Study On Target Tracking Based On Moving Horizon Estimation

The basic problem of target tracking is how to estimate the optimal target states accurately from the measurements, which plays an important role in the civil and military application fields. Target tracking is also called state optimal estimation. In the actual tracking problem, there are various constraints on the states and external disturbance of the moving target inevitably, which are taken by the characters of physical and dynamics of the system or some other reasons. Although the traditional tracking methods, such as Kalman filter for linear system and extended Kalman filter for nonlinear system, can track the moving target quickly, they may obtain some inaccurate or even impractical estimated states for not considering the constraints in the actual system. Therefore, this paper studies the moving horizon estimation (MHE) approach and its application on target tracking with practical constraints.As the constraints and nonlinear characteristics widely exist in target tracking, this paper analyzes the advantage and characteristics of moving horizon estimation, and discusses how to design reasonable inequality constraints to reduce the requirement of precise tracking model and adapt to the laws of physics. The paper also discusses the methods to design and approximate the arrival cost and the conditions to guarantee the stability of estimator.This paper studies the moving horizon estimation approach and its application on target tracking from simple linear situation to complex nonlinear situation. For constrained linear target tracking, applying Kalman filter covariance iteration to approximate the arrival cost of constrained linear system, it can transform the full horizon optimal estimation into limited ones. Simulation results show that, for considering constraints in optimization problem, moving horizon estimation has higher estimated precision than Kalman filter. In order to deal with constrained nonlinear tracking problem, linearization and extended Kalman filter covariance updating approach are applied to the moving horizon estimation to approximate the arrival cost. Another, the unscented transformation and a set of selected sigma points are employed to compute the covariance and then approximate the arrival cost. The selection procedure for the sigma points is the same as used for unscented Kalman filter if the constraints are inactive. However, some modifications are made to satisfy the state variable constraints when the constraints are active. Based on unscented Kalman filter, moving horizon estimation can avoid the linearization of the model and degree the model error. Simulation results show that, moving horizon estimation based on unscented Kalman filter performs slightly better than the commonly used based on extended Kalman filter.In moving horizon estimation, the problem of target tracking is transformed into constrained optimal problem, so that the estimation is more accurate and the solution is more complex. However, for calculating the approximate arrival cost in finite horizon to reduce the computational burden, moving horizon estimation has a good prospect in the off-line processing and real-time application.