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This paper addresses the problem of estimating the attitude and angular velocity of a rigid object by exploiting its second order kinematic model. The approach is particularly useful in cases where angular velocity measurements are not available and the attitude and angular velocity of an object need to be estimated from accelerometers and magnetometers. We propose a novel sensor modality that uses multiple accelerometers to measure the angular acceleration of an object as well as using magnetometers to measure partial attitude. We extend the approach of equivariant observer design to second order attitude kinematics by demonstrating that the special Euclidean group acts as a symmetry group on the system considered. The observer design is based on the lifted kinematics and we prove almost global asymptotic stability and local uniform exponential stability of the estimation error. The performance of the observer is demonstrated in simulation.

Event cameras are ideally suited to capture High Dynamic Range (HDR) visual information without blur but provide poor imaging capability for static or slowly varying scenes. Conversely, conventional image sensors measure absolute intensity of slowly changing scenes effectively but do poorly on HDR or quickly changing scenes. In this paper, we present an asynchronous linear filter architecture, fusing event and frame camera data, for HDR video reconstruction and spatial convolution that exploits the advantages of both sensor modalities. The key idea is the introduction of a state that directly encodes the integrated or convolved image information and that is updated asynchronously as each event or each frame arrives from the camera. The state can be read-off as-often-as and whenever required to feed into subsequent vision modules for real-time robotic systems. Our experimental results are evaluated on both publicly available datasets with challenging lighting conditions and fast motions, along with a new dataset with HDR reference that we provide. The proposed AKF pipeline outperforms other state-of-the-art methods in both absolute intensity error (69.4% reduction) and image similarity indexes (average 35.5% improvement). We also demonstrate the integration of image convolution with linear spatial kernels Gaussian, Sobel, and Laplacian as an application of our architecture.

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Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g., for regular operation) and transient response (e.g., for fast initialization and reset) of such filters are of crucial importance in guaranteeing robust operation of autonomous systems.This paper introduces a new generic formulation for a gyroscope aided attitude estimator using N direction measurements including both body-frame and reference-frame direction type measurements. The approach is based on an integrated state formulation that incorporates navigation, extrinsic calibration for all direction sensors, and gyroscope bias states in a single equivariant geometric structure. This newly proposed symmetry allows modular addition of different direction measurements and their extrinsic calibration while maintaining the ability to include bias states in the same symmetry. The subsequently proposed filter-based estimator using this symmetry noticeably improves the transient response, and the asymptotic bias and extrinsic calibration estimation compared to state-of-the-art approaches. The estimator is verified in statistically representative simulations and is tested in real-world experiments.