Research On Constrained Filtering Algorithm

The target state estimation and fusion method as the core part of the target tracking technology, has attracted more and more people’s attention, has been widely used in the military field and civilian field, for example: information monitoring, traffic control, intelligent navigation, medical diagnosis etc.. However, in the practical process of state estimation, people always confined to the processing of the raw data, and did not to use some of the known priori information, if we can establish the constraint conditions with the priori information, and apply the efficient constraints to the filtering process, so we can get more accurate state estimation results, and make the filtering results tend to the real values. Therefore, research on filtering algorithm under the constraint conditions is necessary.This thesis supported by National Natural Science Foundation “Multiple Target Tracking Method Based on Random Finite Set Theory Some Problems Research”(NO. 61201118) researches on the constrained filtering algorithm, According to the constraint condition of system state, the constrained problem can be divided into two kinds, namely the linear constraint problem and nonlinear constraint problem. People have made a lot of research on the linear constrained filtering, which is easier to solve. Therefore, this article focuses on researching the nonlinear constrained filtering. O n the basis of the existing constrained filtering algorithm, two new filtering algorithms are proposed. The main work in this thesis includes:(1) Iterative shrinkage filters with nonlinear state constraintsThis paper aims at the problem of nonlinear filter with state constraints. Under the assumption that the state vector is subject to the Gaussian distribution, we present a class of iterative shrinkage nonlinear state constraints filt er. The method combines with the cubature Kalman filter(CKF), quadrature Kalman filter(QKF), central divided differences Kalman filter(CDKF), unscented Kalman filter(UKF), respectively, and uses several different numerical methods to approximate the integrals appeared in the process. Consequently, some implemental algorithms are obtained and can be used to solve the problem of nonlinear state constraints. In the process of implementation, in order to diminish the influence of base point error in the filtering results, we apply a series of noises to the nonlinear state constraints function by using the iterative style, as a result, the variance gradually converge in the measurement update step, which improves the precision of the state estimation. The experimental results show the proposed algorithms have higher precision and lower time complexity compared with the other available algorithms. Besides, they can work well without solving the Jacobian matrix or the Hessian matrix.(2) Nonlinear inequality state constrained filter based on sequential quadra tic programmingAiming at the problem of nonlinear inequality filter with state constraints, we present an iterated unscented Kalman filter based on sequential quadratic programming optimization method. The method combines with the idea of optimization met hod, and uses sequential quadratic programming method to solve the optimum nonlinear inequality constrained problem. In iterations, quadratic programming sub-problems are employed to determine a descent direction, and these steps are repeated until the solution of original problem is obtained. In order to guarantee the convergence of the algorithm, we balance between the objective function and the inequality constraints. Furthermore, a positive definite matrix is used to approximate the Hessian matrix to reduce the complexity. The experimental results show that the new algorithm can effectively enhance the accuracy with a low time complexity.