Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing

Yang

2019

214

112

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: Introductionmentioning

confidence: 99%

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

Xiao

Yang

2019

214

112

“…Take the data length L = 300 as the data length, and apply the direct state estimation algorithm in (30)- (36) to estimate the states of the considered system. Take the data length L = 300 as the data length, and apply the direct state estimation algorithm in (30)- (36) to estimate the states of the considered system.…”

Section: Variables Computation Sequences Number Of Multiplications Numentioning

confidence: 99%

“…Take the data length L = 300 as the data length, and apply the direct state estimation algorithm in (30)- (36) to estimate the states of the considered system. Take {v(s)} as a random sequence with the normal distribution, zero mean, and variance R v = 0.10 2 , and {w(s)} as a white noise vector sequence with zero mean and variance R w = 0.05 2 I 6 .…”

Section: Variables Computation Sequences Number Of Multiplications Numentioning

confidence: 99%

“…Parameter estimation and state filtering are basic for system identification [27][28][29] and system analysis and design, [30][31][32][33] and can be applied to many areas. [34][35][36][37][38][39] The Kalman filter (KF) is known as the optimal state filter for linear systems under the Gaussian white noise and has been extended to study the parameter estimation for bilinear systems. [40][41][42] For nonlinear systems, its modifications such as the particle filter, the extended KF, and the unscented KF give approaches for nonlinear filtering problems.…”

Section: Introductionmentioning

confidence: 99%

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Highly computationally efficient state filter based on the delta operator

Xiao

et al. 2019

146

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 multi-innovation identification is the innovation expansion-based identification. [30][31][32][33][34][35] In the aspect of identifying the ExpAR model, many literatures suppose that the parameter of the nonlinear part is known a priori or imposed on certain conditions and then use the LS estimator to identify the parameters of the linear part in the ExpAR model, 14,15,36 some other literatures impose no special conditions on the model parameters but involve few novel identification techniques, 7 such as the hierarchical identification and the multi-innovation identification. 28 In the work of Xu et al, 29 by means of the hierarchical identification and the multi-innovation identification, we derived a hierarchical multiinnovation SG (H-MISG) algorithm for the ExpAR model, which uses the gradient search to deal with both the linear and nonlinear optimization problems arising during the recursive computation.…”

Section: Introductionmentioning

confidence: 99%

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

Sheng

2019

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.