Research On Tracking Model And State Estimation Algorithm For Hypersonic Maneuvering Target

With the gradual advancement of hypersonic flight technology,vehicles can achieve hypersonic maneuvering flight in the high endo-atmosphere,breaking down many conventional assumptions about dynamic model and state estimation algorithm in target tracking,and greatly degrading the estimation performance.Due to the severe and complex aerodynamic effect,more sophisticated maneuvering flight can be performed,which seriously reduces the accuracy of the prior model and then affects the estimation result of the filter.The classical method is extracting motion characteristic parameters to augment the state vector and make up for the model error.However,the nonlinear relationship between state and parameters in the nonlinear dynamics model is not conducive to the convergence and consistency of parameter estimation.Additionally,the linear kinematics model is not precise enough to describe hypersonic motion.Moreover,these defects are adverse to the online recognition of target maneuver mode and overcoming the problem of unknown target mode and switching either.The state estimation algorithm synthesizes the information from dynamic model and measurement data to estimate the target state and parameters jointly,where the performance directly depends on the state dimension and covariance setting.Generally,Riccati equation can be employed to deduce covariance evolution,with which the covariance analysis can be adopted to quantitatively evaluate and design the estimation algorithm.However,as for maneuvering target tracking with less prior information and strong nonlinearity,there are few related studies reported.Simultaneously,the target maneuverability changes the distribution of uncertainty to non-Gaussian characteristics.The nonlinear propagation of non-Gaussian uncertainty can be solved by large-scale random sampling and deterministic sampling based on approximating the object's probability distribution.However,the heavy computational burden of the both is not suitable for hypersonic maneuvering target tracking requiring rapid response.In this thesis,research is carried out on these above issues.To overcome the shortcomings of traditional models,a novel tracking model is proposed based on hypersonic flight motion characteristics,where the intrinsic correlation of ballistic data is investigated and parameterized via the data processing algorithm.The hypersonic dynamics model and typical maneuver mode are established in the ballistic coordinate system,to generate original ballistic data by numerical simulations.Meanwhile,in order to isolate the interference between different data modes,the ensemble empirical mode decomposition technique is introduced to separate the trend term,periodic term and noise term of the ballistic data.Then,the auto-regressive moving average model is uniformly utilized to analyze and parameterize each data term.Trend term fitting is mainly based on the time domain characteristics of the data,and periodic term modeling refers to the related research in signal spectrum analysis and correlation whitening.Finally,the modeling results of the above terms are synthesized by the model congruence algorithm,and the flight state tracking model is established as high-order Markov model.Thus,the motion law is described in the form of the correlation of state variables,which avoids the observability problem of parameters in the dynamics model and achieves a higher accuracy than the kinematics model.In terms of the high-order Markov model mentioned above,a state estimation algorithm is designed for hypersonic maneuvering targets,which mainly involves the selection of state variables,the setting of initial state covariance and process noise covariance.The system is linearized around the nominal trajectory and transformed into a linear time-varying system.The number and direction of observable modes are determined according to the rank test of observability Gramian matrix.Then,the stochastic observability of system states is analyzed based on Riccati equation and covariance analysis,which assists the selection of filtering states.The concepts of stochastic observability and stochastic controllability are introduced to analyze the influence of initial state covariance on the algorithm stability and set it up.The filtering stability is analyzed with the Lyapunov exponential method and function method.The former takes the error covariance as the operation object to exhibit the error trend of estimation trajectory,and the latter discusses the conditions of algorithm stability by linearizing the system.The combination of the two completes the analysis and setting of process noise covariance.The state augmented filter based on the above observability and stability analysis can effectively guarantee the stability and accuracy of the estimation results.Moreover,there exists a filtering-smoothing double estimation mechanism for higher-order states,which can effectively improve the convergence of filtering algorithm.Aiming at the nonlinear propagation of non-Gaussian uncertainties of maneuvering targets,non-Gaussian sample generation strategy and sample processing algorithm are designed based on Bayesian estimation,Gauss integral and polynomial chaos theory.The Bayesian estimation theory provides a sequential filtering framework for arbitrary probability distribution,which transforms the estimation problem into a probability density weighted integra l problem,which can be solved by Gauss integral with a high algebraic accuracy.According to the distribution characteristics of model error,the Wiener-Askey polynomial chaos theory is introduced to determine the corresponding orthogonal polynomial,and generate one-dimensional sample sets and their weights.However,the multi-dimensional non-Gaussian joint probability density function is complex and difficult to solve,and the dimension disaster will occur when the dimension traversal method is adopted to expand these samples from one-dimension to multi-dimension.Thus,the coordinate axis sampling strategy is introduced to generate multi-dimensional sample sets and their weights.Then,the collocation method is improved with the orthogonal basis function matrix to process the sample set and determine the coefficients of the polynomial chaos expansion.With these coefficients,the statistical characteristics of the random process are determined and more approximate to the actual probability distribution.The resulted filter can alleviate the approximate error of calculating covariance to a certain extent.For the model mismatch caused by target maneuver,the online recognition of target motion law is accomplished mainly based on robust filter and linear prediction theory,to suppress the interference from unknown model and possible maneuvering mode switching at any time.According to the high-order Markov model and the state estimation algorithm,the two-stage Kalman filter is introduced to improve the joint estimation of state and model bias and investigate the influence of coupling effect on the algorithm stability via decoupling strategy.Meanwhile,to enhance the robustness to data mutation,a robust filter is designed by introducing Huber function into the strong tracking filter algorithm,which effectively overcomes the problem of over-regulation and achieves stable tracking for maneuvering targets.In order to further improve the tracking accuracy,the linear prediction theory is adopted to process the tracking data with the high-order Markov modeling strategy and online establish an auto-regressive model of the target motion law.In this way,the target maneuver mode is recognized online together with the statistical characteristics of model error,which can be used to design filtering algorithm and improve tracking accuracy.The results demonstrate that the proposed algorithm can effectively overcome the degradation and divergence of filtering performance caused by unknown model and model mutation.