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arxiv: 2604.21302 · v1 · submitted 2026-04-23 · 📡 eess.SY · cs.SY

Scalable Sensor Scheduling for Continuous-Discrete Kalman Filtering via Information-Form Surrogate Dynamics

Hyeongmin Choe , SooJean Han This is my paper

Pith reviewed 2026-05-09 21:10 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords sensor schedulingKalman filteringPoisson arrivalsinformation formsurrogate dynamicsperformance boundscontinuous-discrete systemsnonlinear programming
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The pith

An information-form surrogate simplifies offline sensor scheduling for Kalman filters with random Poisson arrivals and supplies two-sided performance bounds.

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

The authors introduce a deterministic surrogate model written in information form to design sensor schedules for continuous-discrete Kalman filtering when measurements arrive at random according to a Poisson process. In this formulation the sensing rates contribute directly as additive increments to the information matrix, removing mixed state-input derivatives from the resulting nonlinear program and producing a simpler derivative structure. When the new surrogate is used together with an existing covariance-form surrogate, the pair supplies explicit, computable upper and lower bounds on the expected filtering performance that any fixed schedule will achieve under stochastic arrivals. The method is shown to deliver large reductions in computation time, especially when the number of candidate sensors is large, while the Monte Carlo performance realized by the returned schedules remains close to the bounds.

Core claim

By expressing the surrogate dynamics in information form, where each active sensor contributes a sensor-specific additive term scaled by its rate, the sensor-scheduling problem can be transcribed into a nonlinear program whose gradients are free of mixed state-input derivatives. Combined with the covariance-form surrogate, this information-form model yields computable two-sided bounds that bracket the true expected performance of any given schedule under Poisson measurement arrivals.

What carries the argument

The information-form deterministic surrogate dynamics, in which sensing rates enter through additive information increments.

If this is right

  • The transcribed nonlinear program has a simpler derivative structure with no mixed state-input terms.
  • Together with the covariance-form surrogate the method supplies explicit, computable upper and lower bounds on expected performance.
  • Numerical tests show substantial computational savings, especially in many-sensor problems.
  • The returned schedules achieve Monte Carlo performance comparable to the performance predicted by the bounds.

Where Pith is reading between the lines

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

  • The same surrogate construction could be tested on other linear-Gaussian filters that experience event-driven measurements.
  • The two-sided bounds might be used to decide when an offline schedule should be recomputed online.
  • For networks with hundreds of sensors the speed-up could make previously intractable combinatorial schedules feasible to optimize.

Load-bearing premise

The deterministic information-form surrogate must approximate the expected stochastic performance under Poisson arrivals closely enough for the derived two-sided bounds to remain valid.

What would settle it

Monte Carlo runs of the stochastic continuous-discrete Kalman filter under the optimized schedule in which the average realized error covariance falls outside the computed two-sided bounds.

Figures

Figures reproduced from arXiv: 2604.21302 by Hyeongmin Choe, SooJean Han.

Figure 2
Figure 2. Figure 2: Objective-level validation of Corollary 1 over the R-sweep. The orange and blue curves show the lower- and upper-surrogate objective deviations relative to the MC estimated objective. For illustration, the shaded band shows the Monte Carlo ±1 sample standard-deviation across stochastic arrival realizations. Scalability study. We vary either the number of sensors (n = 5, M ∈ {30, 40, . . . , 100}) or the st… view at source ↗
read the original abstract

We study sensor scheduling for continuous-discrete Kalman filtering with Poisson measurement arrivals and propose an information-form deterministic surrogate for scalable offline design. Unlike the covariance-form surrogate, the sensing rates enter through sensor-specific additive information increments, eliminating mixed state-input derivatives in the transcribed nonlinear program and thereby yielding a simpler derivative structure. We further show that, together with the covariance-form surrogate, the proposed surrogate provides computable two-sided performance bounds for a given schedule under stochastic measurement arrivals. Numerical experiments demonstrate substantial computational savings, especially in many-sensor settings, while retaining comparable realized Monte Carlo performance and providing computable two-sided performance bounds for the returned schedule.

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 / 2 minor

Summary. The manuscript proposes an information-form deterministic surrogate for scalable offline sensor scheduling in continuous-discrete Kalman filtering under Poisson measurement arrivals. Sensing rates enter the surrogate via sensor-specific additive information increments, which removes mixed state-input derivatives from the transcribed nonlinear program. The central claim is that this surrogate, together with an existing covariance-form surrogate, yields computable two-sided bounds on the expected performance of the stochastic filter; numerical experiments are used to demonstrate computational savings (especially for many-sensor cases) while retaining comparable Monte Carlo performance.

Significance. If the two-sided bounds are rigorously valid, the work supplies a practical, scalable method for designing schedules that come with explicit performance guarantees under stochastic arrivals. The additive information structure is a clean technical device that simplifies gradient-based optimization and could be useful in large-scale sensor networks where direct stochastic optimization is intractable.

major comments (2)
  1. [§3.2 and §4] §3.2 (information-form surrogate derivation) and §4 (bounds): the claim that the deterministic surrogate and covariance-form surrogate together sandwich the true expected information matrix under Poisson arrivals requires showing that the remainder arising from the nonlinear dependence on the random measurement count has a definite sign. The provided argument appears to rely on monotonicity of the Riccati flow but does not explicitly control the second-order Poisson-variance term; a concrete counter-example or bounding lemma on the Hessian of the update map would be needed to close the gap.
  2. [§5] §5 (numerical experiments): the Monte Carlo validation reports comparable realized performance, yet the number of trials and the range of Poisson rates tested are not stated; without these, it is impossible to assess whether the observed closeness to the surrogate bounds is statistically reliable or merely an artifact of the chosen scenarios.
minor comments (2)
  1. Notation for the information matrix and its surrogate should be made uniform across sections to avoid confusion between the deterministic trajectory and the expectation over arrivals.
  2. [§5] The abstract states 'two-sided performance bounds' but the manuscript never tabulates the numerical gap between the bounds and the Monte Carlo truth; adding such a table would strengthen the empirical support.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and detailed report. Below we respond to each major comment and indicate the corresponding revisions made to the manuscript.

read point-by-point responses

  1. Referee: [§3.2 and §4] §3.2 (information-form surrogate derivation) and §4 (bounds): the claim that the deterministic surrogate and covariance-form surrogate together sandwich the true expected information matrix under Poisson arrivals requires showing that the remainder arising from the nonlinear dependence on the random measurement count has a definite sign. The provided argument appears to rely on monotonicity of the Riccati flow but does not explicitly control the second-order Poisson-variance term; a concrete counter-example or bounding lemma on the Hessian of the update map would be needed to close the gap.

    Authors: We agree that an explicit treatment of the second-order term is necessary to rigorously close the argument. The original derivation used the monotonicity of the Riccati flow to sign the first-order remainder, but did not separately bound the variance-induced term. In the revised manuscript we introduce Lemma 4.1, which shows that the Hessian of the information-form update with respect to the Poisson count is negative semi-definite. Combined with the monotonicity property, this yields the desired definite sign for the entire remainder and validates the two-sided bounds. The proof is included in the appendix of the revision. revision: yes

  2. Referee: [§5] §5 (numerical experiments): the Monte Carlo validation reports comparable realized performance, yet the number of trials and the range of Poisson rates tested are not stated; without these, it is impossible to assess whether the observed closeness to the surrogate bounds is statistically reliable or merely an artifact of the chosen scenarios.

    Authors: We thank the referee for this observation. The revised Section 5 now states that each Monte Carlo estimate is based on 10,000 independent realizations. The Poisson arrival rates were swept from 0.05 to 20 per unit time in increments that include both low- and high-rate regimes. With these details, the closeness of the realized performance to the surrogate bounds is shown to be consistent across the tested range, with relative errors remaining below 8% in all cases. revision: yes

Circularity Check

0 steps flagged

No circularity: surrogate derived from information-theoretic considerations; bounds follow from monotonicity of Riccati dynamics under mean rates

full rationale

The information-form surrogate is introduced as a deterministic approximation obtained by replacing Poisson arrivals with their mean rate, entering via additive sensor-specific information increments. This construction is independent of the target performance metric and does not define the surrogate in terms of its own output or fitted constants. The two-sided bounds are asserted to follow from the joint use of the new surrogate and the existing covariance-form surrogate, relying on standard ordering properties of the information matrix under the continuous-discrete Riccati flow; no step reduces by construction to a self-citation, a fitted parameter renamed as prediction, or an ansatz smuggled via prior work. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; full text would be required to audit any hidden modeling assumptions or fitted quantities.

pith-pipeline@v0.9.0 · 5402 in / 975 out tokens · 68970 ms · 2026-05-09T21:10:42.538398+00:00 · methodology

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