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 *