Quadrature Kalman filter with equality constraints

Abstract

If constraints can be used effectively in the filtering, the accuracy of state estimation will be improved further. The paper aims at the estimation of the nonlinear system with constraints, and a new method to deal with the equality constraints in the nonlinear system is proposed. The main idea is that we employ the projection approach in the quadrature Kalman filtering. Every quadrature point is projected on the constrained subspace, and the nonlinear transformation is more exact than before. The new method has better error performance than that of extended Kalman filter (EKF) with constraints. Target tracking example is presented to illustrate the effectiveness of the new method.