Study Of Robust Filtering For Dynamic Systems With Constraints

Constraints,which emerge in terms of various physical quantities(e.g.,mass,energy,momentum,etc.)or mathematical and physical properties(e.g.,nonnegativity,monotonicity,convexity,etc.),are commonly existing in the complex systems of aerospace,signal processing,industrial processes and so on.Fully exploiting the state constraint information arising from system characteristics and environmental restrictions,the modeling uncertainties such as bounded disturbances,additive-multiplicative noises,unknown parameters,multi-mode uncertainties and model nonlinearities,can be reduced to a certain extent,and thus,the estimated performance can be improved.Therefore,it is of great theoretical significance and practical applications to develop a series of recursive robust filtering methods for constrained systems.This thesis focuses on the key scientific problems of constrained dynamic system state estimation with the following researches:1.A robust interval constrained H∞ filter is proposed for dynamic systems with bounded disturbances under interval constraints.In order to avoid the decision risk caused by inequality detection,the inequality interval constraints are transformed into equality constraints by sine functions with unknown angles.The Lagrange multiplier method is used to obtain the optimal constraint H∞ filtering by maximizing the cost function with respect to the initial state,system disturbances and unknown angles while minimizing it with respect to state estimates.The filtering performance is obviously better than that of the constrained minimum and maximum filtering algorithm based on game and active set in the simulation scene of road target tracking under bounded disturbances.2.A recursive upper bound filter is proposed for multiplicative noise dynamic systems with interval constraints.The interval constraints are transformed into equality constraints by using sine functions with unknown angles,and a new dynamic evolution model with unknown input is reconstructed based on system projection.The upper bounds of the covariance of state estimation error,filter residual error and state prediction error,instead of the corresponding ideal covariance,are constructed recursively.By using linear matrix inequalities and scaling the diagonal sub-block matrices and non-diagonal sub-block matrices of the innovation covariance,the upper bound filtering is given.In the numerical simulation with interval constraints and multiplicative noises,the filtering accuracy of the proposed algorithm is better than that of the upper bound filtering with multiplicative noises only.3.Joint state estimation and unknown parameter identification based on model reduction is proposed for dynamic stochastic systems with uncertain constraints.In EM framework,the equation constraints with unknown parameters are introduced into the dynamic systems to realize the model reduction by constructing the nonsingular matrices,so as to avoid the existence of matrix singularity of likelihood functions.The likelihood equations of unknown constraint parameters are given and iterative optimization is designed to realize the final joint state estimation and identification of unknown constraint parameters.In a typical road target tracking simulation,considering two different scenarios with different unknown constraint parameters,the proposed method not only identifies unknown constraint parameters accurately,but also obtains higher filtering precision than that of Kalman filtering without considering constraint information.4.Considering the multi-mode uncertainty of system state evolution and diversity of state constraints,an interactive multi-hypothesis estimation method for Markov switched systems with jump constraints is proposed.The jump constraints are introduced into the dynamic systems by system projection,and the hypothesis sets containing the possible values of the double jump Markov parameter are defined.A recursive update of the posteriori estimates of state and hypothesis probability is realized based on Gaussian hypothesis.Furthermore,the optimal state estimations are approximately achieved by iteratively linearizing the constraint model and measurement model to pursue the ideal linearized point.In the numerical simulation of maneuvering target tracking under the cross roads,the filtering precision of the proposed algorithm is obviously better than those of the interactive multimodel algorithm without constraint and the interactive multi-model algorithm with constraint filters as sub-filters.5.Considering the stochastic systems with interval constraints,the recursive filtering method of fusing interval constraint information is proposed from the perspective of data fusion.In the framework of covariance intersection,a more accurate filtering result is obtained based on the fusion of the state estimates coming from the real measurements and the constructed state estimate error covariances deriving from interval constraints.The constructed covariances are either exploited in the view of geometry of the super ellipsoids or rapidly developed based on the state estimates with real measurements.The filtering accuracy of the proposed algorithm is obviously better than that of the unscented Kalman filtering algorithm without considering the constraints in the road target tracking scenario with rectangular interval constraints.