Innovation-based sampling reduces data needs in tracking random processes
Innovation-Based Sampling for New Information
Information Theory
Summary
This paper looks at ways to only take new data samples when truly new information appears, instead of sampling all the time. The authors studied this method for a common random process called a Wiener process and found samples become less frequent over time. They also showed that knowing when there is no new information can help estimate the state more accurately than ignoring such gaps. The paper provides simpler methods to use these ideas in practice for better remote monitoring.
What this means in practice
- •For network schedulers: Reduce the number of sensor updates sent over networks by sampling only when significant new data arises, cutting communication load without losing accuracy.
- •For embedded system developers: Design estimators for remote sensors that improve accuracy by factoring in timing and absence of signals, beyond just received measurement values.
Authors
Jiping Luo, Anthony Ephremides, Nikolaos Pappas
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.