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

In this paper, the authors consider a sparse parameter estimation problem in continuous-time 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.