Random forests for detecting weak signals and extracting physical information: a case study of magnetic navigation

TL;DR

This work tackles magnetic navigation in GPS-denied environments by extracting the Earth’s anomaly magnetic field from noisy cockpit signals and mapping it to the aircraft position. It introduces a random-forest framework that uses a carefully selected feature set and PCA to robustly filter weak signals, without relying on the Tolles-Lawson calibration. The approach achieves anomaly-field detection with RMSE around 1.9 nT and sub-10-meter positioning when fused with INS, often outperforming KNN and decision-tree baselines and sometimes negating the need for TL preprocessing. The results demonstrate a calibration-free, efficient signal-filtering strategy with broad applicability to weak-signal problems, and point to future directions in deep learning, transfer learning, and online adaptation within evolving signal environments.

Abstract

It was recently demonstrated that two machine-learning architectures, reservoir computing and time-delayed feed-forward neural networks, can be exploited for detecting the Earth's anomaly magnetic field immersed in overwhelming complex signals for magnetic navigation in a GPS-denied environment. The accuracy of the detected anomaly field corresponds to a positioning accuracy in the range of 10 to 40 meters. To increase the accuracy and reduce the uncertainty of weak signal detection as well as to directly obtain the position information, we exploit the machine-learning model of random forests that combines the output of multiple decision trees to give optimal values of the physical quantities of interest. In particular, from time-series data gathered from the cockpit of a flying airplane during various maneuvering stages, where strong background complex signals are caused by other elements of the Earth's magnetic field and the fields produced by the electronic systems in the cockpit, we demonstrate that the random-forest algorithm performs remarkably well in detecting the weak anomaly field and in filtering the position of the aircraft. With the aid of the conventional inertial navigation system, the positioning error can be reduced to less than 10 meters. We also find that, contrary to the conventional wisdom, the classic Tolles-Lawson model for calibrating and removing the magnetic field generated by the body of the aircraft is not necessary and may even be detrimental for the success of the random-forest method.

Figures (11)

• Figure 1: Configuration of magnetometers on the aircraft. The signals from the magnetometers inside the airplane contain strong complex signals produced by the various electronic devices. The signal from the magnetometer placed at the tail stinger is free from these overwhelming complex signals which, after the TL calibration, leads to the true magnetic anomaly field signal. The measurements from the other four magnetometers contain the anomaly field embedded in strong complex signals. The datasets are from test flights conducted by Sanders Geophysics Ltd. (SGL) near Ottawa, Canada.
• Figure 2: A schematic illustration of a random forest of decision trees. (a) A random forest and (b) a decision tree in the "forest." Prediction of the target variable of interest is achieved by taking the average of median of the predictions from all the trees in the forest.
• Figure 3: Correlation among the selected features in Table \ref{['tab:selfeat']}. The information from the correlation is used to prune the redundant features. High correlation among the features can produce "multicollinearity," where numerous independent variables in a model are interrelated, making it challenging to predict the individual impact of each feature on the dependent variable.
• Figure 4: Colored representation of the normalized Euclidean distance of the dataset instances from the origin. Distinct clusters in the data in relative Euclidean distance can be observed.
• Figure 5: Results of random-forest based detection of weak signals. Selected features are used to detect the weak anomaly magnetic field signal. Compared with a recent work on this topic based on the machine-learning methods of reservoir computing and feed forward neural networks zhai2023detecting, the average RMSEs from the random-forest method are reduced by over 100%.