness gains.
Abstract: no equations, pseudocode, or formal definitions are given for the physical-feasibility constraints, the dynamic trust-allocation rule, or the residual-feedback term; without these, the central claim that feasibility is enforced “at every step” without introducing new inconsistencies cannot be evaluated.

minor comments (1)

The abstract would benefit from a concise statement of the data sources used in the heterogeneous streams and the precise definition of a “stop-event.”

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and will revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

Referee: Abstract: the manuscript supplies no experimental results, error metrics, or validation against real passenger-counting data, so it is impossible to assess whether the Perception-Physical-Fusion loop or residual-feedback mechanism actually delivers the claimed robustness gains.

Authors: We agree that empirical validation is essential to substantiate the claimed robustness gains. The current manuscript focuses on presenting the closed-loop framework and its components. In the revised version, we will add a dedicated experimental section that includes results on real APC and heterogeneous sensor data, along with quantitative error metrics and comparisons demonstrating the benefits of the Perception-Physical-Fusion loop and residual feedback. revision: yes
Referee: Abstract: no equations, pseudocode, or formal definitions are given for the physical-feasibility constraints, the dynamic trust-allocation rule, or the residual-feedback term; without these, the central claim that feasibility is enforced “at every step” without introducing new inconsistencies cannot be evaluated.

Authors: The full manuscript contains the formal definitions, equations, and algorithmic descriptions for physical-feasibility constraints, dynamic trust allocation, and residual feedback in the technical sections. To make these elements more immediately accessible and to directly support the claim of step-by-step enforcement, we will add a summary of the key equations and pseudocode to the abstract and introduction in the revision. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework relies on external physical constraints

full rationale

The paper presents a high-level architecture consisting of a unified stop-event backbone and a Perception-Physical-Fusion loop that enforces physical feasibility and feeds violation residuals back into training. No equations, fitted parameters, or derivation steps are visible in the abstract or summary that reduce by construction to the inputs themselves. The method is described as integrating heterogeneous data streams with dynamic trust allocation and optional macro-correction modules, but these are framed as novel combinations drawing on external physical models rather than self-defining or self-citing in a load-bearing way. The derivation chain remains self-contained against external benchmarks with no evidence of renaming known results, smuggling ansatzes, or forcing predictions from fitted subsets.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review is based solely on the abstract; full details on parameters and assumptions are unavailable.

axioms (1)

domain assumption Physical feasibility can be enforced at every inference step using the stop-event backbone
Stated directly in the abstract as a core property of the method.

pith-pipeline@v0.9.0 · 5687 in / 979 out tokens · 34363 ms · 2026-05-20T06:53:54.653213+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

The core inference engine is a spatial recursion that updates the load state at each stop... (Lphys_k, ephys_k) = P_C (L_{k-1}, B̂_k, Â_k) ... L_k = T(Lphys_k, yload_k, α_k)
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

enforces physical feasibility at every step... feeds physics-derived violation residuals back into training

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

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Personalized predictive public transport crowding infor- mation with automated data sources,

E. Jenelius, “Personalized predictive public transport crowding infor- mation with automated data sources,”Transportation Research Part C: Emerging Technologies, vol. 117, p. 102647, 2020

work page 2020
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[1] [1]

Personalized predictive public transport crowding infor- mation with automated data sources,

E. Jenelius, “Personalized predictive public transport crowding infor- mation with automated data sources,”Transportation Research Part C: Emerging Technologies, vol. 117, p. 102647, 2020

work page 2020

[2] [2]

A two-stage method for bus passenger load prediction using automatic passenger counting data,

P. Wang, X. Chen, J. Chen, M. Hua, and Z. Pu, “A two-stage method for bus passenger load prediction using automatic passenger counting data,”IET Intelligent Transport Systems, vol. 15, no. 2, pp. 248–260, 2021

work page 2021

[3] [3]

Accuracy of automatic passenger counting in open mass transit systems: Insights from italy,

B. Barabino, L. Raccagni, and R. Ventura, “Accuracy of automatic passenger counting in open mass transit systems: Insights from italy,” The Open Transportation Journal, vol. 19, p. e26671212383074, 2025

work page 2025

[4] [4]

Optimal bus bridging service for urban rail transit disruptions with stochastic passenger demand,

Y . Liu, T. Yang, and J. Su, “Optimal bus bridging service for urban rail transit disruptions with stochastic passenger demand,”PLOS ONE, vol. 20, no. 10, p. e0333686, 2025

work page 2025

[5] [5]

Individual path recommendation under public transit service disruptions consid- ering behavior uncertainty,

B. Mo, H. N. Koutsopoulos, Z.-J. M. Shen, and J. Zhao, “Individual path recommendation under public transit service disruptions consid- ering behavior uncertainty,”Transportation Science, vol. 59, no. 6, pp. 1235–1258, 2025

work page 2025

[6] [6]

Evaluating the performance of video-based automated passenger counting systems in real-world conditions: A comparative study,

C. Pronello and X. R. Garz ´on Ruiz, “Evaluating the performance of video-based automated passenger counting systems in real-world conditions: A comparative study,”Sensors, vol. 23, no. 18, p. 7719, 2023

work page 2023

[7] [7]

NAPC: A neural algorithm for automated passenger counting in public transport on a privacy-friendly dataset,

R. Seidel, N. Jahn, S. Seo, T. Goerttler, and K. Obermayer, “NAPC: A neural algorithm for automated passenger counting in public transport on a privacy-friendly dataset,”IEEE Open Journal of Intelligent Transportation Systems, vol. 3, pp. 33–44, 2021

work page 2021

[8] [8]

Engineering the neural automatic passenger counter,

N. Jahn and M. Siebert, “Engineering the neural automatic passenger counter,”Engineering Applications of Artificial Intelligence, vol. 114, p. 105148, 2022

work page 2022

[9] [9]

Large-scale Wi-Fi and Bluetooth data collection for reconstructing passenger flows,

A. Demetrio, F. Elgner, H. Hameister, M. Quinting, D. Warzok, and J. Wendel, “Large-scale Wi-Fi and Bluetooth data collection for reconstructing passenger flows,”Journal of Location Based Services, vol. 18, no. 2, pp. 185–204, 2024

work page 2024

[10] [10]

Self-supervised association of Wi-Fi probe requests under MAC address randomization,

T. He, J. Tan, and S. H. G. Chan, “Self-supervised association of Wi-Fi probe requests under MAC address randomization,”IEEE Transactions on Mobile Computing, vol. 22, no. 12, pp. 7044–7056, 2022

work page 2022

[11] [11]

D. K. Boyle,Passenger Counting Systems, ser. TCRP Synthesis of Transit Practice. Transportation Research Board of the National Academies, 2008, no. 77

work page 2008

[12] [12]

Vdv recommenda- tion 457: Automatic passenger counting systems,

Verband Deutscher Verkehrsunternehmen (VDV), “Vdv recommenda- tion 457: Automatic passenger counting systems,” Verband Deutscher Verkehrsunternehmen (VDV), Tech. Rep. 457, Apr. 2018, version 2.1

work page 2018

[13] [13]

Real time transit demand prediction capturing station interactions and impact of special events,

P. Noursalehi, H. N. Koutsopoulos, and J. Zhao, “Real time transit demand prediction capturing station interactions and impact of special events,”Transportation Research Part C: Emerging Technologies, vol. 97, pp. 277–300, 2018

work page 2018

[14] [14]

Integration of exponential smoothing with state space formulation for bus travel time and arrival time prediction,

S. V . Kumar, K. Chaitanya Dogiparthi, L. Vanajakshi, and S. C. Subramanian, “Integration of exponential smoothing with state space formulation for bus travel time and arrival time prediction,”Transport, vol. 32, no. 4, pp. 358–367, 2017

work page 2017

[15] [15]

Noise detection in agent reputation models using imm filtering,

J. Carbo, J. Garcia, and J. M. Molina, “Noise detection in agent reputation models using imm filtering,” inTrust in Agent Societies. Springer, 2008, pp. 25–42

work page 2008

[16] [16]

A novel adaptive kalman filter based on credibility measure,

Q. Ge, X. Hu, Y . Li, H. He, and Z. Song, “A novel adaptive kalman filter based on credibility measure,”IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 1, pp. 103–120, 2023

work page 2023

[17] [17]

Context- aware automated passenger counting data denoising,

N. Cherrier, B. R ´erolle, M. Graive, A. Dib, and E. Schmitt, “Context- aware automated passenger counting data denoising,” in2023 IEEE 26th International Conference on Intelligent Transportation Systems (ITSC). IEEE, Sep. 2023, pp. 1935–1942

work page 2023

[18] [18]

Adjustment boarding and alighting passengers on a bus transit line using qualitative informa- tion,

J. de O ˜na, P. G´omez, and E. M´erida-Casermeiro, “Adjustment boarding and alighting passengers on a bus transit line using qualitative informa- tion,”Applied Mathematical Modelling, vol. 38, no. 3, pp. 1147–1158, 2014

work page 2014

[19] [19]

ℓ 1-minimization method for link flow correction,

P. Yin, Z. Sun, W.-L. Jin, and J. Xin, “ℓ 1-minimization method for link flow correction,”Transportation Research Part B: Methodological, vol. 104, pp. 398–408, 2017

work page 2017

[20] [20]

Unified occupancy on a public transport network through combination of AFC and APC data,

A. Dib, N. Cherrier, M. Graive, B. R ´erolle, and E. Schmitt, “Unified occupancy on a public transport network through combination of AFC and APC data,” in2023 IEEE 26th International Conference on Intelligent Transportation Systems (ITSC), Sep. 2023, pp. 1963–1970

work page 2023

[21] [21]

On the limitations of physics-informed deep learning: Illustrations using first-order hyperbolic conservation law-based traffic flow models,

A. J. Huang and S. Agarwal, “On the limitations of physics-informed deep learning: Illustrations using first-order hyperbolic conservation law-based traffic flow models,”IEEE Open Journal of Intelligent Transportation Systems, vol. 4, pp. 279–293, 2023

work page 2023

[22] [22]

Physics enhanced residual policy learning (perpl) for safety cruising in mixed traffic platooning under actuator and communication delay,

K. Long, H. Shi, Y . Zhou, and X. Li, “Physics enhanced residual policy learning (perpl) for safety cruising in mixed traffic platooning under actuator and communication delay,”arXiv, 2024

work page 2024

[23] [23]

Logic-informed reinforcement learning for cross-domain optimization of large-scale cyber-physical systems,

G. Wan, P. Zeng, X. Dong, C. Song, S. Cui, D. Li, Q. Dong, Y . Liu, and H. Bai, “Logic-informed reinforcement learning for cross-domain optimization of large-scale cyber-physical systems,”arXiv preprint, 2025

work page 2025