A Robust Iterative Kalman Filter Based On Implicit Measurement Equations Robuster iterativer Kalman-Filter mit implizierten Beobachtungsgleichungen

In the field of robotics and computer vision recursive estimation of time dependent processes is one of the key tasks. Usually Kalman filter based techniques are used, which rely on explicit model functions, that directly and explicitly describe the effect of the parameters on the observations. However, some problems naturally result in implicit constraints between the observations and the parameters, for instance all those resulting in homogeneous equation systems. By implicit we mean, that the constraints are given by equations, that are not easily solvable for the observation vector. We derive an iterative extended Kalman filter framework based on implicit measurement equations. In a wide field of applications the possibility to use implicit constraints simplifies the process of specifying suitable measurement equations. As an extension we introduce a robustification technique similar to [17] and [8], which allows the presented estimation scheme to cope with outliers. Furthermore we will present results for the application of the proposed framework to the structure-from-motion task in the case of an image sequence acquired by an airborne vehicle.