变分非线性滤波方法研究及其在水下潜器组合导航中的应用
发布时间：2018-07-25 20:38
【摘要】：基于贝叶斯估计原理的滤波器具有算法实现简单、滤波精度高、收敛性好等优点,正逐渐成为当前及未来非线性估计理论研究热点和重点之一。本文围绕水下潜器组合导航系统对状态估计器的应用需求,系统开展变分非线性滤波方法研究,论文的主要研究工作归纳如下:针对水下潜器组合导航的特点,建立其状态估计模型,并通过前向科尔莫格洛夫方程给出模型求解的弱解方程(即随机微分模型)。由此提出利用变分解法探索滤波器设计的思路。针对低维状态空间,尝试采用三次样条插值和双二次插值方法逼近一维系统和二维系统的状态概率解,并给出了理论推导和算法流程,分析了算法的计算复杂度与收敛速度。仿真实验采用非线性系统模型评价插值方法的性能,实验结果显示插值稳定性好,插值结果与目标曲线吻合度高,即插值方法可以很好的跟踪系统状态的变化,且与粒子滤波算法相比估计精度高,仿真结果验证了插值方法在低维状态空间中逼近随机微分模型概率解的可行性。针对高维状态空间系统,提出一种基于有限元递推估计的非线性滤波方法(Finite Element Method based Filter,FEMF),利用区域剖分和分片插值思想,理论推导出在函数空间中逼近导航状态概率解的过程,并对算法的收敛性、收敛速度和计算复杂度进行了数学分析。通过与扩展卡尔曼滤波、无迹卡尔曼滤波、粒子滤波算法的对比分析实验,表明有限元方法可以提高滤波估计精度。通过仿真验证该方法较粒子滤波算法具有更好的性能。针对FEMF方法实时性不高的问题,提出一种基于Yau-Yau Method与有限元相结合的混合滤波算法。该算法利用Yau-Yau Method估计形函数构造模型中的估值点,再用有限元估计系统状态概率解,有效地提高了算法的运行效率。该方法与FEMF方法相比极大地降低了算法计算量,并且编程实现较有限元方法简单。采用非线性非高斯系统模型进行仿真实验,仿真结果显示YY-FEMF方法更适合处理目标跟踪等对实时性及精度要求较高场合下的非线性非高斯状态估计问题。针对FEMF方法对插值函数的光滑性限制,提出一种基于Hermit基函数的投影滤波算法。该算法可以建立一个在整个连续空间具有高阶微分导数性质的插值函数,且在求解过程中不涉及矩阵和积分运算,极大地减少了计算量,提高滤波算法的实时性,并且从理论上分析了算法的收敛性。仿真实验中采用两个非线性模型,给出投影滤波与扩展卡尔曼滤波、无迹卡尔曼滤波、粒子滤波算法对比分析实验结果,表明算法有效地提高了滤波估计性能。论文最后选择惯性/地形、惯性/地磁两种应用于水下潜器的新兴组合导航模式进行滤波算法性能评估,仿真结果表明本文提出的方法均具有较好的输出精度和应用效果。
[Abstract]:The filter based on Bayesian estimation principle has the advantages of simple algorithm, high filtering accuracy and good convergence. It is becoming one of the hot and important points in the research of nonlinear estimation theory at present and in the future. In this paper, the research of variational nonlinear filtering method is carried out around the application demand of underwater vehicle integrated navigation system. The main research work of this paper is summarized as follows: aiming at the characteristics of underwater vehicle integrated navigation system, The state estimation model is established, and the weak solution equation (i.e. stochastic differential model) is given through the forward Kolmoglof equation. Therefore, the idea of using variable decomposition method to explore filter design is put forward. For low dimensional state space, cubic spline interpolation and biquadratic interpolation are used to approximate the state probabilistic solutions of one-dimensional and two-dimensional systems. The theoretical derivation and algorithm flow are given, and the computational complexity and convergence rate of the algorithm are analyzed. In the simulation experiment, nonlinear system model is used to evaluate the performance of the interpolation method. The experimental results show that the interpolation method has good stability and high consistency with the target curve, that is, the interpolation method can track the change of the system state. Compared with the particle filter algorithm, the estimation accuracy is higher. The simulation results show that the interpolation method is feasible to approximate the probabilistic solution of the stochastic differential model in the low-dimensional state space. For high dimensional state space system, a nonlinear filtering method (Finite Element Method based filter based on finite element recursive estimation (Finite Element Method based filter FEMF) is proposed. The process of approaching the probabilistic solution of navigation state in function space is derived theoretically by using the idea of region partition and piecewise interpolation. The convergence, convergence speed and computational complexity of the algorithm are analyzed. By comparing with extended Kalman filter, unscented Kalman filter and particle filter, it is shown that the finite element method can improve the estimation accuracy of the filter. Simulation results show that this method has better performance than particle filter algorithm. A hybrid filtering algorithm based on Yau-Yau Method and finite element method is proposed to solve the problem of low real-time performance of FEMF method. The algorithm uses Yau-Yau Method to estimate the estimated points in the model and finite element method to estimate the probabilistic solution of the system state. The efficiency of the algorithm is improved effectively. Compared with the FEMF method, this method greatly reduces the computational complexity of the algorithm, and the programming is simpler than the finite element method. The simulation results show that the YY-FEMF method is more suitable to deal with the nonlinear non-Gao Si state estimation problems with higher real-time and precision requirements such as target tracking by using the nonlinear non-Gao Si system model. A projection filtering algorithm based on Hermit basis function is proposed to limit the smoothness of interpolation function by FEMF method. This algorithm can establish an interpolation function with the property of high-order differential derivative in the whole continuous space, and the matrix and integral operation are not involved in the solution process, which greatly reduces the computational complexity and improves the real-time performance of the filtering algorithm. The convergence of the algorithm is analyzed theoretically. In the simulation experiment, two nonlinear models are used, the projection filter and the extended Kalman filter, the unscented Kalman filter and the particle filter algorithm are compared and the experimental results show that the algorithm can improve the performance of the filter estimation effectively. Finally, two new integrated navigation modes, inertial / topographic, inertial / geomagnetic, are selected to evaluate the performance of the filtering algorithm. The simulation results show that the proposed methods have good output accuracy and application effect.
【学位授予单位】：哈尔滨工程大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：U666.1;TN713;TN967.2
[Abstract]:The filter based on Bayesian estimation principle has the advantages of simple algorithm, high filtering accuracy and good convergence. It is becoming one of the hot and important points in the research of nonlinear estimation theory at present and in the future. In this paper, the research of variational nonlinear filtering method is carried out around the application demand of underwater vehicle integrated navigation system. The main research work of this paper is summarized as follows: aiming at the characteristics of underwater vehicle integrated navigation system, The state estimation model is established, and the weak solution equation (i.e. stochastic differential model) is given through the forward Kolmoglof equation. Therefore, the idea of using variable decomposition method to explore filter design is put forward. For low dimensional state space, cubic spline interpolation and biquadratic interpolation are used to approximate the state probabilistic solutions of one-dimensional and two-dimensional systems. The theoretical derivation and algorithm flow are given, and the computational complexity and convergence rate of the algorithm are analyzed. In the simulation experiment, nonlinear system model is used to evaluate the performance of the interpolation method. The experimental results show that the interpolation method has good stability and high consistency with the target curve, that is, the interpolation method can track the change of the system state. Compared with the particle filter algorithm, the estimation accuracy is higher. The simulation results show that the interpolation method is feasible to approximate the probabilistic solution of the stochastic differential model in the low-dimensional state space. For high dimensional state space system, a nonlinear filtering method (Finite Element Method based filter based on finite element recursive estimation (Finite Element Method based filter FEMF) is proposed. The process of approaching the probabilistic solution of navigation state in function space is derived theoretically by using the idea of region partition and piecewise interpolation. The convergence, convergence speed and computational complexity of the algorithm are analyzed. By comparing with extended Kalman filter, unscented Kalman filter and particle filter, it is shown that the finite element method can improve the estimation accuracy of the filter. Simulation results show that this method has better performance than particle filter algorithm. A hybrid filtering algorithm based on Yau-Yau Method and finite element method is proposed to solve the problem of low real-time performance of FEMF method. The algorithm uses Yau-Yau Method to estimate the estimated points in the model and finite element method to estimate the probabilistic solution of the system state. The efficiency of the algorithm is improved effectively. Compared with the FEMF method, this method greatly reduces the computational complexity of the algorithm, and the programming is simpler than the finite element method. The simulation results show that the YY-FEMF method is more suitable to deal with the nonlinear non-Gao Si state estimation problems with higher real-time and precision requirements such as target tracking by using the nonlinear non-Gao Si system model. A projection filtering algorithm based on Hermit basis function is proposed to limit the smoothness of interpolation function by FEMF method. This algorithm can establish an interpolation function with the property of high-order differential derivative in the whole continuous space, and the matrix and integral operation are not involved in the solution process, which greatly reduces the computational complexity and improves the real-time performance of the filtering algorithm. The convergence of the algorithm is analyzed theoretically. In the simulation experiment, two nonlinear models are used, the projection filter and the extended Kalman filter, the unscented Kalman filter and the particle filter algorithm are compared and the experimental results show that the algorithm can improve the performance of the filter estimation effectively. Finally, two new integrated navigation modes, inertial / topographic, inertial / geomagnetic, are selected to evaluate the performance of the filtering algorithm. The simulation results show that the proposed methods have good output accuracy and application effect.
【学位授予单位】：哈尔滨工程大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：U666.1;TN713;TN967.2
【相似文献】
相关期刊论文 前10条
1 张元林,郑南宁,袁泽剑;一种改进的图像自适应非线性滤波方法[J];西安交通大学学报;2004年02期
2 李俊生;图像非线性滤波技术的研究[J];常州工学院学报;2005年02期
3 鹿传国;冯新喜;孔云波;张迪;;几种非线性滤波只测角跟踪性能评估[J];弹箭与制导学报;2011年04期
4 冯驰;杜云明;;一种高效的非线性滤波技术[J];应用科技;2007年04期
5 赵静;黄晋英;王夙U，
本文编号：2145016
本文链接：https://www.wllwen.com/kejilunwen/wltx/2145016.html
