Quickest Change Detection in Parametric Models With 1-Bit Measurements

2026-08-18

AI Summary

研究通过1比特量化观测值进行快速变化检测，提出AQuTeCUSUM算法在线估计后变化参数并自适应选择量化阈值以最大化KL散度。

Abstract

We consider the quickest change detection from 1-bit quantized observations, where the post-change distribution is a parametric model with unknown parameters and the quantization thresholds are jointly chosen with the detection statistic. We propose an Adaptive-Quantization-Threshold CUSUM (AQuTeCUSUM) algorithm, which estimates the post-change parameter online and adaptively selects the quantization threshold to maximize the induced Kullback-Leibler divergence. Under suitable regularity conditions, we characterize the average run length and worst-case average detection delay of the AQuTe-CUSUM procedure, and show that it is asymptotically optimal in first-order as the average run length goes to infinity. Finally, we assess the performance of AQuTe-CUSUM for two distributions, namely the Gaussian and Poisson.

Problem

• Quickest Change Detection
• 1-bit Quantization
• Parametric Models
• Unknown Parameters
• Quantization Thresholds

Innovation

• Adaptive-Quantization-Threshold CUSUM
• 1-bit Quantized Observations
• Online Parameter Estimation
• Kullback-Leibler Divergence