Robust time-delay estimation for nonlinear systems using inexact output

This paper considers time-delay estimation problem involving nonlinear dynamic systems using inexact system output. We first propose a new robust time-delay formulation, in which the variance of the least-squares error function is minimized subject to a constraint specifying the sacrifice from the optimal expectation of the classical time-delay estimation problem. Then, we show that the gradients of the cost and/or constraint functions in the classical and robust estimation problems can be computed by sequently solving the state system forward in time and auxiliary time-delay systems backward in time. On this basis, new gradient-based optimization algorithms are developed to solve the estimation problems. Finally, a numerical example is used to verify the effectiveness of the proposed algorithms.