This paper presents a new design approach to nonlinear observers for Itï¿oe stochastic nonlinear systems with guaranteed stability. A stochastic contraction lemma is presented which is used to analyze incremental stability of the observer. A bound on the mean-squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity. The observer design is based on a non-unique state-dependent coefficient (SDC) form, which parametrizes the nonlinearity in an extended linear form. The observer gain synthesis algorithm, called linear matrix inequality statedependent algebraic Riccati equation (LMI-SDARE), is presented. The LMI-SDARE uses a convex combination of multiple SDC parametrizations. An optimization problem with statedependent linear matrix inequality (SDLMI) constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances. Two variations of LMI-SDARE algorithm are also proposed. One of them named convex state-dependent Riccati equation (CSDRE) uses a chosen convex combination of multiple SDC matrices; and the other named Fixed-SDARE uses constant SDC matrices that are pre-computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre-computed by a convex LMI optimization problem. A connection between contraction analysis and L2 gain of the nonlinear system is established in the presence of noise and disturbances. Results of simulation show superiority of the LMI-SDARE algorithm to the extended Kalman filter (EKF) and state-dependent differential Riccati equation (SDDRE) filter.

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We propose a method of estimating the motion of a monocular camera looking at moving objects and their range. Unlike the previous studies where the camera and object motion should be constrained in estimating structure and motion (SaM) of moving objects, the proposed method do not require those constraints even though only a monocular camera is used. By first arranging the SaM dynamics in terms of the measurable states, we design robust nonlinear observers in a sequential way for both static (stationary) and dynamic (moving) objects. Through the combination of these estimates obtained by nonlinear observers, the reconstruction of the 3-D structure of the dynamic objects can be achieved using just 2-D images of a monocular camera. Simulations are performed in the case of changing camera and object velocities, such that the advantages of the proposed method can be clearly demonstrated.

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This paper presents a vision-based localization and mapping algorithm developed for an unmanned aerial vehicle (UAV) that can operate in a riverine environment. Our algorithm estimates the three-dimensional positions of point features along a river and the pose of the UAV. By detecting features surrounding a river and the corresponding reflections on the water's surface, we can exploit multiple-view geometry to enhance the observability of the estimation system. We use a robot-centric mapping framework to further improve the observability of the estimation system while reducing the computational burden. We analyze the performance of the proposed algorithm with numerical simulations and demonstrate its effectiveness through experiments with data from Crystal Lake Park in Urbana, Illinois. We also draw a comparison to existing approaches. Our experimental platform is equipped with a lightweight monocular camera, an inertial measurement unit, a magnetometer, an altimeter, and an onboard computer. To our knowledge, this is the first result that exploits the reflections of features in a riverine environment for localization and mapping. C 2015 Wiley Periodicals, Inc.

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