Numerical Methods For Stochastic Filter Equations And The Research Of Micro-object Tracking

For multi-objects tracking, stochastic filter equations can be established to deal with the problem that the state and measurement information is disturbed by the noise and clutter. Stochastic filter equations also have created new insights into a whole series of research perspectives, including physics, economics, biological dynamics and stochastic control science. Therefore, stochastic filter equations is very important in theory and real application.In this dissertation, two main issues of stochastic filter equations are investigated:the numerical solution of continuous time stochastic filter equations, and the application of discrete time stochastic filter equations for the micro-object tracking.The exponential Euler method is extended to semi-linear stochastic filter equation.The convergence order of the exponential Euler method is 0.5. The mean-square stability and its stability region of Euler-Maruyama method are investigated by stochastic analysis theory. The mean-square stability results show that the exponential Euler method has better mean-square stability than EM method.For the stochastic partial differential filter equations(SPDEs) driven by a multiplicative noise(Q-Wiener process), the approximation in space is a projection onto a finite dimensional space by Galerkin method and in time by the stochastic exponential integrator scheme. The truncation number of Galerkin method is different from the truncation number of the driving noise process which is realized by a series expansion. Convergence results in Lpfor the discretization approximation scheme are proved. In experiment, the proposed scheme requires less random variables and more computational savings than the implicit Euler method.For the micro-object tracking problem, the state evolution equation and the measurement equation are established through the discrete time stochastic filter theory. An automated tracking framework is proposed to extract the trajectories of micro-objects.This framework uses a probability hypothesis density particle filtering(PF-PHD) tracker to estimate the target state and obtain the probability density distribution of the state. An ellipse shape model is presented to describe the micro-objects in case that the point-like targets usually lost the shape and structural information. In the target measurement model,we propose a novel likelihood function model based on the shape matrix to improve the accuracy of the state estimation.In the state association part of PF-PHD tracker, the estimated PHD are decomposed into sub-PHDs, which is relevant to each measurement collected. A two-level PHD subdecomposition algorithm is proposed to implement tracking continuity and obtain the dynamic trajectories of micro-objects. The target motion can be tracked by analyzing the association intensity of PHD components at sequential two frames. An orientational and positional constraint model is proposed to refine the state association algorithm for the crossing trajectories.