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Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments

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Original languageEnglish
Title of host publication2025 IEEE/ION Position, Location and Navigation Symposium, PLANS 2025
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages68-79
Number of pages12
ISBN (electronic)9798331523176
ISBN (print)979-8-3315-2318-3
Publication statusPublished - 28 Apr 2025
Event2025 IEEE/ION Position, Location and Navigation Symposium: PLANS 2025 - Marriott Salt Lake Downtown City Creek, Salt Lake City, United States
Duration: 28 Apr 20251 May 2025

Abstract

An observability analysis of a Quantum Inertial Navigation System (QINS) is presented for multiple realistic dynamic scenarios. It is performed on an Error State Extended Kalman Filter (ESEKF), which contains loosely coupled position and velocity measurements and 3-axis differential Cold Atom Interferometer (CAI) sensor measurements. The CAI-based measurements are hybridized with conventional IMU measurements, which results, in combination with position and velocity estimates, in a filter structure that contains position, velocity, acceleration and angular-rate based observations of the system at the same time. This in turn results in increased estimability and observability of the system, as well as lower position, velocity and attitude drift. As CAI-based measurements are only available for low measurement frequencies (i.e. 1-10 Hz), and are also only valid for low dynamics, the improvement in estimability has to be evaluated in realistic scenarios.To this end, realistic trajectories (low frequency deterministic movement) and realistic vibrations (high frequency correlated deterministic movements) are generated and combined for this analysis. With this data, a numerical observability analysis is performed for different combinations of GNSS-based and CAI-based measurements. Furthermore, differences in estimability and observability between vehicle types (cars, aircrafts, trains or ships) are shown.The results demonstrate that, as in a conventional GNSS-IMU sensor fusion, dynamics improve the observability of e.g. scale factors, lever arm components, or misalignment terms. The inclusion of misalignments in the ESEKF, orientation difference between the CAI and IMU, and the introduction of larger lever arms between the CAI and IMU leads to increased dependencies between different bias terms of the IMU, but also between components of the lever arm and misalignments at the CAI-IMU level. They are accentuated when larger vehicle-dependent oscillations are introduced in the system, which is demonstrated by an analysis of singular vectors of the Fisher Information Matrix (FIM).The article provides relevant information about tradeoffs between CAI-IMU model complexity and occurring dynamics, and it gives insights which components of the system need to be pre-calibrated, as their on the fly estimation may lead to an insufficiently resolved state, due to increased dependencies.

Keywords

    ESEKF, Kalman Filtering, Numerical analysis, Observability, Quantum inertial navigation, QUINS, Strapdown Navigation

ASJC Scopus subject areas

Cite this

Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments. / Weddig, Nicolai Ben; Tennstedt, Benjamin; Schon, Steffen.
2025 IEEE/ION Position, Location and Navigation Symposium, PLANS 2025. Institute of Electrical and Electronics Engineers Inc., 2025. p. 68-79.

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer review

Weddig, NB, Tennstedt, B & Schon, S 2025, Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments. in 2025 IEEE/ION Position, Location and Navigation Symposium, PLANS 2025. Institute of Electrical and Electronics Engineers Inc., pp. 68-79, 2025 IEEE/ION Position, Location and Navigation Symposium, Salt Lake City, Utah, United States, 28 Apr 2025. https://doi.org/10.1109/PLANS61210.2025.11028432
Weddig, N. B., Tennstedt, B., & Schon, S. (2025). Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments. In 2025 IEEE/ION Position, Location and Navigation Symposium, PLANS 2025 (pp. 68-79). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/PLANS61210.2025.11028432
Weddig NB, Tennstedt B, Schon S. Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments. In 2025 IEEE/ION Position, Location and Navigation Symposium, PLANS 2025. Institute of Electrical and Electronics Engineers Inc. 2025. p. 68-79 doi: 10.1109/PLANS61210.2025.11028432
Weddig, Nicolai Ben ; Tennstedt, Benjamin ; Schon, Steffen. / Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments. 2025 IEEE/ION Position, Location and Navigation Symposium, PLANS 2025. Institute of Electrical and Electronics Engineers Inc., 2025. pp. 68-79
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title = "Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments",
abstract = "An observability analysis of a Quantum Inertial Navigation System (QINS) is presented for multiple realistic dynamic scenarios. It is performed on an Error State Extended Kalman Filter (ESEKF), which contains loosely coupled position and velocity measurements and 3-axis differential Cold Atom Interferometer (CAI) sensor measurements. The CAI-based measurements are hybridized with conventional IMU measurements, which results, in combination with position and velocity estimates, in a filter structure that contains position, velocity, acceleration and angular-rate based observations of the system at the same time. This in turn results in increased estimability and observability of the system, as well as lower position, velocity and attitude drift. As CAI-based measurements are only available for low measurement frequencies (i.e. 1-10 Hz), and are also only valid for low dynamics, the improvement in estimability has to be evaluated in realistic scenarios.To this end, realistic trajectories (low frequency deterministic movement) and realistic vibrations (high frequency correlated deterministic movements) are generated and combined for this analysis. With this data, a numerical observability analysis is performed for different combinations of GNSS-based and CAI-based measurements. Furthermore, differences in estimability and observability between vehicle types (cars, aircrafts, trains or ships) are shown.The results demonstrate that, as in a conventional GNSS-IMU sensor fusion, dynamics improve the observability of e.g. scale factors, lever arm components, or misalignment terms. The inclusion of misalignments in the ESEKF, orientation difference between the CAI and IMU, and the introduction of larger lever arms between the CAI and IMU leads to increased dependencies between different bias terms of the IMU, but also between components of the lever arm and misalignments at the CAI-IMU level. They are accentuated when larger vehicle-dependent oscillations are introduced in the system, which is demonstrated by an analysis of singular vectors of the Fisher Information Matrix (FIM).The article provides relevant information about tradeoffs between CAI-IMU model complexity and occurring dynamics, and it gives insights which components of the system need to be pre-calibrated, as their on the fly estimation may lead to an insufficiently resolved state, due to increased dependencies.",
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T1 - Observability and Estimability Analysis of a Hybrid Error State CAI-IMU Filter for Different Dynamic Environments

AU - Weddig, Nicolai Ben

AU - Tennstedt, Benjamin

AU - Schon, Steffen

N1 - Publisher Copyright: © 2025 IEEE.

PY - 2025/4/28

Y1 - 2025/4/28

N2 - An observability analysis of a Quantum Inertial Navigation System (QINS) is presented for multiple realistic dynamic scenarios. It is performed on an Error State Extended Kalman Filter (ESEKF), which contains loosely coupled position and velocity measurements and 3-axis differential Cold Atom Interferometer (CAI) sensor measurements. The CAI-based measurements are hybridized with conventional IMU measurements, which results, in combination with position and velocity estimates, in a filter structure that contains position, velocity, acceleration and angular-rate based observations of the system at the same time. This in turn results in increased estimability and observability of the system, as well as lower position, velocity and attitude drift. As CAI-based measurements are only available for low measurement frequencies (i.e. 1-10 Hz), and are also only valid for low dynamics, the improvement in estimability has to be evaluated in realistic scenarios.To this end, realistic trajectories (low frequency deterministic movement) and realistic vibrations (high frequency correlated deterministic movements) are generated and combined for this analysis. With this data, a numerical observability analysis is performed for different combinations of GNSS-based and CAI-based measurements. Furthermore, differences in estimability and observability between vehicle types (cars, aircrafts, trains or ships) are shown.The results demonstrate that, as in a conventional GNSS-IMU sensor fusion, dynamics improve the observability of e.g. scale factors, lever arm components, or misalignment terms. The inclusion of misalignments in the ESEKF, orientation difference between the CAI and IMU, and the introduction of larger lever arms between the CAI and IMU leads to increased dependencies between different bias terms of the IMU, but also between components of the lever arm and misalignments at the CAI-IMU level. They are accentuated when larger vehicle-dependent oscillations are introduced in the system, which is demonstrated by an analysis of singular vectors of the Fisher Information Matrix (FIM).The article provides relevant information about tradeoffs between CAI-IMU model complexity and occurring dynamics, and it gives insights which components of the system need to be pre-calibrated, as their on the fly estimation may lead to an insufficiently resolved state, due to increased dependencies.

AB - An observability analysis of a Quantum Inertial Navigation System (QINS) is presented for multiple realistic dynamic scenarios. It is performed on an Error State Extended Kalman Filter (ESEKF), which contains loosely coupled position and velocity measurements and 3-axis differential Cold Atom Interferometer (CAI) sensor measurements. The CAI-based measurements are hybridized with conventional IMU measurements, which results, in combination with position and velocity estimates, in a filter structure that contains position, velocity, acceleration and angular-rate based observations of the system at the same time. This in turn results in increased estimability and observability of the system, as well as lower position, velocity and attitude drift. As CAI-based measurements are only available for low measurement frequencies (i.e. 1-10 Hz), and are also only valid for low dynamics, the improvement in estimability has to be evaluated in realistic scenarios.To this end, realistic trajectories (low frequency deterministic movement) and realistic vibrations (high frequency correlated deterministic movements) are generated and combined for this analysis. With this data, a numerical observability analysis is performed for different combinations of GNSS-based and CAI-based measurements. Furthermore, differences in estimability and observability between vehicle types (cars, aircrafts, trains or ships) are shown.The results demonstrate that, as in a conventional GNSS-IMU sensor fusion, dynamics improve the observability of e.g. scale factors, lever arm components, or misalignment terms. The inclusion of misalignments in the ESEKF, orientation difference between the CAI and IMU, and the introduction of larger lever arms between the CAI and IMU leads to increased dependencies between different bias terms of the IMU, but also between components of the lever arm and misalignments at the CAI-IMU level. They are accentuated when larger vehicle-dependent oscillations are introduced in the system, which is demonstrated by an analysis of singular vectors of the Fisher Information Matrix (FIM).The article provides relevant information about tradeoffs between CAI-IMU model complexity and occurring dynamics, and it gives insights which components of the system need to be pre-calibrated, as their on the fly estimation may lead to an insufficiently resolved state, due to increased dependencies.

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KW - Observability

KW - Quantum inertial navigation

KW - QUINS

KW - Strapdown Navigation

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BT - 2025 IEEE/ION Position, Location and Navigation Symposium, PLANS 2025

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2025 IEEE/ION Position, Location and Navigation Symposium

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ER -

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