A Switched Systems Framework for Guaranteed Convergence of Image-Based Observers with Intermittent Measurements

Switched systems theory is used to analyze the stability of image-based observers for three-dimensional localization of objects in a scene in the presence of intermittent measurements due to occlusions, feature tracking losses, or a limited camera field of view, for example. Generally, observers or filters that are exponentially stable under persistent measurement availability may have unbounded error growth under intermittent measurement loss, even while providing seemingly accurate state estimates. By constructing a framework that utilizes a state predictor during periods when measurements are not available, a class of image-based observers is shown to be exponentially convergent in the presence of intermittent measurements if an average dwell time, and a total unmeasurability time, condition is satisfied. The conditions are developed in a general form, applicable to any observer that is exponentially convergent assuming persistent visibility, and utilizes object motion knowledge to reduce the amount of time measurements must be available to maintain convergence guarantees. Based on the stability results, simulations are provided to show improved performance compared to a zero-order hold approach, where state estimates are held constant when measurements are not available. Experimental results are also included to verify the theoretical results, to demonstrate applicability of the developed observer and predictor design, and to compare against a typical approach using an extended Kalman filter.