Motion-dependent estimation of a spatial vector field with multiple vehicles

We consider a spatial vector field estimation problem with vehicles modeled as unicycles. The vector field is assumed to affect the motion of the vehicles in an additive fashion. We investigate whether the position information of the vehicles can be used to simultaneously estimate the unknown field parameters and the heading information of the vehicles. Starting with a single vehicle case, we design a stable nonlinear observer and reveal a persistence of excitation (PE) condition on the vehicle's motion that guarantees the convergence of the field parameter estimates and the heading estimates almost globally. We next extend the observer for multiple vehicles with a strongly connected communication topology and provide a PE condition to ensure filter convergence. The effectiveness of the designed observers is demonstrated with simulations of vehicles estimating a rotational field.