Problem
Research questions and friction points this paper is trying to address.
innovation-based sampling
remote estimation
age of information
continuous stochastic processes
minimum mean-square error
Innovation-Based Sampling for New Information
🤖 AI Summary
This study addresses the challenges of information sparsification and missing data processing in the remote estimation of continuous-time stochastic processes. It proposes an innovation-based sampling mechanism that triggers sampling only when novel information emerges, constructing a three-dimensional state representation. By revealing the informational value of innovation-absent signals, this approach transcends conventional zero-order hold limitations to achieve age-evolving MMSE-optimal estimation. Theoretical analysis integrates lattice-structure modeling, limit theorems, and affine/exponential approximation algorithms. The contributions demonstrate that the sampling rate vanishes asymptotically while the mean squared error decreases substantially, establishing both the rarity of direction reversals and the square-root growth law governing innovation frequency.
📝 Abstract
This work introduces innovation-based sampling of continuous stochastic processes, in which a sample is generated only when the process reveals ``sufficiently new'' information relative to all previous samples. The resulting innovation process admits a lattice structure and a three-dimensional state representation. For a Wiener process, we characterize the direction, timing, and frequency of innovations. We show that direction reversals become increasingly rare and establish limit theorems for their number. Innovations also become progressively sparser: the expected number of innovations grows only as the square root of time, and hence the sampling rate vanishes asymptotically. We then study remote estimation from sparsely received innovations. Notably, the absence of an innovation carries information: the minimum mean-square error (MMSE) estimate evolves with the age of information (AoI) and achieves a substantial MSE reduction over the conventional silence-ignorant zero-order hold (ZOH) estimator. Finally, we develop tractable affine-age and exponential-age approximations for practical use. Overall, information is conveyed not only by the content of innovations, but also by their direction and timing.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Innovation-based sampling
Remote estimation
Age of Information (AoI)
Wiener process
Minimum mean-square error (MMSE)
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