Comparison and optimisation of hybridization algorithms for onboard classical and quantum accelerometers

TL;DR

The paper tackles the challenge of obtaining continuous, bias-free acceleration measurements by hybridizing a quantum accelerometer based on atom interferometry with a classical accelerometer. It compares two onboard algorithms: Algo I, which directly extracts QA phase to iteratively estimate the CA's bias $b$ and scale factor $\eta$, and Algo II, a three-measurement fringe-tracking approach that uses phase modulation to jointly update $b$ and $\eta$ (and related terms) without requiring separate $C$ and $P_0$ inputs. Through synthetic data and an airborne Greenland campaign, the study shows that Algo I offers faster convergence under well-known parameters, while Algo II provides robustness to parameter errors; optimizing additional sensitivity coefficients further improves linearity and stability, especially in strapdown scenarios with rotation noise. The results indicate significant improvements in the QA–CA correlation and reductions in bias estimation error, with practical implications for airborne gravity measurements and future strapdown inertial navigation systems using quantum sensors, including the ability to compensate Coriolis and other rotation-induced effects.

Abstract

We study two hybridization algorithms used for the combination of a quantum inertial sensor based on atom interferometry with a classical inertial sensor for onboard acceleration measurements. The first is based on the direct extraction of the interferometer phase, and was previously used in seaborne and airborne gravity measurement campaigns. The second is based on the combination of three consecutive measurements and was originally developed to increase the measurement range of the quantum sensor beyond its linear range. After comparing their performances using synthetic data, we implement them on acceleration data collected in a recent airborne campaign and evaluate the bias and the scale factor error of the classical sensor. We then extend their scope to the dynamical evaluation of other key measurement parameters (e.g. alignment errors). We demonstrate an improvement in the correlation between the two accelerometers' measurements and a significant reduction of the error in the estimation of the bias of the classical sensor.

Figures (8)

• Figure 1: The Allan standard deviations of bias estimates for Algo I (in red) and Algo II (in blue).
• Figure 2: Impact of errors in the contrast $C$ and in the offset $P_0$ used in the algorithms on the stability of bias estimates with no detection noise. The standard deviation of the uncorrelated acceleration noise $\sigma_{\delta_a}$ is 0 (solid line), $1.8\times 10^{-5}~\text{m} \text{s}^2$ (dotted line) and $3.6\times 10^{-5}~\text{m} \text{s}^2$ (dashed line)
• Figure 3: Impact of the detection noise on the stability of the bias estimates. The standard deviation of the uncorrelated acceleration noise $\sigma_{\delta_a}$ is 0 (solid line), $1.8\times 10^{-5}~\text{m} \text{s}^2$ (dotted line) and $3.6\times 10^{-5}~\text{m}$.
• Figure 4: Extracted bias (a) and relative scale factor (b) corrections of the classical accelerometer, for the two different hybridization algorithms.
• Figure 5: Bias and sensitivity coefficients when all optimized.