Norm- and linear-inequality-constrained state estimation: An LMI approach

This paper proposes a method for state estimation that incorporates norm- and linear-inequality constraints using Linear Matrix Inequalities (LMIs). This is accomplished by adopting a prediction-correction filter form and calculating the observer gain matrix by solving a convex optimization problem with LMI constraints where the state constraints are expressed as LMIs. The state constraints considered in this study include norm and linear inequalities. Simulation results are included to assess the performance of the proposed filter in a scenario involving a mobile robot moving within a constrained area taking range and bearing measurements of known landmarks. The filter's performance is compared with a traditional EKF.