Passive Multi-Target Visible Light Positioning Based on Multi-Camera Joint Optimization

Dong Wei; Meng Zhang; Wenxuan Pan; Yang Yang; Zhiyu Zhu

REVIEW 3 major objections 5 minor 15 references

Passive Multi-Target Visible Light Positioning Based on Multi-Camera Joint Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Ceiling cameras locate LED-tagged targets to millimeter accuracy by first solving linear least squares, then refining with nonlinear joint optimization.

desk verdict A modest but sound single-target VLP refinement whose multi-target claims outrun the evidence; the separable 'joint' optimization is the main gap. read the letter →

arxiv 2506.02418 v2 pith:ELHMAJBR submitted 2025-06-03 eess.SP

Wenxuan Pan , Yang Yang , Dong Wei , Meng Zhang , Zhiyu Zhu This is my paper

classification eess.SP PACS 42.79.Pw07.05.Pj

keywords visiblelightpositioningpassivemulti-camerajointoptimizationlinearleastsquaresLevenberg-Marquardtreprojectionerrorindoorcamera-basedVLP

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a passive visible light positioning algorithm, MCJO, that uses multiple pre-calibrated ceiling cameras to locate targets equipped with simple unmodulated LED point sources. The key idea is a two-stage process: first, an initial position estimate is obtained in closed form by linear least squares on the multi-view projection rays; second, this estimate is refined by nonlinear least-squares minimization of the reprojection error across all cameras and targets. The paper claims this two-stage approach achieves millimeter-level accuracy, outperforming the linear-only state of the art by about 19% in simulation and reaching an average error of 5.63 mm in experiments. If true, this makes high-accuracy indoor positioning possible with low-cost infrastructure by reusing existing surveillance cameras and attaching only a small LED to each target.

What carries the argument

The central mechanism is the two-stage estimator: Stage one computes the LLS closed-form solution to minimize the sum of squared distances from the estimated target point to N multi-view projection rays, yielding the initial estimate from Eq. (11). Stage two builds a reprojection error model per Eq. (12)-(13) and minimizes the total squared reprojection error over all targets and cameras via the Levenberg-Marquardt algorithm, initialized with the LLS result. This initialization is the load-bearing connection between the two stages: the paper assumes the LLS estimate is close enough to the true position that L-M converges to the global optimum rather than a local minimum.

What would settle it

One concrete test is to search for target positions and camera layouts where the LLS estimate falls outside the basin of attraction of the true solution, causing the nonlinear stage to converge to a local minimum with a reprojection error higher than the LLS-only baseline. This could be checked by running MCJO on many random configurations and comparing the final reprojection error to the starting LLS error; if the refinement ever increases the error or fails to improve on the baseline, the central claim would be falsified.

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Extended reading notes

Core claim

The central claim is that adding a nonlinear joint refinement stage on top of a linear least-squares ray-intersection estimate improves passive multi-camera VLP accuracy to the millimeter level, surpassing the purely linear MC-VLP baseline. In simulation, MCJO achieves a mean position error of 9.69 mm versus 12.00 mm for the baseline, an improvement of about 19%; in a real three-camera prototype, it reaches an average position error of 5.63 mm with 90% of errors below 1 cm. The paper argues this improvement comes from properly modeling the inherent nonlinearity of the pinhole projection, which the linear ray-intersection method ignores and which makes it sensitive to image noise.

Load-bearing premise

The Levenberg-Marquardt refinement converges to the true target position, which requires the linear least-squares initial estimate to lie within the basin of attraction of the correct solution; the paper provides no convergence or local-minimum analysis for this non-convex optimization step.

Editorial extensions

If this is right

If MCJO works as claimed, indoor positioning systems can be built from off-the-shelf surveillance cameras plus cheap unmodulated LEDs, removing the need for specialized luminaire infrastructure or cameras mounted on each target.
The method simultaneously localizes multiple targets at a server, which suits warehouse object tracking, logistics monitoring, and other multi-target indoor scenarios.
Because targets are passive and unmodulated, the system scales to many targets at low marginal hardware cost, and target motion or LED orientation does not degrade accuracy as long as each target is visible to at least two cameras.
The claimed 19% accuracy improvement suggests that nonlinear projection correction is a meaningful gain over linear ray-intersection methods, motivating similar two-stage designs in other camera-based positioning systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The accuracy gain from the nonlinear stage probably grows with image noise and with camera configurations that produce less favorable ray intersections; the simulations indeed show larger gains under higher noise, which is consistent with this expectation.
The paper's claim that MCJO 'does not suffer from positioning ambiguity' under symmetry relies on an analysis from the dual-camera reference [9]; extending this proof to N-camera layouts and to targets outside the common field of view would strengthen the result.
A testable extension is to quantify how much of the 19% improvement comes from the nonlinear model versus the joint optimization across targets; ablating the joint term would isolate the source of the gain.
Since reprojection error surfaces in multi-camera geometry are not generally convex, a convergence analysis or a comparison with a global-optimization solver would clarify the conditions under which the L-M refinement is guaranteed to improve on the LLS estimate.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Quick take: this is a clean, incremental piece. The idea is to take the existing linear least-squares triangulation from He et al. and add a Levenberg-Marquardt reprojection refinement stage. That is standard bundle-adjustment geometry applied to passive VLP, but I don't think it has been done in exactly this context, so it is a legitimate small contribution.

The math checks out: Eqs. (3)-(11) and (12)-(16) are correct, and the simulation with 10,000 Monte Carlo runs is more thorough than most letters. The experimental work is honest: 98 samples on two height planes, with STDs given, and the single-target result of 5.63 mm MPE is believable. They also openly state that the experiments are single-target only.

The soft spots are all around the multi-target framing. The title and abstract promise simultaneous localization of multiple targets, but the experiments never test that. In the simulation, the pixel-to-target correspondences are known by construction because the targets are randomly generated and projected, so the association problem is never exercised. And the 'joint' cost in Eq. (14) is just a sum over targets; there is no coupling term that would let the optimization disambiguate wrong correspondences. So the stress-test reading is right: the multi-target claim is not supported by the evidence. A wrong correspondence fed into the LLS stack would give a large error, and color-based target separation is only proposed, not validated.

Also, the improvement over MC-VLP is measured against the authors' own implementation of the baseline, so the 19% is a bit soft. That is not a fatal flaw, just a caution.

One minor omission: no convergence analysis for the LM stage when the LLS initialization is poor. In practice it is probably fine, but a sentence about it would have helped.

Who benefits? People working in camera-based VLP looking for a cheap accuracy boost. It is a solid letter-level result, but it should not be sold as a multi-target system until the association question is tackled. If I were editing, I would send this out for peer review, and the referee's main job would be to make the authors scale back the multi-target language and maybe add a synthetic association-error test.

Regards.

Referee Report

3 major / 5 minor

Summary. The letter proposes MCJO, a two-stage passive visible light positioning algorithm for localizing unmodulated LED point sources using multiple pre-calibrated ceiling-mounted cameras. In the first stage, linear least squares (LLS) triangulates each target from multi-view projection rays (Eqs. (3)-(11)). In the second stage, Levenberg-Marquardt refinement minimizes the total reprojection error (Eqs. (12)-(16)). Simulation results with 10,000 random iterations and three targets show an MPE of 9.69 mm, about 19% lower than the MC-VLP baseline from [10]; experiments with 98 samples on two planes report an average position error of 5.63 mm. The paper claims simultaneous multi-target localization, but the experimental section explicitly covers only a single-target scenario, and the simulation assumes known pixel-to-target correspondences.

Significance. If the single-target accuracy result is reliable, MCJO is a practical, low-cost passive VLP method that reuses existing camera infrastructure and avoids dedicated luminaire modulation. The derivations in Eqs. (3)-(11) and (12)-(16) are standard and appear correct, and the empirical effort is reasonable: 10,000 Monte Carlo iterations, 98 experimental samples, and standard deviations are reported. The main significance gap is that the paper's distinctive multi-target and 'joint optimization' claims are not supported by evidence; the current results demonstrate an LLS-plus-nonlinear-refinement improvement for known single-target correspondences, not simultaneous multi-target positioning under association uncertainty.

major comments (3)

[Section IV-B and Section IV-A] The central multi-target claim is not validated. Section IV-B explicitly states that the experiments focused on a single-target scenario, and the multi-target proposal via colored LEDs is presented without any experimental support or robustness analysis. In Section IV-A, the simulation randomly generates three target positions and projects them, so the pixel-to-target correspondences are known by construction; the data-association problem, which is the defining challenge in multi-target passive VLP, is never exercised. The abstract's statement that MCJO can 'simultaneously localize these targets' is therefore not backed by evidence.
[Equation (14)] The optimization in Eq. (14) is a sum of per-target reprojection errors with no coupling term across j; the 'joint' formulation in Eqs. (15)-(16) is only a stacked representation of M independent single-target problems. This means the second stage cannot use geometric consistency among targets to recover from a wrong correspondence. Any incorrect pixel-to-target assignment entering the LLS stage (Eqs. (9)-(11)) or the LM refinement will directly produce a large position error, and the claimed 19% improvement over MC-VLP is contingent on perfect association. The paper should either add a cross-target constraint that exploits multi-target geometry or substantially qualify the 'joint' and multi-target claims.
[Section III-B and Table II] The claimed improvement of 19% over the baseline rests on the Levenberg-Marquardt refinement initialized with the LLS estimate from Eq. (11). The paper provides no convergence or local-minimum analysis, and the reprojection-error surface in multi-camera geometry is not generally convex. If the LLS estimate lies outside the basin of attraction, the refinement can converge to a wrong local minimum. The simulations do not report how often this occurs or whether the improvement is uniform across configurations. At minimum, the authors should report the fraction of Monte Carlo runs in which LM reduces the error relative to the LLS initialization, and show sensitivity to initialization quality.

minor comments (5)

[Fig. 3 caption] The caption contains a duplicated '(a)' label: '(a) CDFs of position errors, (a) MPE versus focal length' should be '(a) CDFs of position errors, (b) MPE versus focal length', with subsequent labels renumbered to match the text in Section IV-A.
[Equation (15)] The definition of the total error vector is imprecise: the expression '[ϵ1(xw_1); . . .; ϵN (xw_M)]' does not enumerate all M times N camera-target error vectors. It should be written as a concatenation over i and j, e.g., '[ϵ_1(x_1^w); ...; ϵ_N(x_1^w); ...; ϵ_1(x_M^w); ...; ϵ_N(x_M^w)]', to match the claimed dimension R^{2MN}.
[Section IV-A] The phrases '86th accuracies' and '73th' should read '86th percentile' and '73rd percentile', respectively.
[Table III] The table header uses 'Principle point' but the correct term is 'Principal point'.
[Section IV-B] The sentence 'The above experiments focused on a single-target scenario' is an important limitation and should appear earlier, for example in the abstract or the introduction, so that the claims are not overstated.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: MCJO's two-stage derivation is self-contained and the performance claims are empirical; the admitted single-target-only experiment is a support gap, not a circular step.

full rationale

MCJO consists of an LLS ray-intersection stage (Eqs. (6)-(11)) followed by Levenberg-Marquardt minimization of reprojection error (Eqs. (12)-(16)). Each stage is derived directly from the pinhole model and measured pixel coordinates; no parameter is fitted to the reported MPE or to the MC-VLP baseline, and the 19% improvement is an empirical comparison against the published algorithm [10], not a quantity that is reused as an input. The paper's self-citations ([2], [7], [8]) appear only in background statements about prior camera-based VLP work and do not carry the derivation. The remark that ambiguity does not occur under a dual-camera setup cites [9], which is by different authors, and is not a self-citation chain. The paper itself admits that the experiments concern a single-target scenario and only proposes color discrimination for multi-target operation without experimental validation; the simulations also provide target correspondences by construction. These are genuine support gaps for the multi-target claim, but they are not circular reasoning: the single-target accuracy result remains self-contained and externally comparable. Score 0: no significant circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No new physical entities or fitted constants are introduced; the method relies on standard camera geometry. The load-bearing premises are calibration accuracy, the Gaussian noise model, and L-M convergence.

assumptions (4)

domain assumption Pinhole camera model with known intrinsics K and extrinsics (Rw_c, tw_c) describes image formation exactly.
Invoked in Section II, Eqs. (1)-(2); all later ray and reprojection calculations depend on this model.
domain assumption Pixel noise in simulation is zero-mean white Gaussian with sigma = 3 px; no other error sources are modeled.
Stated in Section IV-A following [10]; the 19% improvement is measured under this noise-only model.
ad hoc to paper Levenberg-Marquardt initialized with the LLS solution converges to a good local minimum for all target configurations.
Section III-B uses L-M with the LLS estimate as initialization but provides no convergence or global optimality analysis; if the initialization is outside the basin of attraction, the refinement could degrade accuracy.
domain assumption Every target is visible to at least two cameras at all times.
Section II assumes N >= 2; simulation generates positions while ensuring visibility to all cameras, and the prototype uses three cameras with overlapping FoV.

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Cite this review

Pith. "Pith review of Passive Multi-Target Visible Light Positioning Based on Multi-Camera Joint Optimization." pith.science (2026). https://pith.science/paper/ELHMAJBR

@misc{pith2026250602418,
  author       = {Pith},
  title        = {Pith review of: Passive Multi-Target Visible Light Positioning Based on Multi-Camera Joint Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ELHMAJBR}},
  note         = {Machine review of arXiv:2506.02418}
}

read the original abstract

Camera-based visible light positioning (VLP) has emerged as a promising indoor positioning technique. However, the need for dedicated luminaire infrastructure and on-target cameras in existing algorithms may limit their scalability and increase deployment costs. To address these limitations, this letter proposes a passive VLP algorithm based on Multi-Camera Joint Optimization (MCJO). In the considered system, multiple ceiling-mounted pre-calibrated cameras continuously capture images of targets with unmodulated point light sources, and can simultaneously localize these targets at the server. In particular, MCJO comprises two stages: It first estimates target positions via linear least squares (LLS) from multi-view projection rays; then refines these positions through nonlinear joint optimization to minimize the reprojection error. Simulation results show that MCJO can achieve millimeter-level accuracy, with an improvement of 19% over an LLS-based state-of-the-art algorithm. Experimental results further show that MCJO achieves an average position error as low as 5.63 mm.

Figures

Figures reproduced from arXiv: 2506.02418 by the authors.

**Figure 1.** The considered passive VLP system. can achieve millimeter-level accuracy, with an improvement of 19% over the state-of-the-art (SOTA) algorithm in [10]. Experimental results further show that MCJO can achieve an average position error of 5.63 mm. II. SYSTEM MODEL The considered VLP scenario is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** RCT versus number of targets and cameras. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** The prototype of MCJO positioning system. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Figures from the paper (2 more)

**Figure 3.** Figure 3: Simulation Results. (a) CDFs of position errors, (a) MPE versus focal [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]

**Figure 5.** Figure 5: Experimental results. (a) Distribution of 3-D position errors at a height of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [10]

Indoor 3D visible light positioning based on multiple cameras: Algorithm design and error analysis,

J. He, N. Huang, and C. Gong, “Indoor 3D visible light positioning based on multiple cameras: Algorithm design and error analysis,” IEEE Trans. Wirel. Commun. , vol. 23, no. 5, pp. 4331–4346, May 2024

work page 2024

[2] [1]

Positioning using wireless networks: Applications, recent progress, and future challenges,

Y . Yang et al., “Positioning using wireless networks: Applications, recent progress, and future challenges,” IEEE J. Sel. Areas Commun. , vol. 42, no. 9, pp. 2149–2178, Sep. 2024

work page 2024

[3] [2]

A survey on indoor visible light positioning systems: Fundamentals, applications, and challenges,

Z. Zhu, Y . Yang, M. Chen, C. Guo, J. Cheng, and S. Cui, “A survey on indoor visible light positioning systems: Fundamentals, applications, and challenges,” IEEE Commun. Surv. Tut. , vol. 27, no. 3, pp. 1656–1686, Jun. 2025

work page 2025

[4] [3]

Visible light posi- tioning as a next-generation indoor positioning technology: A tutorial,

S. Bastiaens, M. Alijani, W. Joseph, and D. Plets, “Visible light posi- tioning as a next-generation indoor positioning technology: A tutorial,” IEEE Commun. Surv. Tut. , vol. 26, no. 4, pp. 2867–2913, 4th Quart. 2024

work page 2024

[5] [4]

Design and demonstration of robust visible light positioning based on received signal strength,

N. Huang, C. Gong, J. Luo, and Z. Xu, “Design and demonstration of robust visible light positioning based on received signal strength,” J. Lightw. Technol., vol. 38, no. 20, pp. 5695–5707, Oct. 2020

work page 2020

[6] [5]

A novel fingerprint database regeneration method for accurate visible light positioning,

S. Xu, F. Wei, and Y . Wu, “A novel fingerprint database regeneration method for accurate visible light positioning,” IEEE Trans. Instrum. Meas., vol. 73, 2024, Art. no. 2512613

work page 2024

[7] [6]

Camera pose estimation using a VLC-modulated single rectangular LED for indoor positioning,

B. Hussain, Y . Wang, R. Chen, and C. P. Yue, “Camera pose estimation using a VLC-modulated single rectangular LED for indoor positioning,” IEEE Trans. Instrum. Meas. , vol. 71, 2022, Art. no. 8505511

work page 2022

[8] [7]

Positioning using visible light communications: A perspective arcs approach,

Z. Zhu, C. Guo, R. Bao, M. Chen, W. Saad, and Y . Yang, “Positioning using visible light communications: A perspective arcs approach,” IEEE Trans. Wirel. Commun. , vol. 22, no. 10, pp. 6962–6977, Oct. 2023

work page 2023