Concept and evaluation of a hybridization scheme for atom interferometers and inertial measurements units

authored by: Benjamin Tennstedt
supervised by: Steffen Schön
Abstract: By measuring accelerations and angular rates with the help of inertial measurement units (IMU), attitude, velocity and position of a mobile platform in motion can be computed. The integration of errors inherent to the signals leads to a drift of the solution over time. In order to reduce this drift while keeping the advantages of an autonomous measurement principle, quantum sensors are a promising concept. In experiments with cold atom interferometers (CAI), great sensitivities and long term stability for the measurement of accelerations and angular rates have been demonstrated. This technology uses wave-particle characteristics of atoms, which are manipulated by a series of light pulses in order to realize different interferometer schemes. In the Mach-Zehnder pulse pattern, the internal states are split, reversed and recombined, making the setup sensitive to accelerations as well as angular rates. Accurate measurement with this technology is limited to a small bandwidth of signals. The preparation of the atomic wave packet needs time in which the assembly is not able to measure. Additionally, the sinusoidal observation equation of the CAI is generally ambiguous. For those reasons, hybridization with high rate, large bandwidth conventional inertial sensors is the proposed scheme for mobile applications. Up to now, this combination has mainly been explored for stationary experiments with accelerometers only. A full quantum inertial navigation system (QINS) demands inclusion of gyroscope measurement as well as experiments in dynamic applications to validate the models and to further understand the behavior of CAI. The final step toward such a QINS consequently has not yet been taken. This thesis pursues an engineering approach to model CAI and QINS. Using methods from the navigation and physics community, a kinematic model for the center of mass of the atom wave packet is developed and applied, the velocity and position of the atoms computed, and the phase shift ambiguity solved. This allows to integrate gyroscope measurements in the formulation, as well as lever arm and misalignment between the sensor frame of the CAI and the IMU, enabling a parametrization of the often unknown transfer function between the systems. The error state kinematics of the wave packets furthermore allow an assessment of the limits of the CAI and the hybridization in the light of dynamic applications. With the help of an extended Kalman filter (EKF), the biases of the classical IMU are estimated. It can be shown that the acceleration biases are always observable, while the observability of the gyroscope biases demands a displacement or velocity of the atoms perpendicular to the sensitive axis. The requirements to observe state vector augmentations like misalignments and lever arms are discussed. The stability analysis results in a steady state formulation of the QINS. Under stationary conditions, the performance gain of the QINS is evaluated. It can be shown that the QINS navigation solution mainly profits from the long term stability of CAI. An additional focus of this study is the optimal configuration of CAI and IMU, supporting future system integrators in designing high performance QINS. Different designs are presented and evaluated, one centered on a complete IMU with high accuracy CAI support, yielding the best overall performance with positioning errors of less than ten meters after one hour of free inertial navigation, the other one centered on the CAI with high rate accelerometer support for applications under stationary conditions which further enhances the sensitivity to accelerations by an order of magnitude. The methods are demonstrated experimentally based on a static, one dimensional CAI data set. Furthermore, noise models for the application in the EKF are derived. The remaining methods under dynamic conditions are verified with the help of dedicated simulations.
Organisation(s): Institute of Geodesy
Leibniz University Hannover
Type: Doctoral thesis
No. of pages: 164
Publication date: 2024
Publication status: Published
Electronic version(s): https://doi.org/10.15488/18303 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@phdthesis{e0dd5d499f7149be98db24965b573ff2,
title = "Concept and evaluation of a hybridization scheme for atom interferometers and inertial measurements units",
abstract = "By measuring accelerations and angular rates with the help of inertial measurement units (IMU), attitude, velocity and position of a mobile platform in motion can be computed. The integration of errors inherent to the signals leads to a drift of the solution over time. In order to reduce this drift while keeping the advantages of an autonomous measurement principle, quantum sensors are a promising concept. In experiments with cold atom interferometers (CAI), great sensitivities and long term stability for the measurement of accelerations and angular rates have been demonstrated. This technology uses wave-particle characteristics of atoms, which are manipulated by a series of light pulses in order to realize different interferometer schemes. In the Mach-Zehnder pulse pattern, the internal states are split, reversed and recombined, making the setup sensitive to accelerations as well as angular rates. Accurate measurement with this technology is limited to a small bandwidth of signals. The preparation of the atomic wave packet needs time in which the assembly is not able to measure. Additionally, the sinusoidal observation equation of the CAI is generally ambiguous. For those reasons, hybridization with high rate, large bandwidth conventional inertial sensors is the proposed scheme for mobile applications. Up to now, this combination has mainly been explored for stationary experiments with accelerometers only. A full quantum inertial navigation system (QINS) demands inclusion of gyroscope measurement as well as experiments in dynamic applications to validate the models and to further understand the behavior of CAI. The final step toward such a QINS consequently has not yet been taken. This thesis pursues an engineering approach to model CAI and QINS. Using methods from the navigation and physics community, a kinematic model for the center of mass of the atom wave packet is developed and applied, the velocity and position of the atoms computed, and the phase shift ambiguity solved. This allows to integrate gyroscope measurements in the formulation, as well as lever arm and misalignment between the sensor frame of the CAI and the IMU, enabling a parametrization of the often unknown transfer function between the systems. The error state kinematics of the wave packets furthermore allow an assessment of the limits of the CAI and the hybridization in the light of dynamic applications. With the help of an extended Kalman filter (EKF), the biases of the classical IMU are estimated. It can be shown that the acceleration biases are always observable, while the observability of the gyroscope biases demands a displacement or velocity of the atoms perpendicular to the sensitive axis. The requirements to observe state vector augmentations like misalignments and lever arms are discussed. The stability analysis results in a steady state formulation of the QINS. Under stationary conditions, the performance gain of the QINS is evaluated. It can be shown that the QINS navigation solution mainly profits from the long term stability of CAI. An additional focus of this study is the optimal configuration of CAI and IMU, supporting future system integrators in designing high performance QINS. Different designs are presented and evaluated, one centered on a complete IMU with high accuracy CAI support, yielding the best overall performance with positioning errors of less than ten meters after one hour of free inertial navigation, the other one centered on the CAI with high rate accelerometer support for applications under stationary conditions which further enhances the sensitivity to accelerations by an order of magnitude. The methods are demonstrated experimentally based on a static, one dimensional CAI data set. Furthermore, noise models for the application in the EKF are derived. The remaining methods under dynamic conditions are verified with the help of dedicated simulations.",
author = "Benjamin Tennstedt",
year = "2024",
doi = "10.15488/18303",
language = "English",
isbn = "9783769653595",
series = "Wissenschaftliche Arbeiten der Fachrichtung Geod{\"a}sie und Geoinformatik der Leibniz-Universit{\"a}t Hannover",
publisher = "Fachrichtung Geod{\"a}sie und Geoinformatik der Leibniz Universit{\"a}t Hannover",
school = "Leibniz University Hannover",
}