Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation

Vachhani, Pramod; Narasimhan, Shankar; Rengaswamy, Raghunathan

doi:10.1016/j.jprocont.2006.07.002

Cited by 130 publications

(86 citation statements)

References 11 publications

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“…Unscented recursive nonlinear dynamic data reconciliation (URNDDR) [50] is similar to 2UKF. URNDDR projects the a posteriori sigma points onto the constraint surface, and modifies their weights based on their distances from the a posteriori state estimate.…”

Section: Unscented Kalman Filteringmentioning

confidence: 99%

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Simon

2010

IET Control Theory Appl.

781

468

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The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results.

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Section: Unscented Kalman Filteringmentioning

confidence: 99%

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Simon

2010

IET Control Theory Appl.

781

468

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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: 95%

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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“…Each time the sigma points are redefined, the sigma points located out side the constraints are projected to the constraint boundary [18]. A similar approach to constraints handling was used by Vachhani and coworkers [30]. However, their constrained optimization ap proach to update the sigma points is incorrect because the user-de fined sigma points are functions of the state estimate and optimality of the sigma points may not be defined independently [31].…”

Section: Arrival Cost Using Unscented 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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Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation

Cited by 130 publications

References 11 publications

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Constrained state estimation using the Unscented Kalman Filter

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

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