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The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “multiplicative update” and “covariance correction step” are conceived in a natural way. Concepts from manifold theory are used to define the moments of a distribution in a manifold. In particular, the mean and the covariance matrix of a distribution of unit quaternions are defined. Non-linear versions of the Kalman filter are developed applying these definitions. A simulation is designed to test the accuracy of the developed algorithms. The results of the simulation are analyzed and the best attitude estimator is selected according to the adopted performance metric.

This paper presents a framework for processing, modeling, and fusing underwater sensor signals to provide a reliable perception for underwater localization in structured environments. Submerged sensory information is often affected by diverse sources of uncertainty that can deteriorate the positioning and tracking. By adopting uncertain modeling and multi-sensor fusion techniques, the framework can maintain a coherent representation of the environment, filtering outliers, inconsistencies in sequential observations, and useless information for positioning purposes. We evaluate the framework using cameras and range sensors for modeling uncertain features that represent the environment around the vehicle. We locate the underwater vehicle using a Sequential Monte Carlo (SMC) method initialized from the GPS location obtained on the surface. The experimental results show that the framework provides a reliable environment representation during the underwater navigation to the localization system in real-world scenarios. Besides, they evaluate the improvement of localization compared to the position estimation using reliable dead-reckoning systems.

Abstract-An orientation estimation algorithm is presented. This algorithm is based on the Extended Kalman Filter, and uses quaternions as the orientation descriptor. For the filter update, we use measurements from an Inertial Measurement Unit (IMU). The IMU consists in a triaxial angular rate sensor, and an also triaxial accelerometer.Quaternions describing orientations live in the unit sphere of R 4 . Knowing that this space is a manifold, we can apply some basic concepts regarding these mathematical objects, and an algorithm that reminds the also called "Multiplicative Extended Kalman Filter" arises in a natural way.The algorithm is tested in a simulated experiment, and in a real one.

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