A Linear- and Linear-Matrix-Inequality-Constrained Extended Kalman Filter

This study proposes a method for state estimation of nonlinear systems that incorporates linear- and linear-matrix-inequalities as constraints on the state estimate. Rewriting the standard maximum likelihood objective function used to derive the Kalman filter allows the Kalman gain to be found by solving a constrained optimization problem with a linear objective function subject to a linear-matrix-inequality constraint. In this formulation, additional state-estimate constraints are incorporated into the optimization problem as linear- and linear-matrix-inequality constraints. This methodology is applied in the multiplicative extended Kalman filter (MEKF) framework for three-dimensional position and attitude estimation, and is validated on a simulation of a mobile robot translating and rotating in a constrained domain space. Results are presented and compared to those for the unconstrained MEKF.