Navigation-Compatible Hybrid Quantum Accelerometer Using a Kalman Filter

Abstract

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 *

Phase shift in atom interferometers: Corrections for nonquadratic potentials and finite-duration laser pulses

“…Note that in D 2 [φ L ] the terms constant and linear in t disappear so −D 2 [φ L ] = αT 2 while, since z(t) and p(t) are linear in z and p in Eqs. (11,12), then 2z m (t) = z u (t) + z l (t) so…”

“…In the case of the Earth's gradient (γ ≃ 3 × 10 −6 s −2 ) and present day interferometers (T ≃ 1 s), we have 2T √ γ ≪ 1; Eqs. (11,12) can then be expanded in series up to the second order in √ γt and, keeping only terms at most linear in γ, one obtains a simpler approximate expression for δ(t)…”

“…Assuming ideal, rectangular pulses, it is simple to obtain a closed form expression for φ 2 from Eqs. (9,11,12). Here we report only an approximate expression using Eq.…”

“…The increasing ability to control individual quantum systems and their evolution makes it feasible to observe quantum interference over trajectories with very large separation in momentum [2,3] and space [4]. The resulting high sensitivity and the exquisite control of systematic effects are at the basis of the growing number of applications in AI, ranging from tests of general relativity [5,6], measurement of fundamental constants [7,8], search for new physics [9,10], to more applied contexts like inertial navigation [11].…”

Multiport atom interferometry for inertial sensing

“…We confirm experimentally the increase in sensitivity due to quadrature phase detection in the presence of large phase uncertainty, and demonstrate suppression of systematic phases on a single shot basis.Cold atom interferometers have demonstrated extremely high sensitivity as inertial sensors measuring gravity [1][2][3], gravity gradients [4][5][6][7][8], accelerations and rotations [9][10][11][12][13][14][15][16][17]. In addition to precision measurements of physical constants [18][19][20][21][22], tests of general relativity [23][24][25][26][27][28], searches for dark energy [29,30], and gravitational wave detection [31,32], they are promising candidates as on-board inertial measurement units [10,[33][34][35] and as mobile gravimeters for geodesic studies or subterranean exploration [36][37][38][39][40][41]. These prospects provide strong motivation for improving the robustness of atom interferometers while maintaining high phase sensitivity and accuracy under field conditions, such as strong vibrations and drifts in the thermal and magnetic environment.At...…”