Observer Design for Structure from Motion using Concurrent Learning

In this paper, a concurrent learning based observer for a perspective dynamical system (PDS) is developed. The PDS is a widely used model for estimating the depth of the feature point from a sequence of camera images. Building on the current progress of concurrent learning (CL) for parameter estimation in adaptive control, a state observer is developed for a PDS model where the inverse depth appears as a time-varying parameter in the dynamics. Using the data-recorded over a sliding time window in the near past, information about the recent depth values is used in a CL term and an observer is developed. A Lyapunov-based stability analysis is carried out to prove the uniformly ultimately bounded (UUB) stability of the observer. Comparisons in simulations are presented with the existing observers in terms of convergence, and error statistics. Comparisons reveal that CL improves the convergence and accuracy of the presented observer.