Analytical Observability Analysis of INS with Vehicle Constraints

Vehicle constraints have been gaining increased popularity as a means to mitigate drift of Inertial Navigation Systems in GNSS deprived settings. While useful, such constraints cannot compensate for the drift of all state variables in the navigation solution. To study which variables are affected, empirical analyses under typical scenarios are commonly performed, however, no insight is provided into the inner effects amongst error states. Here we propose an analytical observability analysis which evaluates the contribution of vehicle constraint measurements to the solution and determines which error states or linear combination thereof are unobservable. Observability analysis has been mostly directed thus far at GPS/INS aiding. Here we fill this gap by deriving analytical terms for the unobservable subspace of the body velocity constraint, which is already utilized in urban driving scenarios. The resulting terms are verified via numerical degree of observability analyses.