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NAVIGATION Journal of the Institute of Navigation

Atom Strapdown: Toward Integrated Quantum Inertial Navigation Systems

Benjamin Tennstedt, Ashwin Rajagopalan, Nicolai Ben Weddig, Sven Abend, Steffen Schön, Ernst Maria Rasel

Published Jan 1, 2023• 12 citations
Publisher

Abstract

Abstract We present an alternative technique for estimating the response of a cold atom interferometer (CAI). Using data from a conventional inertial measurement unit (IMU) and common strapdown terminology, the position of the atom wave packet is tracked in a newly introduced sensor frame, enabling hybridization of both systems in terms of acceleration and angular rate measurements. The sensor frame allows for an easier mathematical description of the CAI measurement and integration into higher-level navigation systems. The dynamic terms resulting from the transformation of the IMU frame into the CAI sensor frame are evaluated in simulations. The implementation of the method as a prediction model in an extended Kalman filter is explained and demonstrated in realistic simulations, showing improvements of over two orders of magnitude with respect to the conventional IMU strapdown solution. Finally, the implications of these findings for future hybrid quantum navigation systems are discussed.

DOI
10.33012/navi.604

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•Nov 23, 2023•0 citations
Abstract We present an alternative technique for estimating the response of a cold atom interferometer (CAI). Using data from a conventional inertial measurement unit (IMU) and common strapdown terminology, the position of the atom wave packet is tracked in a newly introduced sensor frame, enabling hybridization of both systems in terms of acceleration and angular rate measurements. The sensor frame allows for an easier mathematical description of the CAI measurement and integration into higher-level navigation systems. The dynamic terms resulting from the transformation of the IMU frame into the CAI sensor frame are evaluated in simulations. The implementation of the method as a prediction model in an extended Kalman filter is explained and demonstrated in realistic simulations, showing improvements of over two orders of magnitude with respect to the conventional IMU strapdown solution. Finally, the implications of these findings for future hybrid quantum navigation systems are discussed.
In this paper, an alternative technique to estimate the response of a cold atom interferometer (CAI) is presented. Using data of a conventional inertial measurement unit and the common strapdown terminology, the position of the atom wave packet is tracked in a newly introduced sensor frame. This enables a hybridisation of both systems. The sensor frame allows for an easier mathematical description of the interferometer measurement and makes integration into higher-level navigation systems possible. Equations for a hybrid IMU/CAI system with several arbitrarily placed sensor frames are stated, as well as a compressed Multi-Axis model, following current developments in chip scale atom interferometry. The atom strapdown is compared with another common hybridisation technique which utilizes convolution of accelerometer data with the interferometer response function. The comparison is supported by real data. The dynamic terms resulting from the transformation of the IMU frame into the sensor frame of the CAI are evaluated in simulations and further discussed. Finally, the implications of the findings for future hybrid quantum navigation systems are stated.
The recent development of the atom interferometer and its demonstration as an inertial sensor of acceleration and rotation rate augur a new generation of inertial navigation systems that would rival today's satellite navigation accuracy at the few-meter level. This paper reviews the principles of inertial measurement using the atom interferometer from a rudimentary viewpoint to illustrate the fundamentals and to highlight some of the potential shortcomings with a particular type, the cold-atom interferometer. One of these shortcomings is the fact that this interferometer requires a finite period of time during which the atoms are prepared (cooled) before they enter the interferometer and respond to its dynamics relative to an inertial frame. This lapse in the measurement duty cycle could be supplemented with very precise conventional inertial measurement units (IMUs), or eliminated with multiple, interleaved atom interferometers. Error analyses show that cold-atom interferometric IMUs that capture 50 percent of the dynamics must be coupled with conventional IMUs that are 50 times more accurate than typical navigation-grade units to sustain a horizontal position error of under 5 m (root mean square) after 1 h.
This work presents an approach to assess the quality requirements for classical inertial measurement units (IMU) used in conjunction with a cold atom interferometer (CAI) for application in a hybrid quantum inertial navigations system (QINS). Based on the steady state formulation of an extended Kalman filter used for the hybridization of CAI and IMU, a model for the sensitivity gain of the QINS over the classical IMU is developed. This sensitivity gain depends on the white noise density of the classical sensor, as well as the scale factor and the signal-to-noise ratio of the CAI. Using the example of a single hybridized accelerometer axis it can be shown that for each CAI setting, an optimal white noise density of the classical accelerometer exists for which the sensitivity gain of the QINS yields a maximum. The findings are applied to evaluate existing experimental assemblies.
Quantum technology have attracted strong interest in recent years thanks to its extreme sensitivity to inertial forces and its strong immunity to drifts compared to conventional mechanical sensors. This paper introduces cold atom sensors as six-axis inertial sensors from the engineering point of view. In order to highlight the potential of this technology as needed for inertial navigation, a strapdown closed-loop-simulation has been developed. Furthermore, we present an error model for quantum sensors that includes terms such as quantum shot noise and phase noise of the reference laser. Considering this inherent stochastic characteristics, we made also a comparison with other conventional inertial measurement units. The analysis shows that quantum sensors with the same sensitivity as of for static measuring local gravity can determine their position with accuracy of one-meter level even after one hour, while other quantum sensors with less sensitivity exhibit for the same duration an amplitude up to 1 km, similar to conventional sensors.
In this paper we present our progress towards the development of a complete cold-atom Inertial Measurement Unit (IMU). Our goal is to have a single atomic sensor that will alternatively measure each inertial component (3 accelerations and 3 rotations). Every atomic measurement will be hybridized with a set of classical inertial sensors. Hybridization enables to combine the advantages of both technologies and to provide accurate continuous measurements with high dynamic range, in the scope of onboard inertial navigation compatibility.
Classical inertial navigation systems integrate inertial measurements from triads of accelerometers and gyroscopes to determine their position, but the computed trajectory is typically limited by the intrinsic time-varying bias of these inertial sensors. In addition, the exploitation of quantum physics led to the development of matter-wave interferometers, sensitive to inertial effects due to the mass of the atoms. While they are free-falling, these atoms constitute a perfect inertial frame of reference and allow for an absolute measurement with outstanding accuracy and stability. Substantial technical developments have allowed bringing quantum gravimeters to the market, enabling static, long-term measurements. Nevertheless, the use of cold-atom sensors for navigation and positioning still requires addressing many scientific and technological challenges to be compatible with onboard applications such as compactness, measurement continuity and operation in the presence of strong vibrations and rotations.The Joint Laboratory iXAtom brings together the expertise of the Laboratoire de Photonique, Numérique et Nanosciences (LP2N) in matter-wave interferometry and the French technology company Exail, specialized in high-performance inertial navigation systems and industrial quantum sensors, with the aim of building a new generation of high-end inertial sensors through the hybridization of classical accelerometers and gyroscopes with quantum sensors based on matter-wave interferometry.After successfully building a multi-axis cold-atom interferometer measuring the three components of the acceleration vector with a static apparatus, this quantum inertial sensor has been fully hybridized with a triad of classical accelerometers, increasing the bandwidth and dynamic range without the usual limitation due to the bias drift of the mechanical accelerometers. Moreover, this hybridization technique features a real-time correction of the laser phase which allows retrieving the acceleration information out of atomic fringes scrambled by parasitic vibrations. As regards the rotations of the instrument throughout an interferometer, their compensation remains the next major issue to tackle for strapdown applications as they induce a drastic reduction of the atomic fringes’ visibility coupled to a scrambling of the interferometric phase shift.This thesis work focuses on the mitigation of the rotation-induced performance deterioration of the hybrid accelerometer. Through a theoretical investigation, a model for both the angular velocity-dependent decay of the fringes contrast and the systematic phase shift arising from the complex trajectory of the atomic cloud in the rotating frame of the interrogation laser is established. A real-time rotation compensation system, employing the measurement of the rotation rate with high-end fiber-optic gyroscopes to drive a piezo-actuated tip-tilt platform, has been implemented to stabilize the orientation of the interrogation laser in the external frame in order to preserve the contrast of the atomic interference pattern and extend the measurement range of the rotating atom interferometer. A rectification of the theoretical model accounting for the rotation of the laser as well as the hybridization with the classical accelerometers enables reconstructing the atomic fringes and retrieving the inertial measurement, paving the way for strapdown onboard hybrid accelerometry.