Accuracy Improvement by Boundary Conditions for Inertial Navigation

The term inertial navigation is often automatically associated with the term initial value problem. However, there are many applications where it is possible to end up with a boundary value problem (BVP) as well. We show that in case of a BVP, the finite element method that incorporates boundary conditions can be efficiently used to compute position and velocity estimates not prone to accumulation of errors. For further accuracy enhancements, a method of combining inertial measurements with additional constraints is proposed. This way, we can model sensor errors, known to limit the accuracy of the system. The capabilities of the proposed methods are demonstrated with real-life examples.