Research On Adaptive Filters For Uncertain Systems With Generalized Unknown Disturbances

The state estimation and fusion for dynamic systems widely exists in the field of automatic control,target tracking,information processing and so on.In complex environment,the coexistence of different factors such as system biases,sensor faults,linearization errors and many others,always leads to the model mismatch between the prior nominal measurement model and the ground truth.Such mismatch is depicted as the generalized unknown disturbance added to the nominal measurement model,where it is difficult to be modeled and its characteristics are always unknown.Moreover,due to the existence of the parameter multi-mode,multiplicative noises,nonlinearity,unknown noise parameters,distributed structure and so on,the system modeling should deal with the effect of these complex features.Considering the coexistence of data uncertainty caused by model mismatch and modeling uncertainties due to complex features in the dynamic,this thesis develops a series of adaptive filtering methods under the coupling of the generalized unknown disturbance and modeling uncertainties as follows:1.The state estimation problem in the case of the coexistence of model mismatch and multi-mode is proposed.The framework of adaptive filtering is established for Markovian jump linear systems with generalized unknown disturbances.The upper-bound covariance of the estimate error is constructed by introducing the related free parameter,and a recursive minimum upper-bound filter is further proposed through pursuing the corresponding parameter convex optimization.Meanwhile,the proposed upper bound filter is extended to the fusion structure in the presence/absence of generalized unknown disturbances,via covariance intersection.The proposed method avoids the limitation that the traditional linear minimum mean square error estimator of Markovian jump linear systems needs to know the model parameter and the corresponding statistical characteristics in prior.In the state estimation scenario from maneuvering target tracking with generalized unknown disturbances,the proposed method owns more accurate precision than that of the linear minimum mean square error estimator,and is robust to the initial values of related parameters.2.The filter design problem in the case of the coexistence of multiplicative noises,model nonlinearity and model mismatch is put forward.By utilizing the second- order Taylor expansion,the adaptive upper-bound filtering framework with high precision is proposed.It not only considers the calculation of coupling effect between stochastic multiplicative parameters and high-order moment matrices of the state(such as Hessian matrices),but also brings the adjust parameter to adapt the unknown disturbances online,in order to obtain a satisfactory estimation accuracy.In the state estimation simulation of range-based radar target tracking whose measurement accuracy depends on the relative distance between the target and radar,the proposed method gains a better filtering performance than those of the firstorder/second-order extended Kalman filter and the first-order Kalman filter with multiplicative noises.3.Considered estimation problem for nonlinear systems with the model mismatch and unknown measurement noise covariance,an adaptive variational Bayesian filtering scheme of joint state estimation and unknown parameters processing is designed,based on the matrix eigenvalue decomposition.In the framework of Gaussian filtering,the related covariance is reconstructed via matrix eigenvalue decomposition,and the model nonlinearity is dealt with by applying statistical linear regression to estimate the unknown measurement noise covariance recursively.The proposed method overcomes the barrier that the existing analytical variational Bayesian filter can not be adopted when there exists the generalized unknown disturbances and model nonlinearity.In the filtering scenario of target tracking with generalized unknown disturbances and unknown measurement noise covariance,the proposed method outperforms the interacting multiple model method without complete perfect model set in prior.4.The distributed lower-bound information filter is proposed via network consensus,which is motivated by considering the state estimation in the case of multiple sensor fusion with generalized unknown disturbances.It solves the problem that the related covariances from different sensor nodes can not be fused directly due to the existence of generalized unknown disturbances and avoids the high-dimensional optimization problem in centralized fusion.In each sensor node,the lower-bound information filter mechanism is derived by introducing the free parameter for lowerdimensional convex optimization to adapt the effect of generalized unknown disturbances.Then,combined with average consensus strategy,the distributed implementation with multiple sensors is designed in order to obtain an asymptotic consistency of the estimate results.In the simulation of multi-sensor estimation and fusion with multiple generalized unknown disturbances,the estimation performance of the proposed method is better than those of the Kalman filter,multi-sensor dynamic state and bias filter and upper-bound filter with single sensor node.5.Considered the state smoothing with generalized unknown disturbances,the decoupling upper-bound consistent fusion method,i.e.,the fixed-interval minimum upper-bound smoother,is proposed based on the recursive forward upper-bound filtering and backward upper-bound smoothing,by utilizing the inverse covariance intersection optimization.The proposed method addresses the problem that the estimates from the forward filtering and backward smoothing can't be fused effectively since they are coupled with each other due to the existence of generalized unknown disturbances.To further relax the initial condition including the initial forward filtering covariance and the initial backward smoothing covariance,the recursive decoupled lower-bound information smoother is presented.In the state estimation scenario of target tracking with different types of unknown disturbances including rectangular wave,slop function,sin curve and uniform distribution,the proposed method obtains a more accurate filtering precision that those of the Kalman filter,forward-backward Kalman smoother and upper-bound filter.