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Full-Text Articles in Engineering
Kalman Filtering With Inequality Constraints For Turbofan Engine Health Estimation, Daniel J. Simon, Donald L. Simon
Kalman Filtering With Inequality Constraints For Turbofan Engine Health Estimation, Daniel J. Simon, Donald L. Simon
Electrical and Computer Engineering Faculty Publications
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. Thus, two analytical methods to incorporate state-variable inequality constraints into the Kalman filter are now derived. The first method is a general technique that uses hard constraints to enforce inequalities on the state-variable estimates. The resultant filter is a combination …
H-Infinity Estimation For Fuzzy Membership Function Optimization, Daniel J. Simon
H-Infinity Estimation For Fuzzy Membership Function Optimization, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a specific shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a few variables and the membership optimization problem can be reduced to a parameter optimization problem. The parameter optimization problem can then be formulated as a nonlinear filtering problem. In this paper we solve the nonlinear filtering problem using H∞ state estimation theory. However, the membership functions that result from this approach are not (in general) sum normal. …
Kalman Filtering With Uncertain Noise Covariances, Srikiran Kosanam, Daniel J. Simon
Kalman Filtering With Uncertain Noise Covariances, Srikiran Kosanam, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
In this paper the robustness of Kalman filtering against uncertainties in process and measurement noise covariances is discussed. It is shown that a standard Kalman filter may not be robust enough if the process and measurement noise covariances are changed. A new filter is proposed which addresses the uncertainties in process and measurement noise covariances and gives better results than the standard Kalman filter. This new filter is used in simulation to estimate the health parameters of an aircraft gas turbine engine.
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This …
Kalman Filtering With State Equality Constraints, Daniel J. Simon, Tien Li Chia
Kalman Filtering With State Equality Constraints, Daniel J. Simon, Tien Li Chia
Electrical and Computer Engineering Faculty Publications
Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state …