Statistics

Software engineering

Iterative and incremental development

Artificial intelligence

Estimation theory

Physics

Nonlinear system

Iterative method

Mathematics

Biology

Image (mathematics)

Mathematical optimization

Autoregressive model

Computation

Quantum mechanics

Operating system

Data mining

Computer science

Botany

Process (computing)

Noise (video)

Algorithm

Measure (data warehouse)

Identification (biology)

System identification

International Journal of Adaptive Control and Signal Processing

Summary This article focuses on the parameter estimation issues for a fractional‐order nonlinear system with autoregressive noise. In the process, the challenge and difficulty are to identify the parameters of the system as well as the order. To reduce the complexity of the structure, we split the system into two subsystems by utilizing the hierarchical identification principle and derive a two‐stage gradient‐based iterative (2S‐GI) algorithm by minimizing two criterion functions. Compared with the calculation amount of the gradient‐based iterative algorithm, the computation of the 2S‐GI algorithm is significantly reduced. Moreover, in order to improve the identification accuracy, we propose a two‐stage moving‐data‐window gradient‐based iterative algorithm. Finally, the simulation examples test the effectiveness of the proposed algorithms.

Two‐stage gradient‐based iterative algorithms for the fractional‐order nonlinear systems by using the hierarchical identification principle