Mixed state estimation for a linear Gaussian Markov model

— We consider a discrete-time dynamical system with Boolean and continuous states, with the continuous state propagating linearly in the continuous and Boolean state variables, and an additive Gaussian process noise, and where each Boolean state component follows a simple Markov chain. This model, which can be considered a hybrid or jump-linear system with very special form, or a standard linear Gauss-Markov dynamical system driven by a Boolean Markov process, arises in dynamic fault detection, in which each Boolean state component represents a fault that can occur. We address the problem of estimating the state, given Gaussian noise corrupted linear measurements. Computing the exact maximum a posteriori (MAP) estimate entails solving a mixed integer quadratic program, which is computationally difficult in general, so we propose an approximate MAP scheme, based on a convex relaxation, followed by rounding and (possibly) further local optimization. Our method has a complexity that gr...

• Type: Conference
• Year: 2008
• Where: ICARCV
• Authors: Argyris Zymnis, Stephen P. Boyd, Dimitry M. Gorinevsky
• Keywords: Boolean State, Boolean State Component, Boolean State Variables, ICARCV 2008, Robotics