Know What You Don't Know: Consistency in Sliding Window Filtering with Unobservable States Applied to Visual-Inertial SLAM (Extended Version)

Estimation algorithms, such as the sliding window filter, produce an estimate and uncertainty of desired states. This task becomes challenging when the problem involves unobservable states. In these situations, it is critical for the algorithm to ``know what it doesn't know'', meaning that it must maintain the unobservable states as unobservable during algorithm deployment. This letter presents general requirements for maintaining consistency in sliding window filters involving unobservable states. The value of these requirements for designing navigation solutions is experimentally shown within the context of visual-inertial SLAM making use of IMU preintegration.