The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independe...The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.展开更多
We investigate the possibility for two-mode probability density function （PDF） to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown...We investigate the possibility for two-mode probability density function （PDF） to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state twoor higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.展开更多
经典序贯蒙特卡罗概率假设密度(Sequential Mote Carlo Probability Hypothesis Density,SMC-PHD)滤波中,将目标状态转移密度函数做为建议密度函数,没有利用当前观测信息,导致大部分预测粒子状态偏离目标真实状态,粒子退化严重.针对上...经典序贯蒙特卡罗概率假设密度(Sequential Mote Carlo Probability Hypothesis Density,SMC-PHD)滤波中,将目标状态转移密度函数做为建议密度函数,没有利用当前观测信息,导致大部分预测粒子状态偏离目标真实状态,粒子退化严重.针对上述问题,提出利用均方根容积卡尔曼滤波产生建议密度函数,对其进行采样得到预测粒子状态,该方法有严格理论基础,能有效减轻SMC-PHD滤波中的粒子退化,且适用性很强.仿真实验对比了该算法、经典SMC-PHD和基于无迹卡尔曼的SMC-PHD算法的跟踪性能,验证了该方法无论对势估计还是对目标状态估计的精度都优于其他两种算法.展开更多
基金the General Research Fund of the University of Kansas.
文摘The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.
基金Project supported by the Korean Research Foundation of the Korea Government (MEST) (Grant No. 2009-0073081)
文摘We investigate the possibility for two-mode probability density function （PDF） to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state twoor higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.
文摘经典序贯蒙特卡罗概率假设密度(Sequential Mote Carlo Probability Hypothesis Density,SMC-PHD)滤波中,将目标状态转移密度函数做为建议密度函数,没有利用当前观测信息,导致大部分预测粒子状态偏离目标真实状态,粒子退化严重.针对上述问题,提出利用均方根容积卡尔曼滤波产生建议密度函数,对其进行采样得到预测粒子状态,该方法有严格理论基础,能有效减轻SMC-PHD滤波中的粒子退化,且适用性很强.仿真实验对比了该算法、经典SMC-PHD和基于无迹卡尔曼的SMC-PHD算法的跟踪性能,验证了该方法无论对势估计还是对目标状态估计的精度都优于其他两种算法.
