277 citations · 564 across the 48 of their papers we have counts for
11 papers · 1 filter
Divergence metrics in the study of Markov and hidden Markov processes
Jin Won Kim, Amirhossein Taghvaei, Prashant G. Mehta
This paper is divided into two parts. The first part reviews the formulae for f-divergences in the study of continuous-time Markov processes and explores their applications in area…
A Dual Characterization of the Stability of the Wonham Filter
Jin Won Kim, Prashant G. Mehta
This paper revisits the classical question of the stability of the nonlinear Wonham filter. The novel contributions of this paper are two-fold: (i) definition of the stabilizabilit…
The Conditional Poincaré Inequality for Filter Stability
Jin Won Kim, Prashant G. Mehta, Sean Meyn
This paper is concerned with the problem of nonlinear filter stability of ergodic Markov processes. The main contribution is the conditional Poincaré inequality (PI), which is show…
On the Lyapunov Foster criterion and Poincaré inequality for Reversible Markov Chains
Amirhossein Taghvaei, Prashant G. Mehta
This paper presents an elementary proof of stochastic stability of a discrete-time reversible Markov chain starting from a Foster-Lyapunov drift condition. Besides its relative sim…
A Dual Characterization of Observability for Stochastic Systems
Jin W. Kim, Prashant G. Mehta
This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process a…
Error Analysis of the Stochastic Linear Feedback Particle Filter
Amirhossein Taghvaei, Prashant G. Mehta
This paper is concerned with the convergence and long-term stability analysis of the feedback particle filter (FPF) algorithm. The FPF is an interacting system of particles whe…
An Approach to Duality in Nonlinear Filtering
Jin W. Kim, Amirhossein Taghvaei, Prashant G. Mehta +1
This paper revisits the question of duality between minimum variance estimation and optimal control first described for the linear Gaussian case in the celebrated paper of Kalman a…
Error Analysis for the Linear Feedback Particle Filter
Amirhossein Taghvaei, Prashant G. Mehta
This paper is concerned with the convergence and the error analysis for the feedback particle filter (FPF) algorithm. The FPF is a controlled interacting particle system where the…
Gain Function Approximation in the Feedback Particle Filter
Amirhossein Taghvaei, Prashant G. Mehta
This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation inv…
An Optimal Transport Formulation of the Linear Feedback Particle Filter
Amirhossein Taghvaei, Prashant G. Mehta
Feedback particle filter (FPF) is an algorithm to numerically approximate the solution of the nonlinear filtering problem in continuous time. The algorithm implements a feedback co…
Probabilistic Data Association-Feedback Particle Filter for Multiple Target Tracking Applications
Tao Yang, Prashant G. Mehta
This paper is concerned with the problem of tracking single or multiple targets with multiple non-target specific observations (measurements). For such filtering problems with data…