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2003
Ballantyne, David, Wiersma, Jonathan, Kouritzin, Michael, Hailes, Jarett, Long, Hongwei
A hybrid weighted interacting particle filter, the selectively resampling particle filter (SERP), is used to detect and track multiple ships maneuvering in a region of water. The ship trajectories exhibit nonlinear dynamics and interact in a nonlinear manner such that the ships do not collide....

A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter
Download1994
Heunis, A.J., Kouritzin, Michael
Consider the following random ordinary differential equation: X˙ϵ(τ)=F(Xϵ(τ),τ/ϵ,ω)subject toXϵ(0)=x0, where {F(x,t,ω),t≥0} are stochastic processes indexed by x in Rd, and the dependence on x is sufficiently regular to ensure that the equation has a unique solution Xϵ(τ,ω) over the interval...

2000
Ballantyne, David, Chan, Hubert, Kouritzin, Michael
Particle approximations are used to track a maneuvering signal given only a noisy, corrupted sequence of observations, as are encountered in target tracking and surveillance. The signal exhibits nonlinearities that preclude the optimal use of a Kalman filter. It obeys a stochastic differential...

2004
Zhao, Xingqiu, Long, Hongwei, McCrosky, Jesse, Kim, Surrey, Kouritzin, Michael
In this paper, we discuss multitarget tracking for a submarine model based on incomplete observations. The submarine model is a weakly interacting stochastic dynamic system with several submarines in the underlying region. Observations are obtained at discrete times from a number of sonobuoys...

2014
Kouritzin, Michael, Ren, Y.X.
Let ℓ be Lebesgue measure and X=(Xt,t≥0;Pμ) be a supercritical, superstable process corresponding to the operator −(−Δ)α/2u+βu−ηu2 on Rd with constants β,η>0 and α∈(0,2]. Put View the MathML source, which for each smallθ is an a.s. convergent complexvalued martingale with limit View the MathML...

20140605
The classical particle filter, introduced in 1993, approximates the normalized filter directly. It has two defiencies, over resampling and the inability to distinguish models, the former of which was overcome but the later is fundamental. Conversely, the weighted particle filter, motivated by the...

2004
McCrosky, Jesse, Kouritzin, Michael, Blount, Douglas
A hybrid weighted/interacting particle filter, the selectively resampling particle (SERP) filter, is used to detect and track an unknown number of independent targets on a onedimensional \"racetrack\" domain. The targets evolve in a nonlinear manner. The observations model a sensor positioned...

1997
Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order,εdependent parabolic partial differential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the...

2002
Kouritzin, Michael, Bauer, Will, Kim, Surrey
Predicting the future state of a random dynamic signal based on corrupted, distorted, and partial observations is vital for proper realtime control of a system that includes time delay. Motivated by problems from Acoustic Positioning Research Inc., we consider the continual automated...

2002
In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a wellestablished method of approximating reactiondiffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger...