Sensor Design for Accuracy-Bounded Estimation via Maximum-Entropy Likelihood Synthesis
Authors: Raktim Bhattacharya
Summary
The paper tackles sensor design for large physical systems when you have an accuracy target but don't know what sensors you need. Instead of designing sensors first and checking accuracy later, the authors flip the problem: given an error budget, they synthesize the measurement likelihood function that enforces that budget while adding minimal information beyond what the system dynamics already provide. They do this using maximum-entropy optimization (among all posteriors meeting the accuracy constraint, pick the one closest to the prior), then back out the implied sensor characteristics.
Main takeaways:
- Classical sensor design requires knowing sensor models upfront; this approach inverts the flow by starting with accuracy requirements
- The method constructs a measurement likelihood via constrained maximum-entropy optimization: enforce the error budget while minimizing added information
- Works with various distance metrics (Wasserstein, KL divergence, moment constraints) and provides convex or convex-relaxed formulations
- A two-layer design architecture connects abstract accuracy budgets to concrete sensor placement, precision, and configuration choices
Relevance
No obvious connection to my work on behavioral installation or persona geometry in language models — this is about physical sensor networks and estimation theory.
Abstract
arXiv:2605.11120v1 Announce Type: cross Abstract: Designing the sensing architecture for large-scale spatio-temporal systems is hard when accuracy requirements are specified but sensor models are uncertain or unavailable. Classical design treats sensor placement and estimation sequentially, requiring valid forward models for each sensing modality. This paper inverts the design flow: given an error budget, synthesize the measurement likelihood that enforces it while injecting minimal information beyond the dynamical prior. The likelihood is constructed by constrained optimization: among all posteriors satisfying a prescribed accuracy bound relative to a target, select the one minimizing Kullback-Leibler divergence from the prior. The solution is a maximum-entropy posterior in relative-entropy form, and the induced likelihood is the Radon-Nikodym derivative. The framework accommodates arbitrary discrepancies and is instantiated for Wasserstein distance, maximum mean discrepancy, $f$-divergences, moment constraints, and hybrid metrics. For each, we derive the discrete particle-level problem, analyze its convex or convex-relaxed structure, and present solvers with complexity scaling. A closed-form solution exists for the symmetric exponential-tilt case, and a distillation procedure converts nonparametric likelihood samples into parametric forms. A two-layer sensor design architecture embeds the synthesized likelihood in the recursive predict-update loop, connecting accuracy budgets to physical sensor placement, precision, and configuration. Numerical experiments comparing four metrics on unimodal and multimodal scenarios confirm the accuracy constraints are reliably enforced and reveal how metric choice determines the amount and spatial distribution of injected information.