Stone Soup: ADS-B-based Multi-Target Tracking with Stochastic Integration Filter

Erik Blasch; Jakub Matousek; Jindrich Dunik; John Hiles; Ondrej Straka; Ruixin Niu

REVIEW 4 major objections 5 minor 38 references

Stone Soup: ADS-B-based Multi-Target Tracking with Stochastic Integration Filter

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The third-order stochastic integration filter produces more consistent multi-target tracks than the extended Kalman filter, particularly when targets fly close together.

desk verdict A useful but under-powered extension of SIF to multi-target tracking; the single-run evidence is too thin to support the stated conclusion. read the letter →

arxiv 2506.07889 v2 pith:HAQJD4W4 submitted 2025-06-09 eess.SP

John Hiles , Jakub Matousek , Erik Blasch , Ruixin Niu , Ondrej Straka , Jindrich Dunik This is my paper

classification eess.SP

keywords multi-targettrackingstochasticintegrationfilterextendedKalmanglobalnearestneighbourdataassociationADS-BsurveillanceOSPAmetricSIAPmetrics

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 claims that in multi-target tracking the choice of local state estimator affects not only accuracy but also data-association reliability. Across two air-traffic scenarios built in an open-source tracking framework, the third-order stochastic integration filter (SIF) gives more consistent covariance estimates than the extended Kalman filter (EKF), and in dense, overlapping traffic it avoids the covariance spikes and association-ambiguity jumps the EKF exhibits. The paper argues this makes the SIF a viable EKF alternative in high-density multi-target settings when computation is not the bottleneck, and it quantifies the differences with OSPA, SIAP, and covariance-norm metrics. If true, this matters because dense airspace and cluttered surveillance are exactly where association mistakes degrade tracking.

What carries the argument

The central object is the third-order stochastic integration filter (SIF), a local nonlinear filter that evaluates the Gaussian-weighted integrals in the Kalman update by stochastic numerical integration rather than by linearising the measurement function as the EKF does. The SIF's random integration points give an asymptotically accurate approximation of the conditional mean and covariance, and the resulting covariance estimates stay better scaled in nonlinear geometries. The machinery that carries the argument is the interplay between that covariance realism and the global nearest neighbour data associator, which uses Mahalanobis distance to decide which detection updates which track: when the filter's covariance is too small or misshapen, the associator can lock onto the wrong target. The paper compares the SIF against the EKF (and notes that the UKF with default settings failed to keep covariance positive semidefinite) using OSPA, SIAP ambiguity, SIAP position accuracy, and sum of Frobenius covariance norms.

What would settle it

Rerun both multi-target scenarios many times with independent random seeds and record the OSPA, SIAP ambiguity, and sum-of-covariance-norms traces; if the EKF's covariance spikes are not consistently larger or more frequent than the SIF's across runs, the reported advantage is a single-realization artifact.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central finding is that the third-order SIF demonstrates a notable albeit subtle performance uplift over the EKF in both test scenarios. In the simulated class-B airspace, where ten maneuvering targets follow overlapping trajectories, the SIF's covariance norms remain smooth while the EKF shows large uncertainty spikes at moments of ambiguous association; the EKF also never fully resolves its SIAP ambiguity, while the SIF keeps association clean. In the ADS-B class-A scenario, 84 aircraft are tracked with three simulated radars, and the SIF shows only marginal improvement, which the paper attributes to targets being far apart so that EKF linearization suffices. The paper reads the dense-scenario result as evidence that filter covariance consistency directly improves measurement-to-track association, and it suggests the advantage could grow in cluttered environments, although clutter is not actually simulated in either experiment.

Load-bearing premise

The paper's conclusions rest on one realization of each scenario without repeated trials or error bars, and on the interpretation that EKF covariance spikes are a cause rather than a consequence of association errors.

Editorial extensions

If this is right

In dense multi-target scenarios with overlapping trajectories, switching the local estimator from EKF to third-order SIF should reduce association-induced covariance spikes and keep ambiguity scores closer to the ideal value of one.
In sparse airspace, EKF remains adequate; the SIF's benefit is small enough that its higher computational cost may not be justified there.
Filter covariance consistency is not just an internal property: it directly shapes measurement-to-track association, so improving the filter can improve tracking without changing the association algorithm.
The SIF's advantage is expected to be more pronounced in cluttered environments, though this was not tested in the paper.

Reading between the lines

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

A testable extension the paper leaves implicit: add clutter and false alarms to the class-B scenario; if covariance realism is the mechanism, the SIF's association advantage should widen when spurious detections compete with true ones.
The GNN associator's Mahalanobis gating depends on predicted covariance scale; this suggests that any filter that better calibrates covariance, not only the SIF, could yield similar association benefits in dense scenarios.
One could swap the associator (e.g., joint probabilistic data association or multiple hypothesis tracking) to see whether the SIF advantage shrinks once association decisions are made more robustly, which would clarify how much of the benefit is due to the filter alone.
Because each scenario is shown for a single run, the size of the SIF's advantage should be quantified with repeated runs before relying on it in filter selection.

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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

The new thing here is an extension of the authors' single-target SIF work to multi-target tracking in Stone Soup, with one simulated dense scenario and one real ADS-B scenario. The comparison is legitimate and the code is provided, which is a real strength. The paper uses standard metrics, acknowledges the uplift is "subtle," and positions itself as a follow-up to earlier work. That part is fine.

The problem is the evidence base. Each scenario is run exactly once, and the SIF is a stochastic integration filter with random points. No seeds are reported, so the smooth SIF covariance trace could be a favorable draw, and the EKF spikes could be run-to-run luck. Without Monte Carlo repetitions or error bars, the central claim "notable albeit subtle uplift" is not actually demonstrated. This matters because the effect is subtle; the missing uncertainty quantification is load-bearing.

There are also two smaller issues. First, the UKF is excluded after "stability issues" with default parameters, but no tuning is reported. Since the SIF is essentially a randomized relative of the UKF, this weakens the comparison. Second, the clutter narrative is inconsistent: the introduction says the ADS-B scenario introduces clutter, Section IV.A says "we are not considering clutter," and the conclusion says clutter was not tested. That needs cleaning up.

The interpretation that EKF spikes are caused by association errors is plausible but not proven. The two effects are confounded in a single run, and no oracle-association experiment separates them. Still, the plotted traces do show a consistent qualitative difference in the dense scenario, and the code lets anyone check the result.

Who is this for? People comparing local filters inside Stone Soup, and anyone working on SIF applications. It deserves a real referee, not a desk reject, because it is a honest empirical benchmark with reproducible code. But the revision should add Monte Carlo repetitions with fixed seeds, report variance, reconcile the clutter text, and either tune the UKF or justify its absence. If those are addressed, the result could be credible; as it stands, the evidence is suggestive, not conclusive.

Referee Report

4 major / 5 minor

Summary. The paper evaluates the Stochastic Integration Filter (SIF) against the Extended Kalman Filter (EKF) for multi-target tracking within the Stone Soup framework, using two scenarios: a simulated Class-B airspace scenario with ten maneuvering targets and an ADS-B Class-A scenario with 84 aircraft whose detections are simulated from three radars. Performance is compared through OSPA, SIAP ambiguity, SIAP position accuracy, and sums of covariance norms. The central claim, stated in Section VII, is that the third-order SIF yields a 'notable albeit subtle' performance uplift over the EKF, particularly in the dense Class-B scenario, and that this stems from more consistent covariance propagation that reduces association-induced ambiguity spikes. The authors provide source code for the scenario definitions and Stone Soup setup.

Significance. If the empirical claim is reproducible, the paper is a useful practical demonstration that a stochastic integration filter can improve dense multi-target tracking within an open-source tracking framework. The use of standard Stone Soup metrics, the inclusion of a realistic ADS-B-based scenario, and the release of source code are genuine strengths that make the proposed comparison easy to reuse and extend. However, the significance is currently conditional: the evidence consists of a single realization of each scenario, the filter itself is stochastic, and the load-bearing causal mechanism is asserted rather than isolated. The paper is therefore a promising application study whose central claim needs stronger empirical support before it can be accepted.

major comments (4)

[V.B, VI.C, VII] The paper's central claim rests on a single run of each scenario, but the SIF is a stochastic filter whose integration points are randomized (Section III.B, Eq. (17)). No random seed, number of repetitions, or error bars are reported for the OSPA, SIAP, or covariance-norm traces in Figures 2-8. Since the reported uplift is described as 'subtle,' run-to-run variation is material; the observed SIF advantage may be seed-specific. Please add Monte Carlo repetitions (ideally with a stated number of seeds and mean/quantile traces, or at minimum a fixed reproducible seed plus a sensitivity check) so the reader can assess whether the SIF-EKF gap is signal rather than noise.
[V.B] The prose attributes the EKF covariance spikes to association errors and claims the SIF avoids them through better covariance propagation, but this causal mechanism is not demonstrated. In a single unseeded run, association errors and covariance inflation are confounded: an association error inflates covariance, and an inflated covariance can cause further association errors, as the text itself notes by describing the 'interdependent nature' of the two effects. To separate these effects, please include a controlled comparison with oracle or ground-truth data association; if the SIF advantage persists under perfect association, the covariance-propagation explanation is supported, and if not, the advantage should be attributed to interaction with the GNN associator rather than to the filter alone.
[I.B, IV.B, IV.C, VII] There is a direct contradiction about whether clutter is present. Section I.B says scenario (ii) involves 'introducing the clutter,' Section IV.C says the metrics evaluate performance 'in the presence of clutter,' but Section IV.B states 'for the purpose of this paper, we are not considering clutter,' and Section VII says the clutter scenario 'was not tested in this paper.' The manuscript must specify the actual clutter configuration. If no clutter is used, remove the clutter language from Sections I.B and IV.C and temper the concluding speculation that SIF 'may have a significant advantage in tracking targets in the presence of clutter'; if clutter is used, provide its model, density, and any relevant parameters.
[VI.A, Eq. (26)] The three-dimensional measurement model in Eq. (26) appears to be incorrectly typeset and, as written, does not describe a consistent range-azimuth-elevation model. The elevation expression uses x_{3,k} (east position) where the vertical coordinate should appear, and the second and third components have malformed subscripts/superscripts. The state vector for the 3D case is also not explicitly defined. Please correct Eq. (26), define the state ordering, and verify that the provided code implements the corrected formula.

minor comments (5)

[III.A, Eq. (15)] In Eq. (15), P^{xx}_{k+1|k} is equated to E[x_{k+1}|z_k], which is a mean, not a covariance; the equation should state the covariance expression explicitly (and should use P_{k|k} consistently with the notation introduced earlier).
[II] There is a duplicated word in the sentence 'The Stone Soup project project is an open-source tracking and estimation framework.'
[VI.A] The text refers to 'FightRadar24' in the introduction; this should be 'FlightRadar24.'
[V.A] The simulation region is described as '30 [km] by 300 [km2]'; the units are inconsistent and should be clarified, e.g., 30 km by 300 km.
[IV.B] The UKF is excluded because it failed to maintain a positive semidefinite covariance with default Stone Soup parameters, but no details of the failure or of any attempted tuning are given. Since the stated goal in Section I.B is filter selection, please add a sentence explaining whether the exclusion is a Stone Soup implementation issue or an inherent UKF limitation in these scenarios.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the SIF-vs-EKF comparison is an empirical benchmark with independent metrics and data, not a derivation that reduces to its own inputs.

full rationale

This is an empirical evaluation paper, not a derivation. The central claim (Section VII) that the third-order SIF shows a 'notable albeit subtle performance uplift' over the EKF is supported by Stone Soup metrics (OSPA, SIAP ambiguity, SIAP position accuracy, sum of covariance norms) computed on a simulated Class-B scenario and a real ADS-B Class-A scenario. No parameter is fitted to the reported conclusion and then renamed as a prediction: the SIF and EKF are run as distinct filters, and the metrics are external to the filter designs. The stochastic integration rule in Eq. (17) is a previously published estimator, and the self-citations [8], [10], [11] are used as background support for SIF's general robustness, not as the load-bearing evidence for the present comparison; the actual evidence is the new experiments, standard metrics, and openly provided code. The single-run nature of the scenarios is a reproducibility/statistical-significance concern, which belongs to correctness risk, not circularity. Accordingly, no circular step can be exhibited, and the appropriate score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The benchmark rests on standard Gaussian filtering assumptions, user-chosen tracker thresholds, and the fidelity of ADS-B as ground truth. None of these are fitted to force the SIF result, but they constrain how far the conclusions generalize.

free parameters (4)

OSPA cardinality cutoff c = 10 (Class-B), 250 (Class-A)
Hand-chosen per scenario; weights cardinality errors relative to localization and directly affects the reported OSPA difference between filters.
GNN missed-detection distance threshold = 5
Hand-chosen in Section IV.A; controls which detections can be associated and therefore shapes ambiguity and covariance spikes.
Track deletion time threshold = 10
Hand-chosen in Section IV.A; determines track persistence and affects cardinality metrics.
Process noise intensities qx, qy, qz = 0.05 (Class-B), 10, 10, 5 (Class-A)
Hand-chosen motion-model noise covariances; covariance norms and consistency comparisons depend on them.

assumptions (5)

domain assumption Gaussian-assumed filtering density so local filters are adequate (Eq. 8, Section III.B)
The comparison is conducted inside the Gaussian-assumed local filter paradigm; no nonlinear filter or particle filter baseline is used.
domain assumption Zero-mean Gaussian, mutually independent process/measurement noise with known covariances (Eqs. 3-5)
Standard state-space model assumptions invoked in Section III.A; the OpenSky ground truth is treated as noise-free.
domain assumption ADS-B broadcasts are exact ground truth (Section VI.A)
OpenSky aircraft states are used as truth and radar detections are simulated from them; ADS-B errors or spoofing would bias the evaluation.
domain assumption GNN with 2D assignment and Mahalanobis distance is a sufficient data association solution for the studied scenarios (Section IV.A)
The conclusions about filter differences inherit the chosen association thresholds and the global nearest neighbour rule.
standard math The third-order SIF quadrature (Eq. 17) provides an accurate approximation of the Gaussian integrals
Takes from [8] and [10]; not re-derived in this paper.

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Cite this review

Pith. "Pith review of Stone Soup: ADS-B-based Multi-Target Tracking with Stochastic Integration Filter." pith.science (2026). https://pith.science/paper/HAQJD4W4

@misc{pith2026250607889,
  author       = {Pith},
  title        = {Pith review of: Stone Soup: ADS-B-based Multi-Target Tracking with Stochastic Integration Filter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HAQJD4W4}},
  note         = {Machine review of arXiv:2506.07889}
}

read the original abstract

This paper focuses on the multi-target tracking using the Stone Soup framework. In particular, we aim at evaluation of two multi-target tracking scenarios based on the simulated class-B dataset and ADS-B class-A dataset provided by OpenSky Network. The scenarios are evaluated w.r.t. selection of a local state estimator using a range of the Stone Soup metrics. Source code with scenario definitions and Stone Soup set-up are provided along with the paper.

Figures

Figures reproduced from arXiv: 2506.07889 by the authors.

**Figure 5.** SIAP Ambiguity Metric for Class-B example [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 3.** SIAP position accuracy results for Class-B example. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Covariance norms metrics results for Class-B example. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 6.** Figure 6: OSPA metrics results for ADS-B Dataset [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Covariance norms metrics result for the ADS-B Dataset [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: SIAP Ambiguity Metric for Class-A example [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

Discussion (0). Sign in to comment.

Reference graph

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

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