A M-EKF fault detection strategy of insulation system for marine current turbine

Adaptive Control & Signal

Yang

2019

223

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

223

117

“…• The methods proposed in this paper can combine some statistical optimal strategies [47][48][49] to study the parameter estimation algorithms of linear and nonlinear systems [50][51][52][53][54][55][56] and can be extended to other fields. [57][58][59][60][61][62][63][64][65][66][67][68][69]…”

Section: Resultsmentioning

confidence: 99%

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

Adaptive Control & Signal

2019

171

For a special class of nonlinear systems (ie, bilinear systems) with autoregressive moving average noise, this paper gives the input-output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model and the maximum likelihood principle, a filtering-based maximum likelihood hierarchical gradient iterative algorithm and a filtering-based maximum likelihood hierarchical least squares iterative algorithm are developed for identifying the parameters of bilinear systems with colored noises. The original bilinear systems are divided into three subsystems by using the data filtering technique and the hierarchical identification principle, and they are identified respectively. Compared with the gradient-based iterative algorithm and the multi-innovation stochastic gradient algorithm, the proposed algorithms have higher computational efficiency and parameter estimation accuracy. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems.

“…Moreover, the state estimator-based F-TS-RGLS algorithm could greatly improve the computational efficiency. The methods proposed in this paper could be combined the particle Monte Carlo methods [56,57] and some statistical methods to study the model selection and parameter estimation [58][59][60] for different systems [61][62][63][64][65][66] and could be applied to other fields [67][68][69][70][71][72] such as communication networks [73][74][75].…”

Section: Discussionmentioning

confidence: 99%

“…Compute the gain vector L s,t using (62) and the covariance matrix P s,t using (63). Update the parameter estimatesθ s,t using (61).…”

mentioning

confidence: 99%

A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise

Xiao

et al. 2019

Mathematics

This paper is concerned with the joint state and parameter estimation methods for a bilinear system in the state space form, which is disturbed by additive noise. In order to overcome the difficulty that the model contains the product term of the system input and states, we make use of the hierarchical identification principle to present new methods for estimating the system parameters and states interactively. The unknown states are first estimated via a bilinear state estimator on the basis of the Kalman filtering algorithm. Then, a state estimator-based recursive generalized least squares (RGLS) algorithm is formulated according to the least squares principle. To improve the parameter estimation accuracy, we introduce the data filtering technique to derive a data filtering-based two-stage RGLS algorithm. The simulation example indicates the efficiency of the proposed algorithms.