Description
Information inference from noisy systems is a focus of interest of various research and engineering disciplines. In 1960, Rudolf E. Kalman published a paper on an optimal filtering technique for systems described by linear dynamics and measurement models whose noise statistics is Gaussian [1]. In particular, this so-called Kalman Filter constitutes a way to construct an estimator that allows one to optimally extract the signal encoded in the system dynamics while minimizing the average mean-squared-error, despite the dynamics and measurement all undergoing uncontrolled independent stochastic fluctuations. In opposition to previously known algorithms, Kalman Filters do not require a full history of all previous steps. Because of this the technique can be used for real-time data analysis.
In this work, we applied the described methods for magnetic field inference from an atomic sensor with optical read-out.
Such sensors are widely used in magnetometry both within and beyond the classical limit, achieving precision comparable to cryogenic methods. The linear Kalman Filter has been applied to such systems before [2, 3]. The usability of this technique is very limited though, as the magnetic field obeys a highly non-linear dynamics in most regimes. This suggests that using the Extended Kalman Filter as well as other non-linear Kalman Filtering techniques can greatly improve the estimator beyond the linear regime. In this work, we simulate an output of such a sensor and show that in fact the magnetic field can be successfully estimated in real-time with the non-linear methods.
[1] R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic
Engineering, vol.81, 1960.
[2] Ricardo Jiménez-Martínez et. all Signal Tracking Beyond the Time Resolution of an Atomic
Sensor by Kalman Filtering, PRL, vol. 120, 2018
[3] Jia Kong et. all Measurement-induced, spatially-extended entanglement in a hot, strongly-
interacting atomic system, Nature Communications vol. 11, Article number: 2415, 2020.
| Presenter name | Klaudia Dilcher |
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