| Kalman filters and smoothers form an important class of algorithms used for inference on noisy dynamical systems, and are an industry standard in a wide range of applications, including space exploration, missile guidance systems, general tracking and navigation, and weather prediction. A classical topic in control theory, statistics, and signal processing, Kalman filtering methods can also be studied using optimization techniques, and this approach has led to efficient and accurate algorithms for nonlinear systems and models with inequality constraints.;We build on optimization and statistical perspectives to develop a range of new applications and algorithms, including smoothers robust to measurement errors, smoothers for systems with singular covariance, trend smoothers, and smoothers with state-dependent covariance models. We provide global convergence theory for these algorithms, and we exploit linear algebraic structure in the applications to ensure that the computational effort scales linearly with the number of time points.;We use a similar approach to develop a robust Bundle Adjustment algorithm, which is a well known method for visual reconstruction currently used by NASA Ames to make Digital Elevation Models (DEM). The new algorithm is robust against mistakes in feature matching, and exploits sparse linear algebraic structure in the application to keep the problem computationally tractable. |
