Particle filtering based parameter estimation for systems with output-error type model structures

Adaptive Control & Signal

Yang

2019

224

117

This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems.It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input-single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input-multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.

Section: Discussionmentioning

confidence: 99%

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Xiao

Adaptive Control & Signal

Yang

2019

224

117

“…2. Let k = 1, collect the input-output data u(t) and y(t), t = 1, 2, · · · , L. Form the stacked output vector Y (L) using Equation (37). 3.…”

Section: The Egi Algorithm With Finite Measurementmentioning

confidence: 99%

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

Liu

Intl J Robust & Nonlinear

Hayat

2020

Summary The combined iterative parameter and state estimation problem is considered for bilinear state‐space systems with moving average noise in this paper. There are the product terms of state variables and control variables in bilinear systems, which makes it difficult for the parameter and state estimation. By designing a bilinear state estimator based on the Kalman filtering, the states are estimated using the input‐output data. Furthermore, a moving data window (MDW) is introduced, which can update the dynamical data by removing the oldest data and adding the newest measurement data. A state estimator‐based MDW gradient‐based iterative (MDW‐GI) algorithm is proposed to estimate the unknown states and parameters jointly. Moreover, given the extended gradient‐based iterative (EGI) algorithm as a comparison, the MDW‐GI algorithm can reduce the impact of noise to parameter estimation and improve the parameter estimation accuracy. The numerical simulation examples validate the effectiveness of the proposed algorithm.

“…Adaptive filtering and online parameter estimation play an important role in the control community . Time‐delay systems often exist in communication networks and signal transmission processes for the reason that the measurements sometimes cannot arrive at the filter chronologically due to the processing delays .…”

Section: Introductionmentioning

confidence: 99%

Adaptive parameter estimation for a general dynamical system with unknown states

Xiao

Intl J Robust & Nonlinear

2020

123

Summary This paper is concerned with the design of a state filter for a time‐delay state‐space system with unknown parameters from noisy observation information. The key is to investigate new identification algorithms for interactive state and parameter estimation of the considered system. Firstly, an observability canonical state‐space model is derived from the original model by linear transformation for the purpose of simplifying the model structure. Secondly, a direct state filter is formulated by minimizing the state estimation error covariance matrix on the basis of the Kalman filtering principle. Thirdly, once the unknown states are estimated, a state filter–based recursive least squares algorithm is proposed for parameter estimation using the least squares principle. Then, a state filter–based hierarchical least squares algorithm is derived by decomposing the original system into several subsystems for improving the computational efficiency. Finally, the numerical examples illustrate the effectiveness and robustness of the proposed algorithms.