Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

TL;DR

This work formalizes a processing-network model that jointly accounts for edge preprocessing, communication, and centralized fusion delays in real-time state estimation. It establishes analytic results for a homogeneous continuous-time scalar network, showing a unique optimal preprocessing delay $\tau_{opt}>0$ and illustrating when edge preprocessing improves performance versus sending raw data. For heterogeneous discrete-time networks, it develops a practical greedy approach to jointly select sensors and preprocessing delays, supported by an exact steady-state covariance computation and extensions to multi-rate settings. Numerical experiments demonstrate substantial estimation gains when applying the proposed delay-aware sensor selection and preprocessing policies, highlighting the importance of accounting for both computation and communication latencies in networked estimation.

Abstract

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.

Figures (14)

• Figure 1: Example of processing network: drones track a moving vehicle in the presence of computation and communication constraints. Each drone can preprocess the acquired images before transmitting to a central station.
• Figure 2: Delayed data transmission with two sensors.
• Figure 3: Multi-rate network. Crosses on the bottom axis highlight states observed by sensor 1 but not by sensor 2.
• Figure 4: Left: You-Only-Look-Once (YOLO) and RetinaNet are convolutional neural networks that can trade runtime and classification accuracy (errors on y-axis are computed as the inverse of mAP-50 scores). Right: Randomized Tour Improvement is a classical greedy algorithm which approximates the optimal tour for the traveling salesman problem, shortening an initial route. Adapted from 2018arXiv180402767R, Zilberstein96ai-anytimeAlgorithms.
• Figure 6: Representation of variance $p_{\infty|\infty-\tau_{\textit{tot}}}(\tau)$.

Theorems & Definitions (25)

• Remark 1: Parallel data collection vs. sequential fusion
• Remark 2: Comparison with sensor selection
• Remark 3
• Theorem 1: Optimal preprocessing for continuous-time homogeneous network, ballotta19ifac
• proof
• Example 1: Brownian systems
• Corollary 1: Brownian motion
• Proposition 1
• proof
• Remark 4