Incorporation of a positivity constraint into a Kalman-filter-based algorithm for correction of spectrometric data

Massicotte, Daniel; Morawski, Roman Z.; Barwicz, A.

doi:10.1109/19.368111

Cited by 76 publications

(32 citation statements)

References 6 publications

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“…The equality-constrained problem was dis written as cussed in [2], and so those results can be used to investigate the properties of the inequality-constrained problem. Noting that the Kalman filter estimate is the conditional denote the state estimate of the constrained Kalman filter as given by (24), recalling that (17) and (22) S is the covariance of the unconstrained estimate given in x, (11) and (14), has an error covariance that is less than or Gaussian nature of x 0 , fw k g, and fe k g in (1).…”

Section: Kalman Filtering With Hard Inequality Constraintsmentioning

confidence: 99%

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Kalman filtering with state equality constraints

Simon

Chia²

2002

IEEE Trans. Aerosp. Electron. Syst.

512

435

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Section: Kalman Filtering With Hard Inequality Constraintsmentioning

confidence: 99%

“…However, in the application of Kalman filters there is often available model or signal information that is either ignored or dealt with heuristically [1]. We intend to derive ways to modify the Kalman filter state estimate such that known inequality constraints are satisfied by the state-variable estimates.…”

Section: Introductionmentioning

confidence: 99%

Kalman filtering with state equality constraints

Simon

Chia²

2002

IEEE Trans. Aerosp. Electron. Syst.

512

435

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“…Second, soft constraints can be implemented by adding a regularization term to the standard Kalman filter [6] . Third, soft constraints can be enforced by projecting the unconstrained estimates in the direction of the constraints rather than exactly onto the constraint surface [41].…”

Section: Soft Constraintsmentioning

confidence: 99%

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

Simon

2010

IET Control Theory Appl.

778

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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“…However, in the application of Kalman lters there is often known model or signal information that is either ignored or dealt with heuristically [1]. This paper presents two ways to generalize the Kalman lter in such a way that known inequality constraints among the state variables are satis¯ed by the state variable estimates.…”

Section: Introductionmentioning

confidence: 99%

Kalman filtering with inequality constraints for turbofan engine health estimation

Simon

2006

IEE Proceedings - Control Theory and Applications

130

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Kalman¯lters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman¯lters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not¯t easily into the structure of the Kalman¯lter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman lter. The¯rst method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant¯lter is a combination of a

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Incorporation of a positivity constraint into a Kalman-filter-based algorithm for correction of spectrometric data

Cited by 76 publications

References 6 publications

Kalman filtering with state equality constraints

Kalman filtering with state equality constraints

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

Kalman filtering with inequality constraints for turbofan engine health estimation

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