Constraint Motion Modeling And State Estimation Methods

In many pratical tracking scenarios, the motion trajectory of target is always affected or strictly restrained by the environment. Thus it is not free motion without constraint, such as vehicles moving on the road or ships sailing along the route. However, traditional tracking methods may lead to model mismatch, information waste and performance loss when they are used to process constrained state estimaton problem. Because the prior knowledge of constraint is not considered in these methods. In this thesis, according to the problems of theory and methods appeared in practical applications, research and exploration are processing in two important fields based on the existing results of constraint state estimation:(1) to obtain a comparatively complete method of complex motion modeling and state estimation in complicated constrained space;(2) to address the possible problem of incomplete prior constraint knowledge in practical applications, models and filtering methods of implicit linear equality constaints are presented.First, several commonly used constrained state estimation algorithms are introduced, including four methods: model reduction method, pseudo measurement method, estimate projection method and linear equality constraint Kalman filter method. Implementation of these methods will be presented. And the analysis and comparison is given according to the aspects of numerical stability, computational burden, estimation performance, etc.Then complex motion modeling and state estimation in complicated constraint space is investigated based on one dimentional motion modeling method. One dimensional constraint coordinate Kalman filter(CCKF) is realized. And a joint initialization with multi-dimensional measurements which adopts the minimum mean squarederror fusion will be presented while the posterior Cramer-Rao lower bound of state estimation with linear equality constriaint will be obtained, which provide the theory limitation of state estimation accuracy. Normalized estimation error squared is used to test the consistency of state estimation results. The effectivenesses of the CCKF and joint initialization method is demonstrated by numerical experiments. An one dimensional constraint coordinate interacting multiple model(IMM-CCKF) algorithm is proposed to deal with the problem of complex motion modeling and state estimation in complicated constraint space, which can efficiently prevent the model mismatch problems caused by methods using traditional motion models. Simulations show the validity and superiority of IMM-CCKF.Finally, the concept of implicit equality constraint is proposed, and then on this basis two effective implicit equality constraint modeling and nonlinear filtering methods are presented to handle the problem of incomplete prior constraint knowledge in practical applications. A interacting multiple constraint state estimation method with implicit linear equality constraint is proposed to cope with the practical tracking problem, such as the coexistence of true target and interference sources in anti-radiation missile(ARM) tracking problem. The processing of practical measured data and simulation experiments illustrate the effectiveness of the interacting multiple constraint state estimation method. Two pseudo measurement models are presented to address the problem of the general implicit linear equality state estimation problem: pseudo measurement of velocity constraint, which is affected by measurement noise, and pseudo measurement of hybrid constraint, which is error-free. Nonlinear state estimation methods corresponding to these two pseudo measurements are derived, respectively. Simulation results demonstrate the validities of pseudo measurement models and filtering methods. The incorporation of implicit equality constraint brings significant improvement to the state estimation accuracy.