Performance Analysis of the Auxiliary Model-Based Stochastic Gradient Parameter Estimation Algorithm for State-Space Systems with One-Step State Delay

Circuits Syst Signal Process

2015

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This paper concerns the state and parameter estimation problem for an input nonlinear state-space system with colored noise. By using the data filtering and the over-parameterization technique, we transform the original nonlinear state-space system into two identification models with filtered states: one containing the system parameters and the other containing the noise model's parameters. A combined state and parameter estimation algorithm is developed for identifying the state-space system. The key is that the estimation of system parameters uses the estimated states, and the estimation of states uses the preceding parameter estimates. A simulation example is provided to show that the proposed algorithm can work well.

Section: Introductionmentioning

confidence: 99%

Joint Estimation of States and Parameters for an Input Nonlinear State-Space System with Colored Noise Using the Filtering Technique

Wang

Circuits Syst Signal Process

2015

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“…In this literature, many parameter estimation methods have been proposed such as the recursive methods [16,23], the iterative methods [19,31], the subspace identification methods [26,29], and the maximum likelihood methods [5]. Some methods are based on the lifting technique [11], the auxiliary model [8] and the multi-innovation theory [7]. Most [2,17,34], and this motivates us to study novel identification methods for nonlinear systems to meet the requirement of industrial development.…”

Section: Introductionmentioning

confidence: 99%

Data Filtering-Based Multi-innovation Stochastic Gradient Algorithm for Nonlinear Output Error Autoregressive Systems

Mao

Circuits Syst Signal Process

2015

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This paper discusses the parameter estimation problems of nonlinear output error autoregressive systems and presents a data filtering-based multi-innovation stochastic gradient algorithm for improving the parameter estimation accuracy of the stochastic gradient algorithm by combining the multi-innovation identification theory and the data filtering technique. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the multi-innovation stochastic gradient algorithm. The simulation results confirm this conclusion.

“…However, here the SG-AM algorithm cannot be applied to deal with this non-standard model. Remark 1: Unlike the models in [27], [28], all the process outputs in this non-standard ARX model are unknown, and if we usex(t) = φ T (t)θ(t−1) to replace x(t), then ϵ(t) in Equation (6) becomes zero, thus the SG-AM algorithm proposed in Equations (3)- (7) is invalid for this non-standard ARX model.…”

Section: The Sg Based Particle Filter Algorithmmentioning

confidence: 99%

“…The auxiliary model based algorithms are often used to identify systems with unmeasureable variables [27], [28]. For example, the corresponding auxiliary model based SG (AM-SG) algorithm for the system model in (1) and (2) is below,…”

Section: The Sg Based Particle Filter Algorithmmentioning

confidence: 99%

Gradient-Based Particle Filter Algorithm for an ARX Model With Nonlinear Communication Output

Chen

Liu

IEEE Trans. Syst. Man Cybern, Syst.

et al. 2020

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Abstract-A stochastic gradient based particle filter algorithm is developed for an ARX model with nonlinear communication output in this paper. This non-standard ARX model consists of two submodels, one is a linear ARX model and the other is a nonlinear output model. The process outputs (outputs of the linear submodel) transmitted over a communication channel are unmeasureable, while the communication outputs (outputs of the nonlinear submodel) are available, and both of the twotype outputs are contaminated by white noises. Based on the rich input data and the available communication output data, a stochastic gradient based particle filter algorithm is proposed to estimate the unknown process outputs and parameters of the ARX model. Furthermore, a direct weight optimization method and the Epanechnikov kernel method are extended to modify the particle filter when the measurement noise is a Gaussian noise with unknown variance and the measurement noise distribution is unknown. The simulation results demonstrate that the stochastic gradient based particle filter algorithm is effective.