Reduced Order Observer for Structure from Motion using Concurrent Learning

In this paper, a concurrent learning based reduced order observer for a perspective dynamical system (PDS) is developed. The PDS is a widely used model for estimating the depth of a feature point from a sequence of camera images. Leveraging the recent advances in concurrent learning for adaptive control, the depth 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. Simulations demonstrate the convergence using mean absolute percentage error (MAPE) and root mean squared error (RMSE) metrics in the presence and absence of persistence of excitation (PE).