Tracking with Non-Linear Dynamic Models

In a linear dynamic model with linear measurements, there is always only one peak in the posterior; very small non-linearities in dynamic models can lead to a substantial number of peaks. As a result, it can be very difficult to represent the posterior: it may be necessary to represent all the peaks to be able to compute the mean or the covariance. We discuss these difficulties in section 2.1. There is no general solution to this problem, but there is one mechanism which has proven useful in some practical problems: we present this, rather technical, mechanism in section 2.2, and show some applications in section 2.3. It is quite typical of vision applications that there is some doubt about what measurements to track — for example, a Kalman filter tracker following a series of corner points may need to decide which image measurement corresponds to which track. A poor solution to this problem may lead to apparently good tracks that bear no relationship to the underlying motions. In section ??, we discuss how to attach measurements to tracks.