Optimal joint estimation and identification theorem to linear Gaussian system with unknown inputs

Wang, Shixiong; Li, Chongshou; Lim, Andrew

doi:10.1016/j.sigpro.2019.03.004

Cited by 13 publications

(6 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Besides, what's more interesting, as long as the input keeps same just with some delay, the output will also keeps same with same delay. According to Wang et al (2019), linear system theory takes dominant position in practice in consideration of system analysis and system refactor. For more information on this point, please see Introduction of Wang et al (2019).…”

Section: B1 Linear System Theorymentioning

confidence: 99%

See 1 more Smart Citation

Why Are the ARIMA and SARIMA not Sufficient

Wang,

Li,

Lim

2019

Preprint

Self Cite

View full text Add to dashboard Cite

The autoregressive moving average (ARMA) model takes the significant position in time series analysis for a wide-sense stationary time series. Facing the trend and seasonal component of a time series, the difference operator and seasonal difference operator, which are bases of ARIMA and SARIMA, respectively, are introduced to remove the trend and seasonal component so that the original non-stationary time series could be transformed into a wide-sense stationary time series, which could then be handled by Box-Jenkins methodology (ARMA). However, such difference operators are more practical experiences than exact theories by now. In this paper, we investigate the power of the (seasonal) difference operator from the perspective of spectral analysis, linear system theory and digital filtering, and point out the characteristics and limitations of (seasonal) difference operator. Besides, the general method that transforms a non-stationary (the non-stationarity in the mean sense) stochastic process to be wide-sense stationary will be presented.

show abstract

Section: B1 Linear System Theorymentioning

confidence: 99%

“…According to Wang et al (2019), linear system theory takes dominant position in practice in consideration of system analysis and system refactor. For more information on this point, please see Introduction of Wang et al (2019).…”

Section: B1 Linear System Theorymentioning

confidence: 99%

Why Are the ARIMA and SARIMA not Sufficient

Wang,

Li,

Lim

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…An expectation maximization (EM) algorithm was proposed in [25] to solve the uncertainty of the state model and measurement model in the tracking system; however, it has not been the subject of rigorous theoretical research. Subsequently, the existence and uniqueness of the solution to the joint estimation and identification problem are theoretically proved within the framework of EM [26]. Thus, the purpose of this paper is to enhance the accuracy of the state estimate with an unknown correlation coefficient by resorting to the EM approach.…”

Section: Introductionmentioning

confidence: 99%

An EM algorithm for target tracking with an unknown correlation coefficient of measurement noise

He¹,

Wu²,

Peng³

et al. 2022

Meas. Sci. Technol.

View full text Add to dashboard Cite

In this paper, an expectation maximization based sequential modified unbiased converted measurement Kalman filter is proposed for target tracking with an unknown correlation coefficient of measurement noise between the range and the range rate. Firstly, a pseudo measurement is constructed by multiplying the range and the range rate to reduce the strong nonlinearity between the measurement and the target state. The mean and covariance of converted errors are subsequentlsubsequently derived by modified unbiased converted measurement to weaken the error caused by the linearization of the measurement equation, which is effectively to improve the dynamic accuracy of target tracking. Then, the converted errors of the position and the pseudo measurement are decorrelated by the Cholesky factorization and thus to obtain the posterior probability distribution of the state by using the sequential filtering in the Bayesian framework. Finally, the expectation maximization is introduced in the updating procedure of the pseudo measurement to jointly estimate the target state and the correlation coefficient. The target tracking scenario with an unknown correlation coefficient is built to demonstrate the validness and feasibility of the proposed algorithm. Simultaneously, the results of the normalized error squared validate the consistency of the modified unbiased converted measurement.

show abstract

“…The problem of estimating states under unknown inputs (perturbations, faults, noises, modeling uncertainties, etc.) has been the object of widespread interest, ranging from bias compensation, 2 fault detection and isolation, 3 input reconstruction and estimation, 4 fault diagnosis, 5 robust state estimation 6 to secure state estimation 7 …”

Section: Introductionmentioning

confidence: 99%

Intermediate‐variable‐based Kalman filter for linear time‐varying systems with unknown inputs

Zhou

Chen

2021

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This article proposes a systematic design methodology of unknown input estimation for time‐varying systems in which unknown inputs exist in system dynamic and measurement simultaneously. By introducing intermediate variables, the relationship between unknown inputs and system states is modeled by an intermediate dynamic process, and then a modified Kalman filter is designed to estimate system states and unknown inputs. Moreover, the stability condition is derived such that the mean square error of the intermediate Kalman filter is bounded. An illustrative example is employed to demonstrate the effectiveness of the proposed methods.

show abstract

Optimal joint estimation and identification theorem to linear Gaussian system with unknown inputs

Cited by 13 publications

References 37 publications

Why Are the ARIMA and SARIMA not Sufficient

Why Are the ARIMA and SARIMA not Sufficient

An EM algorithm for target tracking with an unknown correlation coefficient of measurement noise

Intermediate‐variable‐based Kalman filter for linear time‐varying systems with unknown inputs

Contact Info

Product

Resources

About