Performance Analysis of Least Squares of Continuous-Time Model Based on Sampling Data

In this letter, we consider the parameter estimation problem of continuous-time linear stochastic regression models described by stochastic differential equations using the sampling data. An online least squares (LS) algorithm is proposed by minimizing the accumulative prediction error at discrete sampling time instants. By employing both the stochastic Lyapunov function and martingale estimate methods, we establish the convergence analysis of the proposed algorithm under conditions of the excitation of the sampling data and the sampling time interval. We also provide the upper bound of the accumulative regret for the adaptive predictor. A simulation example is given to verify our theoretical results.