Modeling And Tracking Methods With Implicit Constraints

Constrained modeling and estimation is an important research topic in the target tracking area.It has potential applications in a wide range,such as ground target tracking based on airborne/spaceborne radar and surveillance and tracking of vessel targets in a river/harbor in military and civilian fields.Constraint relationships on target motion imposed by roads,routes and channels contain prior information on target states,describe and utilize the constraint information can significantly benefit tracking accuracy.Existing research mainly focus on equality constraint modeling and estimation where the spatial constraints,i.e.,roads or routes,are complete and exactly known.However,in practical applications,the exact equality constraint cannot always be completely determined,which means the existing theories and methods are not applicable.In this dissertation,under the situations where the constraints are only partially known or not completely reliable,the problems of modeling of implicit constraints based on partially known information and constrained state estimation are investigated,including the modeling and constrained estimation methods with two typical implicit constraints:the destination constraint and the trajectory shape constraint,the main content is given as follows:1.For constrained tracking problems with a straight trajectory where only the destination is known,constraint models and corresponding constrained tracking methods with a destination constraint imposed by straight trajectory are proposed.On that basis,constraint models using noisy destination information are presented for cases where the destination information is not accurate.According to the destination constraint models,pseudo-measurements are constructed to incorporate constraint information into the tracking system,resulting in a series of destination constraint target tracking methods with a straight trajectory.Additionally,to objectively evaluate the performance of constrained tracking methods,constraint error is presented as a performance metric and an approximate calculation method of the posterior Cramer–Rao lower bound for constrained estimates is proposed.Simulation results demonstrate that the proposed destination constraint target tracking methods with a straight trajectory are effective to utilize the destination information to enhance estimation accuracy.2.For target tracking problems with a straight trajectory where only the trajectory shape is known,constraint models and corresponding constrained tracking methods with a trajectory shape constraint imposed by straight trajectory are proposed.Trajectory shape constraint models are derived based on the state augmentation method and parameter augmentation method,respectively.Two forms of constraint model are provided based on the state augmentation: one is a redundant model,the other is a minimal one,the equivalence between the two forms is analyzed theoretically.Based on the parameter augmentation,there are also two forms of constraint model: one is a model incorporating the slope and intercept,the other is the one incorporating generalized parameters.According to the destination constraint models,pseudo-measurements are constructed to incorporate constraint information into the tracking system,resulting in a series of trajectory shape constraint tracking methods.Simulation results demonstrate that the proposed trajectory shape constraint tracking method with a straight trajectory is effective to utilize the trajectory shape information to enhance estimation accuracy.The constrained target tracking method based on parameter augmentation provides constrained state estimates along with high accuracy parameter estimates,which can be used as prior information to improve tracking accuracy of subsequent targets traveling along the same straight trajectory.Simulation results also demonstrate that the constraint tracking method using generalized parameters has better robustness.3.For target tracking problems with an implicit constraint imposed by circular trajectory,constraint models and corresponding constrained tracking methods with an implicit constraint imposed by circular trajectory are proposed.Destination constraint models are derived based on the geometrical analysis method and parameter augmentation method,respectively.Trajectory shape constraint models are derived using the parameter augmentation method.According to the circular trajectory implicit constraint models,pseudo-measurements are constructed and a series of circular trajectory implicit constraint tracking methods are proposed.In the filtering process,the sequential process framework and the displacement offset method are employed to deal with the pseudo-measurements with strong nonlinearity.Furthermore,for maneuvering target tracking problems with implicit constraints which is possible in practical applications,a maneuvering target tracking method with implicit constraints is proposed accordingly.Simulation results demonstrate that the proposed circular trajectory constraint target tracking methods are effective to utilize the implicit constraint information to enhance estimation accuracy.4.For target tracking problems with a destination constraint imposed by proportional navigation(PN),constraint models and corresponding constrained tracking methods with a destination constraint imposed by proportional navigation in three-dimensional space are proposed.Based on the state augmentation method,destination constraint models corresponding to three representative PN laws: pure PN,true PN and generalized PN are derived,including cases with exact or noisy destination information and cases where the navigation constant and the bias angle are unknown in practical applications.According to the proportional navigation destination constraint models,pseudo-measurements are constructed and incorporated into the tracking system,resulting in a series of constrained target tracking methods with PN laws.Simulation results demonstrate that the proposed destination constraint target tracking methods with PN laws are effective to utilize the destination constraint information to enhance tracking accuracy.