Compressed Least Squares Algorithm of Continuous-Time Linear Stochastic Regression Model Using Sampling Data  

作　　者：XIE Siyu ZHANG Shujun WANG Ziming GAN Die 

机构地区：[1]School of Aeronautics and Astronautics,University of Electronic Science and Technology of China,Chengdu 611731,China [2]China Academy of Aerospace Science and Innovation,Beijing 100176,China [3]Zhongguancun Laboratory,Beijing 100094,China

出　　处：《Journal of Systems Science & Complexity》2024年第4期1488-1506,共19页系统科学与复杂性学报（英文版）

基　　金：supported by the Major Key Project of Peng Cheng Laboratory under Grant No.PCL2023AS1-2;Project funded by China Postdoctoral Science Foundation under Grant Nos.2022M722926 and2023T160605。

摘　　要：In this paper,the authors consider a sparse parameter estimation problem in continuoustime linear stochastic regression models using sampling data.Based on the compressed sensing(CS)method,the authors propose a compressed least squares(LS) algorithm to deal with the challenges of parameter sparsity.At each sampling time instant,the proposed compressed LS algorithm first compresses the original high-dimensional regressor using a sensing matrix and obtains a low-dimensional LS estimate for the compressed unknown parameter.Then,the original high-dimensional sparse unknown parameter is recovered by a reconstruction method.By introducing a compressed excitation assumption and employing stochastic Lyapunov function and martingale estimate methods,the authors establish the performance analysis of the compressed LS algorithm under the condition on the sampling time interval without using independence or stationarity conditions on the system signals.At last,a simulation example is provided to verify the theoretical results by comparing the standard and the compressed LS algorithms for estimating a high-dimensional sparse unknown parameter.

关 键 词：Compressed excitation condition compressed sensing continuous-time model least squares linear stochastic regression parameter identification sampling data 

分 类 号：O212.1[理学—概率论与数理统计]