Auxiliary Model-Based Recursive Generalized Least Squares Algorithm for Multivariate Output-Error Autoregressive Systems Using the Data Filtering

Yang

2019

Self Cite

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%

“…Let k = 1, set the initial valuesx 1 = 1 n , P 1 = I n , u k−i = 0, and y k−i = 0, for i = 1, 2, … , n, and the system parameters A, B, f, c, and d. 2. Compute the covariance matrixR w,k by (52) and the varianceR v,k by (53). 3.…”

Section: Theorem 1 For the Bilinear System In (1)-(2) And The Bilinementioning

confidence: 99%

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

Xiao

Yang

2019

Self Cite

224

117

“…The methods proposed in this paper can combine some statistical methods [48][49][50][51][52][53][54][55] to study the parameter identification and state filter design for different systems with colored noise and can be applied to other fields. [56][57][58][59][60][61][62][63][64][65][66]…”

Section: Discussionmentioning

confidence: 99%

Highly computationally efficient state filter based on the delta operator

Xiao

et al. 2019

Self Cite

155

The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm.

“…The methods proposed in this paper can combine some statistical methods 47 to study the parameter identification and state filter design for different systems with colored noise [48][49][50][51][52][53][54][55] and can be applied to other fields. To make full use of the data, we combine the multi-innovation identification theory with the gradient search so as to propose a hierarchical LS-MISG algorithm, which has improved parameter estimation accuracy.…”

Section: Discussionmentioning

confidence: 99%

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

Sheng

2019

Self Cite

Modeling an exponential autoregressive (ExpAR) time series is the basis of solving the corresponding prediction and control problems. This paper investigates the hierarchical parameter estimation methods for the ExpAR model.By the hierarchical identification principle, the original nonlinear optimization problem is transformed into the combination of a linear and nonlinear optimization problem, and then, we derive a hierarchical least squares and stochastic gradient (LS-SG) algorithm. Given the difficulty of determining the step-size in the hierarchical LS-SG algorithm, an approach is proposed to obtain the optimal step-size. To improve the parameter estimation accuracy, the multi-innovation identification theory is employed to develop a hierarchical least squares and multi-innovation stochastic gradient algorithm for the ExpAR model. Two simulation examples are provided to test the effectiveness of the proposed algorithms.