Pitfalls of Constraint Kalman Filtering

In this work, the impact of state constraints in Kalman filters is analyzed. Such constraints are commonly used in integrated navigation systems to augment sensor measurements, for example, through zero-velocity updates in personal navigation systems. Constraints may be linear or nonlinear and may be posed as either equality or inequality constraints. It is shown that linear inequality constraints can introduce bias into the state estimate that is not reflected in the estimation error covariance matrix. Furthermore, for nonlinear equality and inequality constraints, projection-based methods that have been used in the design of integrated navigation systems can yield inconsistent estimates, in which the computed state estimation error covariance matrix is a poor proxy for the actual estimation error statistics.