Sigma-Point Kalman Filter with State Constraints

A Kalman filter is introduced which can take into consideration physical constraints as well as ones given in planning. The paper will focus explicitly on the non-linearity in the equations and special features of the stochastic variables. The substance of the paper is based on insights gained from the sigma-point (SP) Kalman filter where linearisation is achieved by transforming the deterministically chosen SP through non-linear equations. Two procedures are introduced for considering constraints. The first one is based on the displacement of the SP (heuristic procedure), the second is based on the projection onto the constraint surface (analytical procedure).