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Long-term inertial navigation is currently limited by the bias drifts of gyroscopes and accelerometers and ultra-stable cold-atom interferometers offer a promising alternative for the next generation of high-end navigation systems. Here, we present an experimental setup and an algorithm hybridizing a stable matter-wave interferometer with a classical accelerometer. We use correlations between the quantum and classical devices to track the bias drift of the latter and form a hybrid sensor. We apply the Kalman filter formalism to obtain an optimal estimate of the bias and simulate experimentally a harsh environment representative of that encountered in mobile sensing applications. We show that our method is more precise and robust than traditional sine-fitting methods. The resulting sensor exhibits a 400 Hz bandwidth and reaches a stability of 10 ng after 11 h of integration.
Many state estimation and control algorithms require knowledge of how probability distributions propagate through dynamical systems. However, despite hybrid dynamical systems becoming increasingly important in many fields, there has been little work
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