[Paper Review] Bandwidth and Energy Efficient Decentralized Sequential Change Detection

Georgios Fellouris, George V. Moustakides|arXiv (Cornell University)|Oct 7, 2012

Fault Detection and Control Systems4 citations

TL;DR

This paper proposes D-CUSUM, a bandwidth- and energy-efficient decentralized sequential change detection scheme where sensors transmit low-bit messages at random stopping times to a fusion center, which runs parallel CUSUM tests. The method achieves second-order asymptotic optimality, with performance loss bounded as false alarm rates approach zero, even under strict communication constraints.

ABSTRACT

The problem of decentralized sequential change detection is considered, where an abrupt change occurs in an area monitored by a number of sensors; the sensors transmit their data to a fusion center, subject to bandwidth and energy constraints, and the fusion center is responsible for detecting the change as soon as possible. A novel sequential detection rule is proposed that requires communication from the sensors at random times and transmission of only low-bit messages, on which the fusion center runs in parallel a CUSUM test. The second-order asymptotic optimality of the proposed scheme is established both in discrete and in continuous time. Specifically, it is shown that the inflicted performance loss (with respect to the optimal detection rule that uses the complete sensor observations) is asymptotically bounded as the rate of false alarms goes to 0, for any fixed rate of communication. When the rate of communication from the sensors is asymptotically low, the proposed scheme remains first-order asymptotically optimal. Finally, simulation experiments illustrate its efficiency and its superiority over a decentralized detection rule that relies on communication at deterministic times.

Motivation & Objective

• Address the challenge of decentralized sequential change detection under strict bandwidth and energy constraints in sensor networks.
• Develop a practical detection scheme that maintains high detection efficiency while minimizing communication load from sensors.
• Overcome the limitations of existing decentralized rules that are either asymptotically optimal but inefficient in practice or efficient but suboptimal.
• Establish second-order asymptotic optimality, ensuring bounded performance loss relative to centralized optimal detection as false alarm rates decrease.
• Demonstrate robustness and efficiency even when communication rates are asymptotically low or the number of sensors is large.

Proposed method

• Sensors communicate with the fusion center at stopping times of their local filtrations, rather than at fixed deterministic intervals.
• Each sensor transmits a low-bit message summarizing the evolution of its local sufficient statistic since the last transmission.
• The fusion center runs a parallel CUSUM test on the received messages to detect the change point.
• The scheme uses random sampling and quantized communication to reduce bandwidth and energy consumption.
• Theoretical analysis is conducted separately for discrete and continuous time settings to establish optimality properties.
• Leverages change-of-measure techniques and Wald's identity to analyze expected detection delays and communication rates.

Experimental results

Research questions

• RQ1 Can a decentralized change detection rule be both asymptotically optimal and practically efficient under communication constraints?
• RQ2 What is the performance loss of a decentralized scheme with random communication and low-bit messages compared to the optimal centralized CUSUM?
• RQ3 How does the detection delay scale as the false alarm rate approaches zero under fixed communication rates?
• RQ4 Does the scheme remain first-order asymptotically optimal when communication rates are asymptotically low?
• RQ5 How does the proposed scheme compare to deterministic communication-based decentralized CUSUM in terms of detection speed and energy efficiency?

Key findings

• The proposed D-CUSUM scheme achieves second-order asymptotic optimality, meaning the performance loss relative to the optimal centralized CUSUM is bounded as the false alarm rate tends to zero.
• Even under fixed communication rates, the performance loss remains bounded, demonstrating strong robustness to bandwidth constraints.
• When communication rates are asymptotically low, the scheme remains first-order asymptotically optimal, maintaining near-optimal detection delay scaling.
• The expected number of transmissions per sensor grows sublinearly with the detection delay, ensuring energy efficiency.
• Simulation results show D-CUSUM significantly outperforms a CUSUM-based rule that relies on deterministic communication times in terms of detection speed and reliability.
• Theoretical bounds on overshoot and expected communication count confirm the scheme's stability and scalability with increasing sensor counts.