Robust Kalman filtering with constraints: a case study for integrated navigation

When certain constraints in the kinematic state parameters of a multi-sensor navigation system exist, they should be taken into account for the improvement of the positioning accuracy and reliability. In this paper, two types of robust estimators for integrated and two stages of Kalman filtering with state parameter constraints are derived based on the generalized maximum likelihood Lagrangian condition, respectively. The properties of the two estimators are discussed. The changes of the state estimates and their covariance matrices as well as the residual vector caused by the constraints are derived and analyzed. It is shown by a simulated example that the precision of the state estimates provided by the Kalman filtering with constraints is better than that provided by the Kalman filtering without considering the state parameter constraints; and the robust Kalman filtering with constraints further improves the reliability and robustness of the state estimates.