Kalman filtering with inequality constraints for turbofan engine health estimation

Simon, Daniel J.; Simon, Donald L.

doi:10.1049/ip-cta:20050074

Cited by 130 publications

(106 citation statements)

References 17 publications

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“…For example, inequality constraints can be incorporated in a less rigorous way as soft constraints [4,22]. Another more rigorous approach is to treat a general nonlinear constrained state estimation problem as a constrained parameter estimation problem.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Simon

2006

European Journal of Control

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Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters 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 fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints has been shown to generally improve the filter's estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy.After all, the Kalman filter is theoretically optimal, so the incorporation of heuristic constraints may degrade the optimality of the filter. This paper proposes a way to switch the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. * Corresponding author. Email address d.j.simon@csuohio.edu. This work was supported by the NASA Aviation Safety and Security Program at NASA Glenn Research Center. 1When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. If some measurement residuals are low, and those residuals are highly sensitive to a given state, then we are confident that the unconstrained estimate of that state is correct.Otherwise, we incorporate our heuristic knowledge as state constraints. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Simon

2006

European Journal of Control

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“…In practice, according to the physical laws or design specification, some additional information is known as prior knowledge, which can be formulated as inequality constriants about state variables (some engineering applications can be found in [23]). In this paper, we consider the state inequality constraints [26][27][28]. Specifically, for the dynamics (1), the inequality constraints about the state can be given as follows, q t (x) ≤ 0, t = 1, .…”

Section: Problem Formulationmentioning

confidence: 99%

Distributed State Estimation under State Inequality Constraints with Random Communication over Multi-Agent Networks

Lin

et al. 2018

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Abstract:In this paper, we investigate distributed state estimation for multi-agent networks with random communication, where the state is constrained by an inequality. In order to deal with the problem of environmental/communication uncertainties and to save energy, we introduce two random schemes, including a random sleep scheme and an event-triggered scheme. With the help of Kalman-consensus filter and projection on the constrained set, we propose two random distributed estimation algorithm. The estimation of each agent is achieved by projecting the consensus estimate, which is obtained by virtue of random exchange information with its neighbors. The estimation error is shown to be bounded with probability one when the agents randomly take the measurement or communicate with their neighbors. We show the stability of proposed algorithm based on Lyapunov method and projection and demonstrate their effectiveness via numerical simulations.

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“…First, the perfect measurement approach can be extended to soft constraints by adding small nonzero measurement noise to the perfect measurements [9,10,39,40]. 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.

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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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Kalman filtering with inequality constraints for turbofan engine health estimation

Cited by 130 publications

References 17 publications

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Distributed State Estimation under State Inequality Constraints with Random Communication over Multi-Agent Networks

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

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