A closed-loop output error approach for physics-informed trajectory inference using online data

While autonomous systems can be used for a variety of beneficial applications, they can also be used for malicious intentions and it is mandatory to disrupt them before they act. So, an accurate trajectory inference algorithm is required for monitoring purposes that allows to take appropriate countermeasures. This article presents a closed-loop output error approach for trajectory inference of a class of linear systems. The approach combines the main advantages of state estimation and parameter identification algorithms in a complementary fashion using online data and an estimated model, which is constructed by the state and parameter estimates, that inform about the physics of the system to infer the followed noise-free trajectory. Exact model matching and estimation error cases are analyzed. A composite update rule based on a least-squares rule is also proposed to improve robustness and parameter and state convergence. The stability and convergence of the proposed approaches are assessed via the Lyapunov stability theory under the fulfilment of a persistent excitation condition. Simulation studies are carried out to validate the proposed approaches.