sensor system designers

Abstract: This paper presents upper and lower bounds on the minimax risk of a parameter estimation problem where the estimator not only observes independent and identically distributed observations but also a quantized version of the parameter, where the quantization has a limitation on the number of levels, but can be optimized otherwise. Our upper and lower bounds have similar decay rates for large number of observation samples and quantization levels.

Abstract: Multi-step revealing can make off-policy evaluation tractable under memoryless logging. With history-dependent logging, state decodability and target-relevant evidence can separate. For every horizon $H\ge3$, we construct two exactly realizable POMDPs with four actions, at most four states per layer, a known logger, and a memoryless target. Action overlap, history coverage, and observation-only revealing remain bounded independently of $H$, yet the target values differ by $1/2$ and the KL divergence between the logged laws is $Θ(4^{-(H-1)})$, forcing exponential sample complexity. Logger memory makes states distinguishable, while reset erases the model-distinguishing evidence preserved by the target. A separate construction retains this barrier with common, known observation-only revealing operators. Under action and history coverage, we give a finite-class OPE guarantee using common observable value representations that remain valid at every history. The sample bound depends polynomially on their second-moment cost. In the common-operator construction, the same value direction has constant marginal decoding cost but exponential history-conditioned cost. Finally, on a fixed four-action continuum, we derive matching passive and budgeted readout rates. With one known channel and unit read cost, early reads are optimal. With unknown sensor bias, early reads alone remain exponentially costly. Combining them with post-reset calibration gives sample complexity independent of $H$ when both read types receive fixed positive expected budgets per trajectory.

Abstract: Bayesian filtering provides a principled framework for online state estimation under uncertainty, yet its application to systems with high-dimensional states and complicated posterior distributions remains challenging. Recent generative models, such as flow matching, have shown potential in Bayesian filtering. However, they still rely on particle-based representations of the posterior, which lose the rich information of the full distribution, or tackle a trajectory-level inverse problem that conflicts with the recursive structure of Bayesian filtering. To address this, we propose a new perspective of directly encoding the evolving distribution into flow matching model weights, namely, the Belief Flow Filter (BFF). It is a generative filtering framework that updates model weights via gradient descent at test time to track the posterior evolution. Thereby, BFF bypasses the scalability issue of particle representations or the flexibility limitation of Gaussian assumptions in conventional filters. We theoretically justify that the BFF design is structurally aligned with Bayesian filtering, and its training objective targets the recursive filtering operator. BFF is empirically verified across 5 different physical systems, including ones with chaotic dynamics and highly sparse, non-linear observations. The results show that BFF attains the best score in 8 of 9 metric-benchmark cells across the three standard 1D and 2D PDE benchmarks, and similarly leads on the extreme single-moving-sensor setting and on a real-world-grounded tokamak plasma estimation task, demonstrating its potential to accurately approximate the Bayesian filtering operator in high-dimensional probability space.

Abstract: Joint source localization and geoacoustic inversion requires optimizing an objective built from an expensive normal mode propagation model. Bayesian optimization (BO) with a Gaussian process (GP) surrogate can obtain accurate parameter estimates within a limited number of forward model evaluations, but its performance depends on the choice of kernel family. With few observations in a seven-dimensional search space, no single kernel can be expected to perform consistently well across individual inversions. To reduce this dependence, we use a weighted ensemble of GPs with different kernel families, allowing the surrogate to adapt to the observed objective without committing to one kernel in advance. The ensemble is combined with an optimum-conditioned acquisition function that determines where the expensive objective should be evaluated next. Experiments on simulated and measured SWellEx-96 data show that the resulting method achieves the lowest mean final objective among the considered BO strategies and reduces parameter estimation error on most coordinates. Ablation results further show that the ensemble provides robustness to kernel choice, while the acquisition function accounts for most of the optimization gain.

Abstract: We introduce the logic EDMon---an epistemic dynamic logic meant to model monitorability concepts in noisy runtime verification. Its syntax and semantics are defined and explained and the connection between EDMon and monitorability and noisy runtime verification concepts is explored. We then demonstrate that EDMon is sufficient to capture many of the results in the noisy runtime verification literature and catalog its relation to nearby logics and describe a large class of its theorems.