A method of reactive zoom control from uncertainty in tracking

The tuning of a constant velocity Kalman filter, used for tracking by a camera fitted with a variable focal-length lens, is shown to be preserved under a scale change in process noise if accompanied by an inverse scaling in the focal length, provided the image measurement error is of fixed size in image coordinates. Based on this observation, a practical method of zoom control has been built by setting an upper limit on the probability that the innovation (and hence fixation error) exceeds the image half-width. The innovation covariance matrix used to determine the innovation limit is derived over two timescales, which enables a rapid zooming out response and slower zooming in. Experimental simulations are presented, before results are given from a video-rate implementation using a camera with two motorized orientation axes and fitted with a computer-controlled zoom lens. The delays in the feedback loops, comprising image capture delay, platform response lag and zoom lens response lag, are carefully calibrated by fitting to their frequency responses. It is found that the cumulative uncertainty in delay gives rise to an image error which is part constant and part proportional to focal length, resulting in a beneficial adaptation of the filter.