约束条件下的滤波算法研究

发布时间：2018-07-23 13:28

【摘要】：目标状态估计及其融合滤波方法作为目标跟踪技术的核心部分,一直以来备受人们的关注,在军事领域和民用领域都得到了广泛应用,例如:情报监控、交通管制、智能导航、医学诊断等。然而,在状态估计的实际过程中,人们总是将研究重点局限于原始数据,并没有使用一些已知的先验信息,如果我们能用先验信息建立约束条件,并将有效的约束应用于滤波过程,那么我们就能提高算法的滤波精度,从而能够使得滤波后所得到的估计值更加趋近于系统的真实值。因此,针对约束条件下的滤波算法的研究是非常必要的。本课题来源于国家自然科学基金项目“基于随机有限集理论的多目标跟踪方法若干问题研究”(NO.61201118),针对约束条件下的滤波算法进行了分析研究,根据系统状态所受到的约束条件可将约束问题分为两种,即线性约束滤波问题和非线性约束滤波问题,线性约束条件下的滤波问题与非线性约束条件下的滤波问题相比较更为容易解决,人们已经提出了很多有效的解决方法处理该问题。所以,本文着重于研究非线性约束条件下的滤波问题,并在已有受约束滤波算法的基础上给出了两种新的滤波算法解决约束问题。实验结果表明,新算法在处理约束问题时,能够有效提高状态估计精度,算法时间复杂度较低。本文的主要工作内容归纳如下:(1)迭代收缩非线性状态约束滤波非线性状态约束滤波是实际中经常遇到的问题,针对该问题,在状态向量的高斯假定下,提出了一类迭代收缩非线性状态约束滤波方法。该方法结合容积卡尔曼滤波、求积分卡尔曼滤波、中心差分卡尔曼滤波和不敏卡尔曼滤波思想,分别采用几种不同的数值方法对积分进行近似,获得了几种解决非线性状态约束的实现算法。在实现过程中,为了减小基点误差对于滤波结果的影响,采用迭代的方法,给非线性状态约束函数施加一系列噪声,从而在量测更新过程中使得经过滤波后的方差逐步收敛,改善了滤波估计结果。实验结果表明,该类方法的几种实现算法滤波精度较高,时间复杂度较为适中,无需求解雅可比矩阵或黑森矩阵。(2)基于序列二次规划的非线性不等式状态约束滤波算法针对非线性不等式状态约束滤波问题,提出了一种基于序列二次规划的迭代不敏卡尔曼滤波算法。该算法在迭代不敏卡尔曼滤波的基础上结合了优化算法的思想,采用序列二次规划优化法求解非线性不等式约束条件下的最优解。在实验验证中,将每一迭代问题看做一个二次规划子问题,其下降方向通过求解该子问题来确定,重复上述步骤即可获得约束问题的最优解。为了保证算法具有较强的收敛性,利用效益函数最小化目标函数,并将其与不等式约束条件进行权衡。此外,利用正定矩阵近似海森矩阵,以减少算法所花费的时间。实验结果表明,新算法在处理非线性不等式状态约束滤波问题时,能够有效地提高状态估计精度,获得较高的滤波精度,算法时间复杂较低。
[Abstract]:Target state estimation and fusion filtering, as the core part of target tracking technology, have been paid much attention to and widely used in military and civil fields, such as intelligence monitoring, traffic control, intelligent navigation, medical diagnosis, etc. However, in the actual process of state estimation, people always have to do a lot of research. The point is limited to the original data and does not use some known prior information. If we can use prior information to establish constraints and apply the effective constraints to the filtering process, then we can improve the filtering accuracy of the algorithm, thus making the estimated value of the filter closer to the true value of the system. Therefore, the needle is more close to the true value of the system. Therefore, the needle is more close to the true value of the system. It is necessary to study the filtering algorithm under the constraint conditions. This topic comes from the research on several problems of the multi-objective tracking method based on the stochastic finite set theory (NO.61201118), which is based on the National Natural Science Foundation of China. The filtering algorithm under the constraint conditions is analyzed and studied, and the constraint conditions are based on the state of the system. The constraint problems can be divided into two kinds, namely, linear constrained filtering and nonlinear constrained filtering. The filtering problem under linear constraints is more easily solved than the filtering problem under the nonlinear constraints. Many effective solutions have been put forward to deal with the problem. So, this paper focuses on the study of the nonlinear contract. Two new filtering algorithms are given on the basis of existing constrained filtering algorithms to solve the problem of constraints. Experimental results show that the new algorithm can effectively improve the precision of state estimation and the time complexity of the algorithm is low. The main work contents of this paper are as follows: (1) iterative shrinkage Nonlinear state constraint filtering nonlinear state constraint filtering is a problem often encountered in practice. Under the Gauss assumption of state vector, a class of iterative shrinkage nonlinear state constraint filtering method is proposed. This method combines with volume Calman filter, integral Calman filter, central differential Calman filter and unsensitive. Several different numerical methods are used to approximate the integral, and several algorithms to solve the nonlinear state constraints are obtained by using several different numerical methods. In order to reduce the influence of the base point error to the filtering results, an iterative method is used to apply a series of noise to the non linear state constraint function in the process of implementation, so that the quantity of the non linear state constraint function is applied. In the process of updating, the filtered variance is gradually converged and the filter estimation results are improved. The experimental results show that the filtering accuracy is higher, the time complexity is moderate, the Jacobi matrix or the Hessen matrix is not required. (2) the nonlinear inequality state constraint filtering based on the sequence column two times programming. In this algorithm, an iterative unsensitive Calman filtering algorithm based on sequence two order programming is proposed for nonlinear inequality constraint filtering problem. The algorithm combines the idea of optimization algorithm on the basis of iterative unsensitive Calman filtering and the optimal solution of nonlinear inequality constraints is solved by sequential two programming optimization. In experimental verification, each iteration problem is considered as a two time programming subproblem. Its descent direction is determined by solving the subproblem, and the optimal solution of the constraint problem can be obtained by repeating the above steps. In order to ensure the convergence of the algorithm, the goal function is minimized by the benefit function, and the constraint conditions are entered into the inequality constraints. In addition, the positive definite matrix is used to approximate the hahson matrix to reduce the time spent in the algorithm. The experimental results show that the new algorithm can effectively improve the precision of state estimation, obtain higher filtering precision, and have a low time complexity when dealing with the nonlinear inequality state constraint filtering problem.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713

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