Constrained Extended Kalman Filter for Nonlinear State Estimation

Ungarala, Sridhar; Dolence, Eric; Li, Keyu

doi:10.3182/20070606-3-mx-2915.00058

Cited by 46 publications

(28 citation statements)

References 5 publications

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“…The fundamental reason for this inability is the constraints on the model variables due to their physical limitations. This problem has also been reported in the context of nonlinear state estimation [63][64][65]. Therefore, future work is needed to incorporate this important information into the proposed method (constraints on model variables).…”

Section: Real Casementioning

confidence: 78%

Development of a Regularized Dynamic System Response Curve for Real-Time Flood Forecasting Correction

Sun

Bao

Jiang

et al. 2018

Water

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Abstract:The dynamic system response curve (DSRC) is commonly applied as a real-time flood forecasting error correction method to improve the accuracy of real-time flood forecasting. It has been widely recognized that the least squares (OLS/LS) method, employed by DSRC, breaks down ill-posed problems, and therefore, the DSRC method may lead to deterioration in performance caused by meaningless solutions. To address this problem, a diagnostically theoretical analysis was conducted to investigate the relationship between the numerical solution of the Fredholm equation of the first kind and the DSRC method. The analysis clearly demonstrates the derivation of the problem and has implications for an improved approach. To overcome the unstable problem, a new method using regularization techniques (Tikhonov regularization and L-Curve criterion) is proposed. Moreover, in this study, to improve the performance of hydrological models, the new method is used as an error correction method to correct a variable from a hydrological model. The proposed method incorporates the information from a hydrological model structure. Based on the analysis of the hydrological model, the free water storage of the Xinanjiang rainfall-runoff (XAJ) model is corrected to improve the model's performance. A numerical example and a real case study are presented to compare the two methods. Results from the numerical example indicate that the mean Nash-Sutcliffe efficiency value (NSE) of the regularized DSRC method (RDSRC) decreased from 0.99 to 0.55, while the mean NSE of DSRC decreased from 0.98 to −1.84 when the noise level was increased. The overall performance measured by four different criteria clearly demonstrates the robustness of the RDSRC method. Similar results were obtained for the real case study. The mean NSE of 35 flood events obtained by RDSRC method was 0.92, which is significantly higher than the mean NSE of DSRC (0.7). The results demonstrate that the RDSRC method is much more robust than the DSRC method. The applicability and usefulness of the RDSRC approach for real-time flood forecasting is demonstrated via the numerical example and the real case study.

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Section: Real Casementioning

confidence: 78%

Development of a Regularized Dynamic System Response Curve for Real-Time Flood Forecasting Correction

Sun

Bao

Jiang

et al. 2018

Water

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“…The updated EKF estimates can be adjusted to reconcile with simple linear equality constraints using methods based on Lagrange multipliers and projection methods [28,29]. More general state constraints may be imposed on the iterated form of the EKF implemented as a separate MHE in a horizon of one to formulate the arrival cost.…”

Section: Arrival Cost Using Extended Kalman Filtermentioning

confidence: 99%

Computing arrival cost parameters in moving horizon estimation using sampling based filters

Ungarala

2009

Journal of Process Control

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“…There are some approaches in the literature extending the EKF in this direction (e.g. [10], [11]), but as far as we are aware, there have been no such attempts for the UKF except the work reported in [13]. The aim of this paper is to demonstrate how a simple projection of the sigma points can give good constraint handling in the UKF, while applying the same projection to the EKF estimate does not give good performance.…”

Section: Introductionmentioning

confidence: 99%

“…In Kalman filter theory, there is no general way of incorporating these constraints into the estimation problem. However, the constraints can be incorporated in the KF by projecting the unconstrained KF estimates onto the boundary of the feasible region at each time step [10], [11]. An other way of nonlinear state estimation with constraints is Moving Horizon Estimation (MHE), in which the constraints can be included in the estimation problem in a natural way [9].…”

Section: State Estimation With Constraintsmentioning

confidence: 99%

Constrained state estimation using the Unscented Kalman Filter

Kandepu¹,

Imsland

Foss³

2008

2008 16th Mediterranean Conference on Control and Automation

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Abstract-A simple procedure to include state inequality constraints in the Unscented Kalman Filter is proposed. With this procedure, the information of active state constraints influences the state covariance matrix, resulting in better estimates. In a numerical example, the approach outperforms the Extended Kalman Filter implemented with constraint handling via "clipping". I. INTRODUCTIONIn the process industries one of the main goals is to make the end product at the lowest possible cost while satisfying product quality constraints. State estimation often play an important role in accomplishing this goal in process control and performance monitoring applications. There are many uncertainties to deal with in process control; model uncertainties, measurement uncertainties and uncertainties in terms of different noise sources acting on the system. In this kind of environment, representing the model state by an (approximated) probability density function (pdf) has distinct advantages. State estimation is a means to propagate the pdf of the system states over time in some optimal way. It is most common to use the Gaussian pdf to represent the model state, process and measurement noises. The Gaussian pdf can be characterized by its mean and covariance. The Kalman Filter (KF) propagates the mean and covariance of the pdf of the model state in an optimal (minimum mean square error) way in case of linear dynamic systems [5].All practical systems possess some degree of nonlinearity. Depending on the type of process and the operating region of the process, some processes can be approximated with a linear model and the KF can be used for state estimation. In some cases the linear approximation may not be accurate enough, and state estimator designs using nonlinear process models are necessary. The most common way of applying the KF to a nonlinear system is in the form of the Extended Kalman Filter (EKF). In the EKF, the pdf is propagated through a linear approximation of the system around the operating point at each time instant. In doing so, the EKF needs the Jacobian matrices which may be difficult to obtain for higher order systems, especially in the case of timecritical applications. Further, the linear approximation of the system at a given time instant may introduce errors in the state which may lead the state to diverge over time. In other words, the linear approximation may not be appropriate for some systems. In order to overcome the drawbacks of the

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Constrained Extended Kalman Filter for Nonlinear State Estimation

Cited by 46 publications

References 5 publications

Development of a Regularized Dynamic System Response Curve for Real-Time Flood Forecasting Correction

Development of a Regularized Dynamic System Response Curve for Real-Time Flood Forecasting Correction

Computing arrival cost parameters in moving horizon estimation using sampling based filters

Constrained state estimation using the Unscented Kalman Filter

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