Magnetostatics play a crucial role in the detection and localisation of naval vessels. Also, minimising a vessel’s magnetic signature is essential to reduce the risk posed by naval mines, which often rely on magnetic detection. This research aims to improve the calculation of magnetic signatures using the Method of Moments (MoM) by implementing it in Julia, a high-performance programming language. A simplified version of TNO’s current MATLAB-based approach is implemented in Julia to establish a baseline for the accuracy and efficiency. Linear basis functions and automatic differentiation (AD) are incorporated into the methodology to explore potential improvements. These extended methods are compared to the baseline to evaluate their performance.
Results show that Julia can be of great value, since it significantly improves the assembly time of the interaction matrix. Point matching is not a suitable approach when using linear basis functions. The Galerkin method shows promising results, though its computational performance remains a significant drawback. Also, using AD shows potential to simplify the implementation of the MoM by eliminating the need for analytical integral expressions. However, AD disappoints in terms of computational performance. Moreover, the AD implementation relies on a mesh-dependent parameter.

A severe incident with the cargo ship MSC Zoe, which lost hundreds of containers near the Dutch coast, shows how important it can be to detect and localise hidden objects at sea quickly. Also in defence applications localisation of hidden objects in water is important. If the objects are made of magnetic materials, they disturb the Earth magnetic field. This disturbance is called the object's magnetic signature. An aerial drone that carries magnetic field sensors could in principle be able to locate magnetic objects autonomously. Another defence-related application of such a drone would be estimating magnetic signatures of ships under water, using measurements above water - signature translation. For both applications, algorithms need to be developed that process magnetic field data, and computes estimates. In this thesis, data-driven techniques are applied to the localisation problem and the magnetic signature translation problem.

For the localisation problem, an algorithm is proposed to localise a magnetic dipole using a limited number of noisy measurements from a sensor array forming a horizontal grid. The algorithm is based on the theory of compressed sensing. In the algorithm, a number of sensors is chosen which perform each a measurement of the three magnetic field components. The sensors can be chosen randomly from the sensor array, but also optimal placement using QR pivoting is considered. Using the obtained field measurements, a sparse representation in the location domain is computed using L1-optimisation. Based on the resulting sparse representation, a classification is produced, which consists of estimates on its location and on its magnetic moment magnitude and orientation. The possibility of performing iterations is explored, where the basis and chosen sensors improve after every location estimate. Using results from simulations as well as experiments, the algorithm is shown to be effective in localising magnetic dipoles.

To solve the signature translation problem, two approaches are investigated. One algorithm was developed using the Gappy POD technique, and one using neural networks. Using only a few measurements (a gappy measurement), a full signal can be reconstructed. This method is adapted to also be able to translate from a field above a ship to a field below a ship. Tikhonov regularisation is applied in the process to obtain better results. Second, different neural networks are created, trained using data above and below a ship. Linear and non-linear networks are compared, and standard loss functions are compared to physics-guided losses. Both the Gappy POD based algorithm and linear neural networks are shown to give good magnetic signature estimates. The Gappy POD method is greatly improved by applying Tikhonov regularisation. Results show to improve when more basis modes are considered, and when more sensors are used for measurements. Linear neural networks show the same results as Gappy POD using Tikhonov regularisation, indicating that some regularisation is done while training the neural network. Non-linear neural networks show no improvement over linear ones, and a physics-guided loss function is not needed for a resulting field that obeys known laws of magnetism.

Eddy currents are currents which are induced in a conducting object by a varying magnetic field. These currents generate a magnetic field of their own. Modelling this phenomenon constitutes a diverse and challenging set of problems, for which many applications exist. One such application is the degaussing system of a naval ship. To guarantee safety on missions, a ship uses a degaussing system to reduce its magnetic signature. Being able to model the effect of eddy current fields is necessary to improve the accuracy of future degaussing systems.

This thesis will examine how eddy current effects can be modeled, and how such a model can be validated. An analytical solution for a sphere is derived and investigated. A boundary element method (BEM) is implemented, which is able to numerically approximate the electromagnetic fields in terms of the modified magnetic vector potential A* and the reduced magnetic scalar potential. The approximation using the BEM is compared to the analytical solution. The BEM shows promising results, being able to model the shape of the magnetic signature of a sphere accurately. The model is also applied to more realistic geometries resembling naval ships, making it a strong candidate for further development and potential implementation in a future degaussing system.

This thesis explores different methodes to optimally guide a swarm of drones towards a steel shipping container. It does this using techniques such as Simulated Annealing and Magnetic Anomaly Detection. The drones will use Simulated Annealing in combination with Magnetic Anomaly Detection to estimate where the steel shipping container is located. To optimally share information between the different drones in the swarm four methods are proposed and analysed.

In this thesis a model for interpolation of magnetic fields is constructed using Gaussian processes. This model takes the curl- and divergence-free properties of magnetic fields into account. The Gaussian process regression, or kriging, is tested on both simulated and real data. It is also attempted to reconstruct the magnetization of objects based on measurement data.