Maximum likelihood extended gradient‐based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable‐gain nonlinearity

Abstract Variable‐gain nonlinearity is a piecewise‐linear characteristic to describe the process with different gains in different input regions. This article studies the parameter estimation issue of the input nonlinear controlled autoregressive moving average system with variable‐gain nonlinearity. Through introducing a suitable switching function, we describe the variable‐gain nonlinearity by a linear‐in‐parameter form and derive the identification model of the system. Based on the obtained identification model, a maximum likelihood extended stochastic gradient algorithm is presented to estimate the unknown parameters. To make sufficient use of the observation data and improve the identification accuracy, we deduce a maximum likelihood (multiinnovation) extended gradient‐based iterative algorithm by using the maximum likelihood principle. An extended gradient‐based iterative algorithm is given for comparison. A simulation example is employed to validate that the proposed algorithms can effectively identify the unknown parameters and the maximum likelihood extended gradient‐based iterative algorithm has better estimation accuracy and fitting performance than the maximum likelihood extended stochastic gradient algorithm and the extended gradient‐based iterative algorithm.