随机滤波方程数值解法及显微目标跟踪研究

发布时间：2019-03-31 19:34

【摘要】：在多目标跟踪中,随机滤波方程可以用来建立模型,解决多目标状态和观测信息受到噪音和杂波干扰的问题。随机滤波方程不仅在多目标跟踪领域中占有非常重要的地位,而且与物理学、经济学、生物动力学、随机控制等领域的实际问题都密切相关。因此,随机滤波方程具有很重要的理论研究和实际应用意义。本文主要研究了随机滤波方程的两大方面问题:连续时间随机滤波方程的状态过程数值求解,以及离散的随机滤波方程在显微目标跟踪中的应用。针对半线性随机滤波状态方程,应用指数Euler方法对其进行求解,证明该方法求解半线性方程时的收敛阶为0.5,同时利用随机分析理论,研究该数值格式的均方渐进稳定性以及均方稳定区域,并与已有的Euler-Maruyama方法进行比较,指数Euler方法具有更好的均方稳定性。针对连续时间的随机偏微分滤波方程,考虑乘性Q-Wiener过程驱动的噪音情况,通过Galerkin方法对空间离散,随机指数积分方法对时间离散,并且噪音的截断数目与Galerkin的截断数目不一样,得到了解的Lp收敛性。本文数值解法可以采用较少的随机变量来近似噪音,比隐式Euler计算效率高。对于显微视频序列目标跟踪问题,通过离散时间的随机滤波理论建立显微目标的状态进化方程和测量方程,采用粒子概率假设密度滤波方法对显微目标的状态过程进行估计,得到滤波方程解状态的概率密度分布,建立自动的跟踪框架。针对点目标导致形状特征信息丢失的情况,将显微目标用椭圆形状建模,并且构造基于形变矩阵的似然函数模型,提高随机滤波方程的状态估计精确度。在显微目标的状态关联轨迹形成部分,按照测量信息将估计目标的概率假设密度在粒子权值空间进行分解,并且构建概率假设密度率滤波的双层分解状态关联算法,根据相邻时刻估计目标的概率密度关联强度,对显微目标的状态估计进行关联,得到显微目标的动态运动轨迹。针对显微目标轨迹交叉时候的复杂场景,提出了位置和方位角约束模型,对交叉轨迹的状态关联算法进行优化。
[Abstract]:In multi-target tracking, the random filtering equation can be used to build a model to solve the problem that multi-target state and observation information are disturbed by noise and clutter. The stochastic filtering equation not only plays a very important role in the field of multi-target tracking, but also is closely related to the practical problems in the fields of physics, economics, biodynamics, stochastic control and so on. Therefore, the stochastic filtering equation has important theoretical and practical significance. In this paper, we mainly study two aspects of stochastic filtering equation: the numerical solution of the state process of the continuous-time stochastic filtering equation, and the application of discrete stochastic filtering equation in the tracking of microscopic targets. For the semilinear stochastic filtering equation of state, the exponential Euler method is used to solve it. It is proved that the convergence order of this method is 0.5 when solving the semilinear equation. At the same time, the stochastic analysis theory is used. The asymptotic mean square stability and the mean square stability region of the numerical scheme are studied. Compared with the existing Euler-Maruyama method, the exponential Euler method has better mean square stability. For the stochastic partial differential filtering equation with continuous time, the noise driven by multiplicative Q-Wiener process is considered. The space is discretized by the Galerkin method, and the time is discrete by the random exponential integral method. Moreover, the number of truncation of noise is different from that of Galerkin, and the Lp convergence of the solution is obtained. The numerical method in this paper can use fewer random variables to approximate the noise, which is more efficient than the implicit Euler method. For the target tracking problem of microscopic video sequence, the state evolution equation and measurement equation of microscopic target are established by discrete time stochastic filtering theory, and the state process of microscopic target is estimated by particle probability hypothesis density filtering method. The probability density distribution of the solution state of the filter equation is obtained and an automatic tracking framework is established. In order to improve the accuracy of state estimation of stochastic filtering equation, the microscopic target is modeled by ellipse shape, and the likelihood function model based on deformation matrix is constructed to improve the accuracy of the state estimation of stochastic filtering equation in order to solve the problem of loss of information of shape feature caused by point target. The probability hypothetical density of the estimated target is decomposed in the particle weight space according to the measurement information in the formation part of the state association trajectory of the microscopic target, and a two-level decomposed state association algorithm based on probability hypothesis density rate filtering is constructed. Based on the estimation of the probability density correlation intensity of the target at the adjacent time, the state estimation of the microscopic target is correlated, and the dynamic trajectory of the microscopic target is obtained. A position and azimuth constraint model is proposed to optimize the state association algorithm for the complex scene when the trajectory of micro-objects is crossed.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O241.8

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