State Estimation And Fault Detection For Systems Based On Kalman Filter

Kalman filter (KF) has the optimal estimation performance anditerative calculation form. It can be used not only as a filter but also as a predictor. Theproblems of state estimation, state prediction, constraints, and fault detection based onKalman filter are investigated. The main contributions of the dissertation are as follows:Firtly, we give a review of previous work on KF. Moreover, the state estimationalgrithms including KF, extended Kalman filter (EKF), unscented Kalman filter (UKF)are also be given.Secondly, we consider networked constrained Kalman filtering with observationlosses. Based on physical consideration, at each time step through projecting theunconstrained Kalman filter solution onto the state constraint surface, the constrainedestimation can be derived, which significantly improves the prediction accuracy of thefilter. We study the statistical convergence properties of the error covariance matrix,showing the existence of a critical value for the arrival rate of the observation, beyondwhich a transition to an unbounded state error covariance occurs. We give the upperbound and lower bound of the critical value, and also show that, when the systemobservation matrix restricted to the observable subspace is invertible, the criticalprobability is an exact value.Thirdly, the state prediction based on KF for linear stochastic discrete-time systemand the state prediction based on the UKF for nonlinear stochastic discrete-time systemsare investigated. A confidence interval (CI) of prediction errors can be used to correctthe predictive states, and thereby it improves the prediction accuracy and also providesinformation about states coverage, which is useful for target tracking, fault prognosisand Condition Based Maintenance.Then, fault detection for nonlinear system with unknown input and stateconstraints, state estimation and constrained state estimation for nonlinear systems withunknown input are investigated. The constraints which can improve the quality ofestimation are imposed on individual updated sigma points as well as the updated state. The advantage of algorithm is that it is able to deal with arbitrary constraints on thestates during the estimation procedure. Least-squares unbiased estimation algorithm canbe used to obtain unknown input, and the unknown input which can be any signalaffects both the system and the outputs. The state estimation problem is transformedinto a standard Unscented Kalman filter problem which can easily be solved. By testingthe mean of the innovation process, a real-time fault detection approach is proposed.This approach does not require a priori statistical characteristics of the faults, and thecomputation burden is not very heavy.Finally, The Fault detection which is based on fuzzy modeling is investigated.Takagi-Sugeno (TS) fuzzy model can be derived by structure and parameteridentification, where only the input-output data of the identified system are available. Inthe structure identification step, Gustafson-Kessel clustering algorithm (GKCA) is usedto detect clusters of different geometrical shapes in the data set and to obtain thepoint-wise membership function of the premise. In the parameter identification step,Unscented Kalman filter (UKF) is used to estimate the parameters of the premise’smembership function. In the consequence part, Kalman filter (KF) algorithm is appliedas a linear regression to estimate parameters of the TS model using the input-output dataset. Then, the obtained fuzzy model is used to detect the fault.Simulations are provided to demonstrate the effectiveness of the theoretical results.The summary and forecast is presented in the end.