Expectation maximization estimation for a class of input nonlinear state space systems by using the Kalman smoother

Ma, Junxia; Wu, Ouyang; Huang, Biao; Ding, Feng

doi:10.1016/j.sigpro.2017.12.019

Cited by 20 publications

(11 citation statements)

References 49 publications

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“…The initial value of the EM algorithm will influence the precision of identification. Therefore, the choose of initial problem of EM algorithm is another important question, which can be known in 45‐47 …”

Section: Parameter Estimation For Wiener‐fir System Using Em Algorithmmentioning

confidence: 99%

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

Jin

Wang

Cai

et al. 2021

Adaptive Control & Signal

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Summary In this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener‐FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener‐FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.

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Section: Parameter Estimation For Wiener‐fir System Using Em Algorithmmentioning

confidence: 99%

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

Jin

Wang

Cai

et al. 2021

Adaptive Control & Signal

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“…Equation (26) shows that the unbiased estimateθ C (k) is related to the estimates of R and r (i.e., the noise variance δ and the noise parameter vector ϑ v ). The following derives their estimates based on the interactive identification.…”

Section: The Parameter Estimation Algorithmmentioning

confidence: 99%

“…The steps for implementing the bias compensation-based parameter and state estimation (BC-PSE) algorithm in Equations (26) and (47) for state-space systems with colored noise are listed as follows.…”

Section: The State Estimation Algorithmmentioning

confidence: 99%

“…In this aspect, Pavelková and Kárný investigated the state and parameter estimation problem of the state-space model with bounded noise, providing a maximum estimator based on Bayesian theory [25]. By transforming the single-input multiple-output Hammerstein state-space model into the multivariable one, Ma et al used the Kalman smoother to estimate the system states and the expectation maximization algorithm to compute parameter estimates [26]. Li et al presented a maximum likelihood-based identification algorithm for the Wiener nonlinear system with a linear state-space subsystem [27].…”

Section: Introductionmentioning

confidence: 99%

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The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise

2018

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This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise variance and noise model, a bias correction term is added into the least squares estimate, and the system parameters and states are computed interactively. The proposed algorithm can generate the unbiased parameter estimate. Two illustrative examples are given to show the effectiveness of the proposed algorithm.

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“…In one category, it is proposed to characterise both the linear and non‐linear elements by a hybrid model, whose parameters are then estimated simultaneously in a single step, see, e.g. over‐parameterisation methods [5, 6], subspace methods [7]. The other category is based on the idea of decomposition to reduce the dimensionality.…”

Section: Introductionmentioning

confidence: 99%

Fixed point iteration‐based subspace identification of Hammerstein state‐space models

Hou

Chen

et al. 2019

IET Control Theory & Applications

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Expectation maximization estimation for a class of input nonlinear state space systems by using the Kalman smoother

Cited by 20 publications

References 49 publications

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise

Fixed point iteration‐based subspace identification of Hammerstein state‐space models

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