Confidence Set-Membership State Estimation

In the field of state estimation,two main methods for describing uncertainty are the probabilitybased approach and the set-membership approach.The probability-based approach requires complete knowledge of the probability distribution information of uncertainties,whereas the set-membership approach requires only knowledge of their boundaries.However,in practical engineering problems,many situations fall between the applicable ranges of the two,where partial probability distribution information is easy to obtain,while another part is difficult to acquire.Therefore,studying state estimation problems under these conditions has widespread practical value.This paper focuses on systems that simultaneously include Gaussian and bounded uncertainties,proposing a class of confidence set-membership estimation within the framework of probability measure sets.The proposed estimation method incorporates a probabilistic approach based on set-membership estimation and uses the confidence set of the state as the estimation result,thus achieving a better balance between accuracy and robustness.Considering computational efficiency,this thesis discusses the specific algorithm implementations of such confidence set-membership estimators in different systems and scenarios,enriching existing theoretical achievements in state estimation to better meet engineering practical needs.Specifically:1.For linear time-varying systems with both Gaussian and bounded noise,this thesis proposes a confidence set-membership estimation method based on the finite impulse response(FIR)structure.This method provides a confidence set of the true state at a certain confidence level and minimizes the given confidence state set.The FIR structure in design increases the degrees of freedom of the estimator gain,and the mixed Gaussian and bounded uncertainty noise description enhances the robustness of the estimator.Simulation results show that the precision of the estimator can be adjusted by various means,and the estimator exhibits strong robustness to unknown faults and inaccurate noise information.2.For linear time-varying systems with known noise bounds and partial variances,this thesis combines set-membership estimation with Moving Horizon Estimation(MHE)to propose a novel estimation method.Specifically,set-membership estimation serves as a precursor to MHE and provides sets with a confidence level of 1 for the state and decision variables.Then,MHE is used to find the optimal estimate of the state.Simulation results indicate that the proposed method can simultaneously provide point estimates and set estimates,and MHE based on set-membership methods improves computational efficiency and robustness.3.For linear parameter time-varying(LPV)systems with both Gaussian noise and bounded noise,as well as scheduling variable-bounded uncertainty,this thesis derives and optimizes the propagation of Gaussian and bounded errors in parameter-bounded uncertain systems,providing and optimizing the confidence set of the state.4.For Markov jump systems with bounded noise and known modal transition probabilities,this thesis proposes both methods for confidence set-membership estimation and state value estimation.By detecting whether intersecting,the confidence sets of connected states under the same mode are merged,and confidence is updated based on empty sets and merging information,effectively avoiding the problem of the exponential growth of the number of sets over time.5.For general nonlinear systems with both Gaussian and bounded noise,this thesis uses the Koopman operator to linearize the system,transforming it into a special type of linear system.To enhance the robustness of the model,the linearization error generated in this process is considered as bounded uncertainty.Based on this linear model,this thesis proposes a recursive structured reduced-order confidence set-membership estimator,providing and minimizing the state confidence set.6.Building upon the linear model derived from the Koopman operator,this thesis further presents a reduced-order FIR-structured confidence-set-membership estimator.Compared to the recursive structured infinite impulse response(IIR)structure estimator mentioned earlier,this method sacrifices a slight amount of estimation precision but enhances the estimator’s robustness against unknown faults and inaccurate noise information.