Long-term inertial navigation is currently limited by the bias drifts of gyroscopes and accelerometers. 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.Inertial navigation systems determine the position of a moving vehicle by continuously measuring its acceleration and rotation rate, and subsequently integrating the equations of motion [1]. These systems are limited by slow drifts of the biases inherent to their inertial sensors, which ultimately lead to large speed and position errors after integration. Currently, the long-term bias stability of navigation-grade accelerometers is on the order of 10 µg-which, in the absence of aiding sensors such as satellite navigation systems, leads to horizontal position oscillations of 60 m at the characteristic Schuler period of 84.4 minutes [1,2].Since their first demonstration in the early 1990s, atom interferometers (AIs) have proven to be excellent absolute inertial sensors-having been exploited as ultra-high sensitivity instruments for fundamental tests of physics [3][4][5][6][7][8], and as state-of-the-art gravimeters with accuracies in the range of 1 − 10 ng achieved both in laboratories [9][10][11][12][13][14] and with compact transportable systems [15][16][17][18][19]. As a result, they have been proposed for the next generation of inertial navigation systems [20][21][22][23]. However, cold-atom-based sensors generally possess a small bandwidth, and suffer from low repetition rates (with the exceptions of Refs. [24,25]) and dead times during which no inertial measurements can be made. In comparison, mechanical accelerometers exhibit broad bandwidths compatible with navigation applications [26], but are afflicted by long-term bias and scale factor drifts. These two types of sensors can thus be hybridized [27] in order to benefit from the best of both worlds-in strong analogy with the strategy employed in atomic clocks [28].Here, we use correlations between an AI and a classical accelerometer to track the bias of the latter, and we present an approach based on a non-linear Kalman *

Robust and accurate acceleration tracking remains a challenge in many fields. For geophysics and economic geology, precise gravity mapping requires onboard sensors combined with accurate positioning and navigation systems. Cold atom–based quantum inertial sensors can potentially provide these high-precision instruments. However, current scalar instruments require precise alignment with vector quantities. Here, we present the first hybrid three-axis accelerometer exploiting the quantum advantage to measure the full acceleration vector by combining three orthogonal atom interferometer measurements with a classical navigation-grade accelerometer triad. Its ultralow bias permits tracking the acceleration vector over long time scales, yielding a 50-fold improvement in stability (6 × 10 −8 g ) over our classical accelerometers. We record the acceleration vector at a high data rate (1 kHz), with absolute magnitude accuracy below 10 μ g , and pointing accuracy of 4 μrad. This paves the way toward future strapdown applications with quantum sensors and highlights their potential as future inertial navigation units.